Semi-supervised multi-label learning (SSMLL) aims to address the challenge of limited labeled data in multi-label learning (MLL) by leveraging unlabeled data to improve the model’s performance. While pseudo-labeling has become a dominant strategy in SSMLL, most existing methods assign equal weights to all pseudo-labels regardless of their quality, which can amplify the impact of noisy or uncertain predictions and degrade the overall performance. In this paper, we theoretically verify that the optimal weight for a pseudo-label should reflect its correctness likelihood. Empirically, we observe that on the same dataset, the correctness likelihood distribution of unlabeled data remains stable, even as the number of labeled training samples varies. Building on this insight, we propose Distribution-Calibrated Pseudo-labeling (DiCaP), a correctness-aware framework that estimates posterior precision to calibrate pseudo-label weights. We further introduce a dual-thresholding mechanism to separate confident and ambiguous regions: confident samples are pseudo-labeled and weighted accordingly, while ambiguous ones are explored by unsupervised contrastive learning. Experiments conducted on multiple benchmark datasets verify that our method achieves consistent improvements, surpassing state-of-the-art methods by up to 4.27%.

Label distribution learning (LDL) is a novel paradigm that describe the samples by label distribution of a sample. However, acquiring LDL dataset is costly and time-consuming, which leads to the birth of incomplete label distribution learning (IncomLDL). All the previous IncomLDL methods set the description degrees of "missing" labels in an instance to 0, but remains those of other labels unchanged. This setting is unrealistic because when certain labels are missing, the degrees of the remaining labels will increase accordingly. We fix this unrealistic setting in IncomLDL and raise a new problem: LDL with hidden labels (HidLDL), which aims to recover a complete label distribution from a real-world incomplete label distribution where certain labels in an instance are omitted during annotation. To solve this challenging problem, we discover the significance of proportional information of the observed labels and capture it by an innovative constraint to utilize it during the optimization process. We simultaneously use local feature similarity and the global low-rank structure to reveal the mysterious veil of hidden labels. Moreover, we **theoretically** give the recovery bound of our method, proving the feasibility of our method in learning from hidden labels. Extensive recovery and predictive experiments on various datasets prove the superiority of our method to state-of-the-art LDL and IncomLDL methods.

Typical deep clustering methods, while achieving notable progress, can only provide one clustering result per dataset. This limitation arises from their assumption of a fixed underlying data distribution, which may fail to meet user needs and provide unsatisfactory clustering outcomes. Our work investigates how multi-modal large language models (MLLMs) can be leveraged to achieve user-driven clustering, emphasizing their adaptability to user-specified semantic requirements. However, directly using MLLM output for clustering has risks for producing unstructured and generic image descriptions instead of feature-specific and concrete ones. To address these issues, our method first discovers that MLLMs' hidden states of text tokens are strongly related to the corresponding features, and leverages these embeddings to perform clusterings from any user-defined criteria. We also employ a lightweight clustering head augmented with pseudo-label learning, significantly enhancing clustering accuracy. Extensive experiments demonstrate its competitive performance on diverse datasets and metrics.

As Large Language Models (LLMs) serve a global audience, alignment must transition from enforcing universal consensus to respecting cultural pluralism.We demonstrate that dense models, when forced to fit conflicting value distributions, suffer from Mean Collapse, converging to a generic average that fails to represent diverse groups.We attribute this to Cultural Sparsity, where gradient interference prevents dense parameters from spanning distinct cultural modes.To resolve this, we propose CUMA (Cultural Mixture of Adapters), a framework that frames alignment as a conditional capacity separation problem.By incorporating demographic-aware routing, CUMA internalizes a Latent Cultural Topology to explicitly disentangle conflicting gradients into specialized expert subspaces.Extensive evaluations on WorldValuesBench, Community Alignment, and PRISM demonstrate that CUMA achieves state-of-the-art performance, significantly outperforming both dense baselines and semantic-only MoEs.Crucially, our analysis confirms that CUMA effectively mitigates mean collapse, preserving cultural diversity.Our code is available at https: //github.com/Throll/CuMA.

Alternative splicing generates transcriptomic and proteomic diversity essential for eukaryotic complexity, yet genetic variants disrupting the splicing code underlie numerous human diseases. Deep learning (DL) models and genomic foundation models (GFMs) have achieved outstanding accuracy for predicting splicing variant effects in humans. However, their transferability to non-human species remains poorly understood, limiting applications in agricultural genomics, comparative biology, and non-model organism research, where experimentally validated variant datasets are limited or lacking. In this study, we comprehensively reviewed 35 computational approaches in terms of their architectural characteristics for splicing site and variant prediction and analysis. We systematically benchmarked the performance of 10 representative models for splicing variant prediction across human, rat, pig, and chicken, including four task-specific DL models and six GFMs, using our manually assembled benchmark datasets. Our benchmarking results revealed a substantial cross-species performance decrease (~21%-33% in the area under the receiver operating characteristic curve - AUROC) using task-specific models from human to non-human species datasets. We then applied a supervised adaptation to frozen GFM embeddings (DNABERT-2, Evo 2, Genos) by adding a lightweight classifier (i.e. a multi-layer perceptron) and reduced the cross-species performance decrease for rat and pig (8.56%-23.84% in AUROC), while performance on chicken was very close to human (decline within 1%, even exceeding by 0.52% when using the Evo 2 embedding). We proposed several directions to improve the prediction performance of splicing variants, including feature representation transfer and multi-modal fusion integrating global context, universal embeddings, and species-aware conditioning. We hope our comprehensive review and performance benchmarking can provide useful computational insights for further advancement of splicing variant prediction.

Label Distribution Learning (LDL) is a novel machine learning paradigm that addresses the problem of label ambiguity and has found widespread applications. However, obtaining complete label distributions in real-world scenarios is challenging, which has led to the emergence of Incomplete Label Distribution Learning (InLDL). Existing InLDL methods attempt to utilize low-rank label correlations to recover the complete label distribution. However, we find that real-world LDL datasets have animbalancednature; that is, the sum of the description degrees for normal labels is significantly larger than that for tail labels, which disrupts the low-rank assumption underlying the recovery of the label distribution. To solve the above problem, we propose Incomplete and Imbalance Label Distribution Learning (I2LDL), which makes the use of low-rank label correlations more reasonable for InLDL. Our method decomposes the recovered label distribution matrix into a low-rank component for frequent labels and a sparse component for tail labels, effectively capturing the structure of both head and tail labels. We further require that the entries in the observed positions of the recovered label distribution matrix be close to the observed values, and that the recovered label distribution for every instance forms a probability simplex (i.e., nonnegative entries summing to unity). Finally, the proposed model is optimized via the Alternating Direction Method of Multipliers (ADMM). We provide a theoretical analysis of its exact recovery guarantee under standard assumptions of incoherence, sparsity, and sufficient sampling. Furthermore, we establish a generalization error bound based on Rademacher complexity, offering theoretical insights into the learning performance of our method. Extensive experiments on 16 real-world datasets demonstrate the effectiveness and robustness of our framework compared to existing InLDL methods. The code is available at https://anonymous.4open.science/r/IncomLDL-tailaware-C021.

Vision Transformer (ViT) and its variants have witnessed a significant success in computer vision. However, their performance may degrade in underwater dense prediction tasks due to challenges like complex underwater environments, quality degradation, and light scattering in underwater images. To solve this problem, we propose the Vision Transformer Underwater-Adapter (ViT-UWA), the first detail-focused and adapted ViT backbone for underwater dense prediction tasks, without requiring task-specific pretraining. In ViT-UWA, we first introduce High-frequency Components Prior (HFCP) to add high-frequency information of underwater images to the plain ViT, which can help recover and capture lost high-frequency information of underwater images. Then, we propose a Detail Aware Module (DAM) to obtain a detail-focused multi-scale convolutional feature pyramid, which can be used in kinds of dense prediction tasks. Through the ViT-DAM Cross Fusion (VDCF), we achieve bidirectional feature cross fusion between ViT and DAM. We evaluate ViT-UWA on multiple underwater dense prediction tasks, including semantic segmentation, instance segmentation, and object detection. With only ImageNet-22K pretraining, our ViT-UWA-B yields state-of-the-art 46.4 box AP and 44.2 mask AP on USIS10K dataset, which demonstrates the superiority of our method. Our code is available at https://github.com/Linqirui/ViT-UWA.

Partial multi-label learning (PML) aims to train a classifier on dataset whose instances are over-annotated with not only relevant labels but also irrelevant labels, which is common when datasets are collected from crowd-sourcing platform. Existing works primarily approach it from a curriculum learning perspective, leveraging the memorization effect to disambiguate noisy labels and produce robust predictions. However, these methods are based on non-adaptive weighting functions and lack theoretical guidance for optimal weighting. To overcome these issues, a calibrated disambiguation model named PML-CD is proposed. We firstly formulate the optimal weighting function for curriculum-based disambiguation, which is equivalent to the calibration of the model's predicted confidences, thus provide a guidance for curriculum designing. To obtain the optimal weighting function from PML dataset during the training, a transferable calibrator is designed, which takes the histogram of positive samples' confidences as input, and outputs the optimal curriculum weighting for training. Prototype alignment regularization is also proposed to promote the model's performance. Experiments conducted on Pascal VOC, MS-COCO, NUS-WIDE and CUB have verified that our method outperforms existing state-of-the-art PML methods.

Jinghan He, Kuan Zhu, Haiyun Guo, Junfeng Fang, Zhenglin Hua, Yuheng Jia, Ming Tang, Tat-Seng Chua, Jinqiao Wang. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Deep clustering has exhibited remarkable performance; however, the over confidence problem, i.e., the estimated confidence for a sample belonging to a particular cluster greatly exceeds its actual prediction accuracy, has been over looked in prior research. To tackle this critical issue, we pioneer the development of a calibrated deep clustering framework. Specifically, we propose a novel dual head (calibration head and clustering head) deep clustering model that can effectively calibrate the estimated confidence and the actual accuracy. The calibration head adjusts the overconfident predictions of the clustering head, generating prediction confidence that matches the model learning status. Then, the clustering head dynamically selects reliable high-confidence samples estimated by the calibration head for pseudo-label self-training. Additionally, we introduce an effective network initialization strategy that enhances both training speed and network robustness. The effectiveness of the proposed calibration approach and initialization strategy are both endorsed with solid theoretical guarantees. Extensive experiments demonstrate the proposed calibrated deep clustering model not only surpasses the state-of-the-art deep clustering methods by 5× on average in terms of expected calibration error, but also significantly outperforms them in terms of clustering accuracy. The code is available at https://github.com/ChengJianH/CDC.

Deep clustering has made remarkable progress in recent years. However, most existing deep clustering methods assume that distributions of different clusters are balanced or roughly balanced, which are not consistent with the common long-tailed distributions in reality. In nature, the datasets often follow long-tailed distributions, leading to biased models being trained with significant performance drop. Despite the widespread proposal of many long-tailed learning approaches with supervision information, research on long-tailed deep clustering remains almost uncharted. Unaware of the data distribution and sample labels, long-tailed deep clustering is highly challenging. To tackle this problem, we propose a novel contrastive mixup method for long-tailed deep clustering, named ConMix. The proposed method makes innovations to mixup representations in contrastive learning to enhance deep clustering in long-tailed scenarios. Neural networks trained with ConMix can learn more discriminative representations, thus achieve better long-tailed deep clustering performance. We theoretically prove that ConMix works through re-balancing loss for classes with different long-tailed degree. We evaluate our method on widely used benchmark datasets with different imbalance ratios, suggesting it outperforms many state-of-the-art deep clustering approaches. The code is available at https://github.com/LZX-001/ConMix.

Complementary label learning (CLL) is a weakly supervised learning paradigm that constructs a multi-class classifier only with complementary labels, specifying classes that the instance does not belong to. We reformulate CLL as an inverse problem that infers the full label information from the output space information. To be specific, we propose to split the inverse problem into two subtasks: positive label guessing (PLG) and negative label enhancement (NLE), collectively called PLNL. Specifically, we use well-designed criteria for evaluating the confidence of the model output, accordingly divide the training instances into three categories: highly-confident, moderately-confident and under-confident. For highly-confident instances, we perform PLG to assign them pseudo labels for supervised training. For moderately-confident and under-confident instances, we perform NLE by enhancing their complementary label set at different levels and train them with the augmented complementary labels iteratively. In addition, we unify PLG and NLE into a consistent framework, in which we can view all the pseudo-labeling-based methods from the perspective of negative label recovery. We prove that the error rates of both PLG and NLE are upper bounded, and based on that we can construct a classifier consistent with that learned by clean full labels. Extensive experiments demonstrate the superiority of PLNL over the state-of-the-art CLL methods, e.g., on STL-10, we increase the classification accuracy from 34.96\% to 55.25\%. The source code is available at https://github.com/yhli-ml/PLNL.

Partial label learning is a weakly supervised learning problem in which an instance is annotated with a set of candidate labels, among which only one is the correct label. However, in practice the correct label is not always in the candidate label set, leading to the noisy partial label learning (NPLL) problem. In this paper, we theoretically prove that the generalization error of the classifier constructed under NPLL paradigm is bounded by the noise rate and the average length of the candidate label set. Motivated by the theoretical guide, we propose a novel NPLL framework that can separate the noisy samples from the normal samples to reduce the noise rate and reconstruct the shorter candidate label sets for both of them. Extensive experiments on multiple benchmark datasets confirm the efficacy of the proposed method in addressing NPLL. For example, on CIFAR100 dataset with severe noise, our method improves the classification accuracy of the state-of-the-art one by 11.57%. The code is available at: https://github.com/pruirui/PLRC.

This paper studies the long-tailed semi-supervised learning (LTSSL) with distribution mismatch, where the class distribution of the labeled training data follows a long-tailed distribution and mismatches with that of the unlabeled training data. Most existing methods introduce auxiliary classifiers (experts) to model various unlabeled data distributions and produce pseudo-labels, but the expertises of various experts are not fully utilized. We observe that different experts are good at predicting different intervals of samples, e.g., long-tailed expert is skilled in samples located in the head interval and uniform expert excels in samples located in the medium interval. Therefore, we propose a dynamic expert assignment module that can estimate the class membership (i.e., head, medium, or tail class) of samples, and dynamically assigns suitable expert to each sample based on the estimated membership to produce high-quality pseudo-label in the training phase and produce prediction in the testing phase. We also theoretically reveal that integrating different experts' strengths will lead to a smaller generalization error bound. Moreover, we find that the deeper features are more biased toward the head class but with more discriminative ability, while the shallower features are less biased but also with less discriminative ability. We, therefore, propose a multi-depth feature fusion module to utilize different depth features to mitigate the model bias. Our method demonstrates its effectiveness through comprehensive experiments on the CIFAR-10-LT, STL-10-LT, and SVHN-LT datasets across various settings.

Deep clustering, an unsupervised technique independent of labels, necessitates tailored supervision for model training. Prior methods explore supervision like similarity and pseudo labels, yet overlook individual sample training analysis. Our study correlates sample stability during unsupervised training with clustering accuracy and network memorization on a per-sample basis. Unstable representations across epochs often lead to mispredictions, indicating difficulty in memorization and atypicality. Leveraging these findings, we introduce supervision signals for the first time based on sample stability at the representation level. Our proposed strategy serves as a versatile tool to enhance various deep clustering techniques. Experiments across benchmark datasets showcase that incorporating sample stability into training can improve the performance of deep clustering. The code is available at https://github.com/LZX-001/LFSS.

Label distribution learning (LDL) is an effective method to predict the relative label description degree (a.k.a. label distribution) of a sample. However, the label distribution is not a complete representation of an instance because it overlooks the absolute intensity of each label. Specifically, it’s impossible to obtain the total description degree of hidden labels that not in the label space, which leads to the loss of information and confusion in instances. To solve the above problem, we come up with a new concept named background concentration to serve as the absolute description degree term of the label distribution and introduce it into the LDL process, forming the improved paradigm of concentration distribution learning. Moreover, we propose a novel model by probabilistic methods and neural networks to learn label distributions and background concentrations from existing LDL datasets. Extensive experiments prove that the proposed approach is able to extract background concentrations from label distributions while producing more accurate prediction results than the state-of-the-art LDL methods. The code is available in https://github.com/seutjw/CDL-LD.

Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess risk and consistency. We derive a convergence rate of generalization error bound and excess risk bound both of $\mathcal{O}(\sqrt{\frac{\log n}{m}}+\frac{1}{\sqrt{n}})$, with $n$ and $m$ being the numbers of samples and base clusterings. Based on this, we prove that when $m$ and $n$ approach infinity and $m$ is significantly larger than log $n$, i.e., $m,n\to \infty, m\gg \log n$, ensemble clustering is consistent. Furthermore, recognizing that $n$ and $m$ are finite in practice, the generalization error cannot be reduced to zero. Thus, by assigning varying weights to finite clusterings, we minimize the error between the empirical average clusterings and their expectation. From this, we theoretically demonstrate that to achieve better clustering performance, we should minimize the deviation (bias) of base clustering from its expectation and maximize the differences (diversity) among various base clusterings. Additionally, we derive that maximizing diversity is nearly equivalent to a robust (min-max) optimization model. Finally, we instantiate our theory to develop a new ensemble clustering algorithm. Compared with SOTA methods, our approach achieves average improvements of 6.0%, 7.3%, and 6.0% on 10 datasets w.r.t. NMI, ARI, and Purity. The code is available at https://github.com/xuz2019/GPEC.

Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels and only one label is the ground-truth label. For the first time, this paper investigates the partial label clustering problem, which takes advantage of the limited available partial labels to improve the clustering performance. Specifically, we first construct a weight matrix of examples based on their relationships in the feature space and disambiguate the candidate labels to estimate the ground-truth label based on the weight matrix. Then, we construct a set of must-link and cannot-link constraints based on the disambiguation results. Moreover, we propagate the initial must-link and cannot-link constraints based on an adversarial prior promoted dual-graph learning approach. Finally, we integrate weight matrix construction, label disambiguation, and pairwise constraints propagation into a joint model to achieve mutual enhancement. We also theoretically prove that a better disambiguated label matrix can help improve clustering performance. Comprehensive experiments demonstrate our method realizes superior performance when comparing with state-of-the-art constrained clustering methods, and outperforms PLL and semi-supervised PLL methods when only limited samples are annotated. The code and appendix are publicly available at https://github.com/xyt-ml/PLC.

Multi-label learning (MLL) has gained attention for its ability to represent real-world data. Label Distribution Learning (LDL), an extension of MLL to learning from label distributions, faces challenges in collecting accurate label distributions. To address the issue of biased annotations, based on the low-rank assumption, existing works recover true distributions from biased observations by exploring the label correlations. However, recent evidence shows that the label distribution tends to be full-rank, and naive apply of low-rank approximation on biased observation leads to inaccurate recovery and performance degradation. In this paper, we address the LDL with biased annotations problem from a novel perspective, where we first degenerate the soft label distribution into a hard multi-hot label and then recover the true label information for each instance. This idea stems from an insight that assigning hard multi-hot labels is often easier than assigning a soft label distribution, and it shows stronger immunity to noise disturbances, leading to smaller label bias. Moreover, assuming that the multi-label space for predicting label distributions is low-rank offers a more reasonable approach to capturing label correlations. Theoretical analysis and experiments confirm the effectiveness and robustness of our method on real-world datasets.

In partial label learning (PLL), every sample is associated with a candidate label set comprising the ground-truth label and several noisy labels. The conventional PLL assumes the noisy labels are randomly generated (instance-independent), while in practical scenarios, the noisy labels are always instance-dependent and are highly related to the sample features, leading to the instance-dependent partial label learning (IDPLL) problem. Instance-dependent noisy label is a double-edged sword. On one side, it may promote model training as the noisy labels can depict the sample to some extent. On the other side, it brings high label ambiguity as the noisy labels are quite undistinguishable from the ground-truth label. To leverage the nuances of IDPLL effectively, for the first time we create class-wise embeddings for each sample, which allow us to explore the relationship of instance-dependent noisy labels, i.e., the class-wise embeddings in the candidate label set should have high similarity, while the class-wise embeddings between the candidate label set and the non-candidate label set should have high dissimilarity. Moreover, to reduce the high label ambiguity, we introduce the concept of class prototypes containing global feature information to disambiguate the candidate label set. Extensive experimental comparisons with twelve methods on six benchmark data sets, including four fine-grained data sets, demonstrate the effectiveness of the proposed method. The code implementation is publicly available at https://github.com/Yangfc-ML/CEL.

Learning from Label Proportions (LLP) is a weakly-supervised paradigm that uses bag-level label proportions to train instance-level classifiers, offering a practical alternative to costly instance-level annotation. However, the weak supervision makes effective training challenging, and existing methods often rely on pseudo-labeling, which introduces noise. To address this, we propose RLPL, a two-stage framework. In the first stage, we use unsupervised contrastive learning to pretrain the encoder and train an auxiliary classifier with bag-level supervision. In the second stage, we introduce an LLP-OTD mechanism to refine pseudo labels and split them into high- and low-confidence sets. These sets are then used in LLPMix to train the final classifier. Extensive experiments and ablation studies on multiple benchmarks demonstrate that RLPL achieves comparable state-of-the-art performance and effectively mitigates pseudo-label noise.

Current long-tailed semi-supervised learning methods assume that labeled data exhibit a long-tailed distribution, and unlabeled data adhere to a typical predefined distribution (i.e., long-tailed, uniform, or inverse long-tailed). However, the distribution of the unlabeled data is generally unknown and may follow an arbitrary distribution. To tackle this challenge, we propose a Controllable Pseudo-label Generation (CPG) framework, expanding the labeled dataset with the progressively identified reliable pseudo-labels from the unlabeled dataset and training the model on the updated labeled dataset with a known distribution, making it unaffected by the unlabeled data distribution. Specifically, CPG operates through a controllable self-reinforcing optimization cycle: (i) at each training step, our dynamic controllable filtering mechanism selectively incorporates reliable pseudo-labels from the unlabeled dataset into the labeled dataset, ensuring that the updated labeled dataset follows a known distribution; (ii) we then construct a Bayes-optimal classifier using logit adjustment based on the updated labeled data distribution; (iii) this improved classifier subsequently helps identify more reliable pseudo-labels in the next training step. We further theoretically prove that this optimization cycle can significantly reduce the generalization error under some conditions. Additionally, we propose a class-aware adaptive augmentation module to further improve the representation of minority classes, and an auxiliary branch to maximize data utilization by leveraging all labeled and unlabeled samples. Comprehensive evaluations on various commonly used benchmark datasets show that CPG achieves consistent improvements, surpassing state-of-the-art methods by up to **15.97\%** in accuracy. The code is available at https://github.com/yaxinhou/CPG.

Pseudo label based semi-supervised learning (SSL) for single-label and multi-label classification tasks has been extensively studied; however, semi-supervised label distribution learning (SSLDL) remains a largely unexplored area. Existing SSL methods fail in SSLDL because the pseudo-labels they generate only ensure overall similarity to the ground truth but do not preserve the ranking relationships between true labels, as they rely solely on KL divergence as the loss function during training. These skewed pseudo-labels lead the model to learn incorrect semantic relationships, resulting in reduced performance accuracy. To address these issues, we propose a novel SSLDL method called \textit{RankMatch}. \textit{RankMatch} fully considers the ranking relationships between different labels during the training phase with labeled data to generate higher-quality pseudo-labels. Furthermore, our key observation is that a flexible utilization of pseudo-labels can enhance SSLDL performance. Specifically, focusing solely on the ranking relationships between labels while disregarding their margins helps prevent model overfitting. Theoretically, we prove that incorporating ranking correlations enhances SSLDL performance and establish generalization error bounds for \textit{RankMatch}. Finally, extensive real-world experiments validate its effectiveness.

Recent deep clustering models have produced impressive clustering performance. However, a common issue with existing methods is the disparity between global and local feature structures. While local structures typically show strong consistency and compactness within class samples, global features often present intertwined boundaries and poorly separated clusters. Motivated by this observation, we propose **DCBoost, a parameter-free plug-in** designed to enhance the global feature structures of current deep clustering models. By harnessing reliable local structural cues, our method aims to elevate clustering performance effectively. Specifically, we first identify high-confidence samples through adaptive $k$-nearest neighbors-based consistency filtering, aiming to select a sufficient number of samples with high label reliability to serve as trustworthy anchors for self-supervision. Subsequently, these samples are utilized to compute a discriminative loss, which promotes both intra-class compactness and inter-class separability, to guide network optimization. Extensive experiments across various benchmark datasets showcase that our DCBoost significantly improves the clustering performance of diverse existing deep clustering models. Notably, our method improves the performance of current state-of-the-art baselines (e.g., ProPos) by more than 3\% and amplifies the silhouette coefficient by over $7\times$. **Code is available at [https://github.com/l-h-y168/DCBoost](https://github.com/l-h-y168/DCBoost).**

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available athttps://github.com/JinaLeejnl/TSNMF.

Spectral variations pose a common challenge in analyzing hyperspectral images (HSI). To address this, low-rank tensor representation has emerged as a robust strategy, leveraging inherent correlations within HSI data. However, the spatial distribution of ground objects in HSIs is inherently irregular, existing naturally in tensor format, with numerous class-specific regions manifesting as irregular tensors. Current low-rank representation techniques are designed for regular tensor structures and overlook this fundamental irregularity in real-world HSIs, leading to performance limitations. To tackle this issue, we propose a novel model for irregular tensor low-rank representation tailored to efficiently model irregular 3D cubes. By incorporating a non-convex nuclear norm to promote low-rankness and integrating a global negative low-rank term to enhance the discriminative ability, our proposed model is formulated as a constrained optimization problem and solved using an alternating augmented Lagrangian method. Experimental validation conducted on four public datasets demonstrates the superior performance of our method compared to existing state-of-the-art approaches. The code is publicly available at https://github.com/hb-studying/ITLRR.

Hyperspectral image (HSI) clustering groups pixels into clusters without labeled data, which is an important yet challenging task. For large-scale HSIs, most methods rely on superpixel segmentation and perform superpixel-level clustering based on graph neural networks (GNNs). However, existing GNNs cannot fully exploit the spectral information of the input HSI, and the inaccurate superpixel topological graph may lead to the confusion of different class semantics during information aggregation. To address these challenges, we first propose a structural-spectral graph convolutional operator (SSGCO) tailored for graph-structured HSI superpixels to improve their representation quality through the co-extraction of spatial and spectral features. Second, we propose an evidence-guided adaptive edge learning (EGAEL) module that adaptively predicts and refines edge weights in the superpixel topological graph. We integrate the proposed method into a contrastive learning framework to achieve clustering, where representation learning and clustering are simultaneously conducted. Experiments demonstrate that the proposed method improves clustering accuracy by 2.61%, 6.06%, 4.96% and 3.15% over the best compared methods on four HSI datasets. Our code is available at https://github.com/jhqi/SSGCO-EGAEL.

Label distribution learning (LDL) is a novel learning paradigm that assigns each instance with a label distribution. Although many specialized LDL algorithms have been proposed, few of them have noticed that the obtained label distributions are generally inaccurate with noise due to the difficulty of annotation. Besides, existing LDL algorithms overlooked that the noise in the inaccurate label distributions generally depends on instances. In this article, we identify the instance-dependent inaccurate LDL (IDI-LDL) problem and propose a novel algorithm called low-rank and sparse LDL (LRS-LDL). First, we assume that the inaccurate label distribution consists of the ground-truth label distribution and instance-dependent noise. Then, we learn a low-rank linear mapping from instances to the ground-truth label distributions and a sparse mapping from instances to the instance-dependent noise. In the theoretical analysis, we establish a generalization bound for LRS-LDL. Finally, in the experiments, we demonstrate that LRS-LDL can effectively address the IDI-LDL problem and outperform existing LDL methods.

Researchers have proposed to exploit label correlation to alleviate the exponential-size output space of label distribution learning (LDL). In particular, some have designed LDL methods to consider local label correlation. These methods roughly partition the training set into clusters and then exploit local label correlation on each one. Each sample belongs to one cluster and therefore has only one local label correlation. However, in real-world scenarios, the training samples may have fuzziness and belong to multiple clusters with blended local label correlations, which challenge these works. To solve this problem, we propose in LDL fuzzy label correlation (FLC)-each sample blends, with fuzzy membership, multiple local label correlations. First, we propose two types of FLCs, i.e., fuzzy membership-induced label correlation (FC) and joint fuzzy clustering and label correlation (FCC). Then, we put forward LDL-FC and LDL-FCC to exploit these two FLCs, respectively. Finally, we conduct extensive experiments to justify that LDL-FC and LDL-FCC statistically outperform state-of-the-art LDL methods.

In partial label learning (PLL), each instance is associated with a set of candidate labels, among which only one is correct. The traditional PLL almost all implicitly assume that the distribution of the classes is balanced. However, in real-world applications, the distribution of the classes is imbalanced or long-tailed, leading to the long-tailed partial label learning problem. The previous methods solve this problem mainly by ameliorating the ability to learn in the tail classes, which will sacrifice the performance of the head classes. While keeping the performance of the head classes may degrade the performance of the tail classes. Therefore, in this paper, we construct two classifiers, i.e., a head classifier for keeping the performance of dominant classes and a tail classifier for improving the performance of the tail classes. Then, we propose a classifier weight estimation module to automatically estimate the shot belongingness (head class or tail class) of the samples and allocate the weights for the head classifier and tail classifier when making prediction. This cooperation improves the prediction ability for both the head classes and the tail classes. The experiments on the benchmarks demonstrate the proposed approach improves the accuracy of the SOTA methods by a substantial margin. Code and data are available at: https://github.com/pruirui/HTC-LTPLL.

This paper studies the semi-supervised partial label learning (SSPLL) problem, which aims to improve the partial label learning (PLL) by leveraging unlabeled samples. Both the existing SSPLL methods and the semi-supervised learning methods exploit the information in unlabeled samples by selecting high-confidence unlabeled samples as the pseudo labels based on the maximum value of the model output. However, the scarcity of labeled samples and the ambiguity from partial labels skew this strategy towards an unfair selection of high-confidence samples on each class, most notably during the initial phases of training, resulting in slower training and performance degradation. In this paper, we propose a novel method FairMatch, which adopts a learning state aware self-adaptive threshold for selecting the same number of high-confidence samples on each class, and uses augmentation consistency to incorporate the unlabeled samples to promote PLL. In addition, we adopt the candidate label disambiguation to utilize the partial labeled samples and mix up the partial labeled samples and the selected high-confidence unlabeled samples to prevent the model from overfitting on partial label samples. FairMatch can achieve maximum accuracy improvements of 9.53%, 4.9%, and 16.45% on CIFAR-10, CIFAR-100, and CIFAR-100H, respectively. The codes can be found at https://github.com/jhjiangSEU/FairMatch.

This paper addresses the problem of partial multi-label learning (PML), a challenging weakly supervised learning framework, where each sample is associated with a candidate label set comprising both ground-true labels and noisy labels. We theoretically reveal that an increased number of noisy labels in the candidate label set leads to an enlarged generalization error bound, consequently degrading the classification performance. Accordingly, the key to solving PML lies in accurately removing the noisy labels within the candidate label set. To achieve this objective, we leverage prior knowledge about the noisy labels in PML, which suggests that they only exist within the candidate label set and possess binary values. Specifically, we propose a constrained regression model to learn a PML classifier and select the noisy labels. The constraints of the model strictly enforce the location and value of the noisy labels. Simultaneously, the supervision information provided by the candidate label set is unreliable due to the presence of noisy labels. In contrast, the non-candidate labels of a sample precisely indicate the classes to which the sample does not belong. To aid in the selection of noisy labels, we construct a competitive classifier based on the non-candidate labels. The PML classifier and the competitive classifier form a competitive relationship, encouraging mutual learning. We formulate the proposed model as a discrete optimization problem to effectively remove the noisy labels, and we solve it using an alternative algorithm. Extensive experiments conducted on 6 real-world partial multi-label data sets and 7 synthetic data sets, employing various evaluation metrics, demonstrate that our method significantly outperforms state-of-the-art PML methods. The code implementation is publicly available at https://github.com/Yangfc-ML/NLR.

Deep neural networks (DNNs) have demonstrated remarkable success on various learning problems, but they face a formidable challenge in the form of adversarial attacks. Especially, when dealing with complex classification tasks for numerous classes with a hierarchical structure, the adversarial robustness of a DNN model may drop seriously. In this paper, we investigate the adversarial robustness of DNN models on such complex classification tasks. In response, we propose a two-stage hierarchical classification framework, which is composed of a coarse-grained classifier and a series of fine-grained classifiers. A data correction sampling module is designed between the two stages, in order to mitigate the influence of misclassification caused by the coarse-grained classifier; and a discriminative filter learning module is employed in the fine-grained classification, in order to gain better distinguish abilities among fine-grained categories. Experiments on the well-known dataset CIFAR-100 and a newly-constructed hierarchical dataset mini-ImageNet76 demonstrate that employing a hierarchical framework can effectively improve the model robustness on such complex classification tasks.

In the field of unmanned aerial vehicles (UAVs), their potential as aerial base stations for post-disaster communication recovery or providing communication coverage in remote areas has gained global recognition. However, the challenge of striking a balance between maximizing coverage and minimizing energy consumption persists. To address this issue, we introduce a novel distributed Three-Dimensional (3D) deployment approach for UAV-based Base Stations (UAV-BSs) called 3D deployment for effective communication coverage (DECC). Firstly, the 3D deployment problem is decoupled into a horizontal placement subproblem and an altitude determination subproblem. Then, we propose an enhanced genetic algorithm to obtain the optimal horizontal location of UAV-BSs, which incorporates adaptive two-point crossover and an inferior value replacement strategy. Finally, a gray wolf optimization with the dynamic weight is adopted to determine the altitude to optimize the transmit power while ensuring quality of service for the users. The simulation results demonstrate that the proposed algorithm can get a better coverage compared to the current deployment strategies.

We exploit the hyperspectral image (HSI) clustering problem, which partitions an input HSI into several groups without relying on any supervision information. The previous methods mainly focus on developing an HSI clustering technique, which neglects learning a discriminative representation. To this end, this letter proposes a novel discriminative low-rank representation method to exploit the spatial and spectral information of HSIs. The proposed method is formulated as a concave-convex optimization problem and solved by alternating direction method of multipliers. By applying a simple clustering technique (such as K-means) on the obtained discriminative low-rank representation, our method can produce better clustering performance than the state-of-the-art HSI clustering methods. Experiments on four benchmark datasets confirm the superior clustering performance of the proposed method. The code of this letter is available at:https://github.com/LZX-001/Discriminative_Low_Rank_Representation_for _HSI_Clustering.

Incorrect labeling (i.e., noisy label learning) in HSI classification has attracted so much attention in recent years, which holds the assumption that the given pixels of an HSI may be incorrectly labeled and only one candidate label is required to provide for a typical pixel. However, instead of offering only one candidate label that may be incorrect, partial label learning often provides a candidate label set that contains the ground-truth label for each pixel in an HSI, which is also an essential problem of great practical value and has recently started to attract attention. This paper proposes a novel framework for partial label learning in HSI classification, namely unlabeled data guided partial label learning (UPLL). The proposed framework is an iterative process that can fully exploit the benefits of unlabeled data. Specifically, during each iteration, we conduct the semi-supervised label propagation; the resulting labeling confidence matrices of the original training samples and the unlabeled testing samples are further enhanced by exploiting the spatial information. Then, we select qualified original training samples and unlabeled testing samples with high confident predictions to disambiguate and expand the original training set, leading to a more robust representation of training data. Such phases are repeated until convergence. The comprehensive experiments show the superiority of the proposed UPLL method over the existing state-of-the-art methods. Especially, the classification accuracy improves more than 5% with very few training samples than the second best comparing method.

Label distribution learning (LDL) trains a model to predict the relevance of a set of labels (called label distribution (LD)) to an instance. The previous LDL methods all assumed the LDs of the training instances are accurate. However, annotating highly accurate LDs for training instances is time-consuming and extremely expensive, and in reality the collected LDs are often inaccurate. This paper first investigates the inaccurate LDL (ILDL) problem—learn an LDL method from the inaccurate LDs. We assume that the inaccurate LD blends the ground-truth LD and sparse noise. Consequently, the ILDL problem becomes an inverse problem, whose objective is to recover the ground-truth LD and noise from the inaccurate LD. We hypothesize that the ground-truth LD exhibits low rank due to label correlations. Besides, we leverage the local geometric structure of instances (represented as graph) to further recover the ground-truth LD. Finally, the proposed method is formulated as a graph-regularized low-rank and sparse decomposition problem. Next, we induce an LDL predictive method by learning from recovered LD. Extensive experiments conducted on multiple datasets demonstrate the better performance of our method, especially for ILDL problem.

Hyperspectral images (HSI) clustering is an important but challenging task. The state-of-the-art (SOTA) methods usually rely on superpixels, however, they do not fully utilize the spatial and spectral information in HSI 3-D structure, and their optimization targets are not clustering-oriented. In this work, we first use 3-D and 2-D hybrid convolutional neural networks to extract the high-order spatial and spectral features of HSI through pre-training, and then design a superpixel graph contrastive clustering (SPGCC) model to learn discriminative superpixel representations. Reasonable augmented views are crucial for contrastive clustering, and conventional contrastive learning may hurt the cluster structure since different samples are pushed away in the embedding space even if they belong to the same class. In SPGCC, we design two semantic-invariant data augmentations for HSI superpixels: pixel sampling augmentation and model weight augmentation. Then sample-level alignment and clustering-center-level contrast are performed for better intra-class similarity and inter-class dissimilarity of superpixel embeddings. We perform clustering and network optimization alternatively. Experimental results on several HSI datasets verify the advantages of the proposed SPGCC compared to SOTA methods. Our code is available athttps://github.com/jhqi/spgcc.

Accurately estimating spatiotemporal traffic states on freeways is a significant challenge due to limited sensor deployment and potential data corruption. In this study, we propose an efficient and robust low-rank model for precise spatiotemporal traffic speed state estimation (TSE) using low-penetration vehicle trajectory data. Leveraging traffic wave priors, an oblique grid-based matrix is first designed to transform the inherent dependencies of spatiotemporal traffic states into the algebraic low-rankness of a matrix. Then, with the enhanced traffic state low-rankness in the oblique matrix, a low-rank matrix completion method is tailored to explicitly capture spatiotemporal traffic propagation characteristics and precisely reconstruct traffic states. In addition, an anomaly-tolerant module based on a sparse matrix is developed to accommodate corrupted data input and thereby improve the TSE model robustness. Notably, driven by the understanding of traffic waves, the computational complexity of the proposed efficient method is only correlated with the problem size itself, not with dataset size and hyperparameter selection prevalent in existing studies. Extensive experiments demonstrate the effectiveness, robustness, and efficiency of the proposed model. The performance of the proposed method achieves up to a 12% improvement in Root Mean Squared Error (RMSE) in the TSE scenarios and an 18% improvement in RMSE in the robust TSE scenarios, and it runs more than 20 times faster than the state-of-the-art (SOTA) methods.

Rapid advancements in traffic monitoring and sensing technologies have permitted the multiplex and democratized gathering of numerous traffic data (e.g. speed, volume), depicting identical traffic dynamics from various but complementary views. Incomplete values are ubiquitous in these data, which undermines their utility in subsequent applications. In order to manage and enhance traffic data quality, most existing methods recover single traffic variable data independently based on intra-view spatiotemporal correlations, while the inter-view complementarities are ignored. In this paper, we leverage both intra-view and inter-view correlations for multiple traffic variable data simultaneous recovery. To explore the inter-view relationships, a multi-view subspace consistency learning module is developed to bridge connections and activate complementarities among multi-view traffic data. Specifically, the latent subspace features of each data view are extracted and organized as a multi-view subspace tensor with low-rank regularization. The multi-view low-rank tensor captures the consistent subspace structure across multiple data views while reserving unique features within each data view. To characterize the intra-view dependencies, a tensor-based low-rank representation is presented to explore the distinct spatiotemporal patterns within single-view traffic data. For model validation, we additionally design a nonrandom missing pattern to simulate sensor permanent failure cases in practice. Extensive experiments implemented on three real-world multi-view traffic datasets demonstrate the effectiveness and robustness of the proposed model.

Data missing phenomena and random anomalies are ubiquitous in intelligent transportation systems (ITS), resulting in poor data quality and usability, which is a major impediment to real-world ITS applications. Most studies regarding traffic data recovery either assume that the original data are clean or complete, while such two issues often coexist in reality due to inevitable data measurement errors like detector malfunctions. In this paper, we fully exploit the algebraically low-rank property of traffic spatiotemporal data and develop an innovative tensor completion approach (termed SCPN) based on the tensor Schatten capped$ p $norm, a unified representation of tensor norms with a high flexibility. Furthermore, we extend the proposed method to a robust form (termed RSCPN) by leveraging the sparsity of unstructured outliers, with the aim to reconstruct ground-truth values from corrupted and incomplete observations. Finally, associated optimization solutions based on the alternating direction multiplier method are derived. Extensive experiments on four datasets substantiate the significant superiority of our proposed models over other state-of-the-art methods on both missing data imputation and corrupted data recovery tasks with miscellaneous simulated scenarios.

Exploiting label correlations is important to multi-label classification. Previous methods capture the high-order label correlations mainly by transforming the label matrix to a latent label space with low-rank matrix factorization. However, the label matrix is generally a full-rank or approximate full-rank matrix, making the low-rank factorization inappropriate. Besides, in the latent space, the label correlations will become implicit. To this end, we propose a simple yet effective method to depict the high-order label correlations explicitly, and at the same time maintain the high-rank of the label matrix. Moreover, we estimate the label correlations and infer model parameters simultaneously via the local geometric structure of the input to achieve mutual enhancement. Comparative studies over twelve benchmark data sets validate the effectiveness of the proposed algorithm in multi-label classification. The exploited high-order label correlations are consistent with common sense empirically.Our code is publicly available athttps://github.com/Chongjie-Si/HOMI.

Multi-label ensemble can achieve superior performance on multi-label learning problems by integrating a number of base classifiers. In existing multi-label ensemble methods, the base classifiers are usually trained with the same original features; it is difficult for each base classifier to capture label-relevant or label subset-relevant information. Meanwhile, the manually designed integrating strategies cannot automatically distinguish the importance of the base classifiers, which also lack flexibility and scalability. In order to resolve these problems, this paper proposes a new multi-label ensemble framework, named Attention-aware Multi-label Ensemble with Label Subset-specIfic FeaTures (AME-LSIFT). It utilizes$c$-means clustering to produce Label Subset-specIfic FeaTures (LSIFT), constructs a neural network based model for each label subset, and integrates the base models with a dynamic and automatic attention-aware mechanism. Moreover, an objective function that considers both the label subset accuracy and ensemble accuracy is developed for training the proposed AME-LSIFT. Experiments conducted on ten benchmark datasets demonstrate the superior performance of the proposed method compared with state-of-the-art approaches.

Ensemble clustering integrates a set of base clustering results to generate a stronger one. Existing methods usually rely on a co-association (CA) matrix that measures how many times two samples are grouped into the same cluster according to the base clusterings to achieve ensemble clustering. However, when the constructed CA matrix is of low quality, the performance will degrade. In this article, we propose a simple, yet effective CA matrix self-enhancement framework that can improve the CA matrix to achieve better clustering performance. Specifically, we first extract the high-confidence (HC) information from the base clusterings to form a sparse HC matrix. By propagating the highly reliable information of the HC matrix to the CA matrix and complementing the HC matrix according to the CA matrix simultaneously, the proposed method generates an enhanced CA matrix for better clustering. Technically, the proposed model is formulated as a symmetric constrained convex optimization problem, which is efficiently solved by an alternating iterative algorithm with convergence and global optimum theoretically guaranteed. Extensive experimental comparisons with 12 state-of-the-art methods on ten benchmark datasets substantiate the effectiveness, flexibility, and efficiency of the proposed model in ensemble clustering. The codes and datasets can be downloaded at https://github.com/Siritao/EC-CMS.

Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels among which only one is the ground-truth label. Existing works on partial label dimensionality reduction only exploit the disambiguated labels, but overlook the available semantic dissimilarity relationship hidden in the disambiguated labeling confidence, i.e., the smaller the inner product of the labeling confidences of two instances, the less likely they have the same ground-truth label. By combining such global dissimilarity relationship with local neighborhood information, we propose a novel partial label dimensionality reduction method named SDLPP, which employs an alternating procedure including candidate label disambiguation, semantic dissimilarity generation and dimensionality reduction. The labeling confidences of candidate labels and semantic dissimilarity relationship are constantly updated through the alternating procedure, where the processes in each iteration are based on the low-dimensional data obtained in the previous iteration. After the alternating procedure, SDLPP maps the original data to a pre-specified low-dimensional feature space. Comprehensive experiments on both synthetic and real-world data sets validate that SDLPP can improve the generalization performance of different PLL algorithms, and outperform state-of-the-art partial label dimensionality reduction methods. The codes can be publicly accessible on the link https://github.com/jhjiangSEU/SDLPP.

In partial label learning (PLL), each training sample is associated with a set of candidate labels, among which only one is valid. The core of PLL is to disambiguate the candidate labels to get the ground-truth one. In disambiguation, the existing works usually do not fully investigate the effectiveness of the non-candidate label set (a.k.a. complementary labels), which accurately indicates a set of labels that do not belong to a sample. In this paper, we use the non-candidate labels to induce a complementary classifier, which naturally forms an adversarial relationship against the traditional PLL classifier, to eliminate the false-positive labels in the candidate label set. Besides, we assume the feature space and the label space share the same local topological structure captured by a dynamic graph, and use it to assist disambiguation. Extensive experimental results validate the superiority of the proposed approach against state-of-the-art PLL methods on 4 controlled UCI data sets and 6 real-world data sets and reveal the usefulness of complementary learning in PLL. The code has been released in the link https://github.com/Chongjie-Si/PL-CL

In partial label learning (PLL), each sample is associated with a group of candidate labels, among which only one label is correct. The key of PLL is to disambiguate the candidate label set to find the ground-truth label. To this end, we first construct a constrained regression model to capture the confidence of the candidate labels, and multiply the label confidence matrix by its transpose to build a second-order similarity matrix, whose elements indicate the pairwise similarity relationships of samples globally. Then we develop a semantic dissimilarity matrix by considering the complement of the intersection of the candidate label set, and further propagate the initial dissimilarity relationships to the whole data set by leveraging the local geometric structure of samples. The similarity and dissimilarity matrices form an adversarial relationship, which is further utilized to shrink the solution space of the label confidence matrix and promote the dissimilarity matrix. We finally extend the proposed model to a kernel version to exploit the non-linear structure of samples and solve the proposed model by the inexact augmented Lagrange multiplier method. By exploiting the adversarial prior, the proposed method can significantly outperform state-of-the-art PLL algorithms when evaluated on 10 artificial and 7 real-world partial label data sets. We also prove the effectiveness of our method with some theoretical guarantees. The code is publicly available at https://github.com/Yangfc-ML/DPCLS.

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available athttps://github.com/GuanxingLu/Subspace-Clustering.

Existing deep embedding clustering methods fail to sufficiently utilize the available off-the-shelf information from feature embeddings and cluster assignments, limiting their performance. To this end, we propose a novel method, namely deep attention-guided graph clustering with dual self-supervision (DAGC). Specifically, DAGC first utilizes a heterogeneity-wise fusion module to adaptively integrate the features of the auto-encoder and the graph convolutional network in each layer and then uses a scale-wise fusion module to dynamically concatenate the multi-scale features in different layers. Such modules are capable of learning an informative feature embedding via an attention-based mechanism. In addition, we design a distribution-wise fusion module that leverages cluster assignments to acquire clustering results directly. To better explore the off-the-shelf information from the cluster assignments, we develop a dual self-supervision solution consisting of a soft self-supervision strategy with a Kullback-Leibler divergence loss and a hard self-supervision strategy with a pseudo supervision loss. Extensive experiments on nine benchmark datasets validate that our method consistently outperforms state-of-the-art methods. Especially, our method improves the ARI by more than 10.29% over the best baseline. The code will be publicly available athttps://github.com/ZhihaoPENG-CityU/DAGC.

Existing graph clustering networks heavily rely on a predefined yet fixed graph, which can lead to failures when the initial graph fails to accurately capture the data topology structure of the embedding space. In order to address this issue, we propose a novel clustering network called Embedding-Induced Graph Refinement Clustering Network (EGRC-Net), which effectively utilizes the learned embedding to adaptively refine the initial graph and enhance the clustering performance. To begin, we leverage both semantic and topological information by employing a vanilla auto-encoder and a graph convolution network, respectively, to learn a latent feature representation. Subsequently, we utilize the local geometric structure within the feature embedding space to construct an adjacency matrix for the graph. This adjacency matrix is dynamically fused with the initial one using our proposed fusion architecture. To train the network in an unsupervised manner, we minimize the Jeffreys divergence between multiple derived distributions. Additionally, we introduce an improved approximate personalized propagation of neural predictions to replace the standard graph convolution network, enabling EGRC-Net to scale effectively. Through extensive experiments conducted on nine widely-used benchmark datasets, we demonstrate that our proposed methods consistently outperform several state-of-the-art approaches. Notably, EGRC-Net achieves an improvement of more than 11.99% in Adjusted Rand Index (ARI) over the best baseline on the DBLP dataset. Furthermore, our scalable approach exhibits a 10.73% gain in ARI while reducing memory usage by 33.73% and decreasing running time by 19.71%. The code for EGRC-Net will be made publicly available at https://github.com/ZhihaoPENG-CityU/EGRC-Net.

Person re-identification (re-ID) has many applications in intelligent transportation systems. Clustering-based methods, which alternate between the generation of pseudo labels via clustering and the optimization of the feature extractor, have obtained leading performance in unsupervised person re-ID. But there are still two issues not well addressed: 1) Most methods measure the feature similarity without considering the domain shift between cameras, degrading the clustering performance. 2) Outliers, which usually correspond to hard samples with large discrepancy from other images of the identical person, are in most cases directly excluded from the network training. To tackle the above issues, this paper proposes a plug-and-play pseudo label rectification framework, which jointly utilizes CAmera Shift adapTation module and Outlier progressive Recycling strategy ($CASTOR$) to improve the quality of pseudo labels from both pre-clustering and post-clustering. Specifically, we first compute the camera similarity of two samples by utilizing a pretrained camera classification network and subtract the feature similarity by the camera similarity, the value of which is weighted in an exponential decay manner throughout the network training, in order to adaptively remedy the adverse impact of inter-camera distribution shift upon clustering. Besides, we carefully design an outlier progressive recycling strategy to reassign part of the outliers into the clustered groups to make full use of the useful information of outliers. Extensive experiments on three large scale unsupervised and unsupervised domain adaptive (UDA) person re-ID benchmarks validate the effectiveness of$CASTOR$and its wide compatibility with the state-of-the-art clustering-based methods.

Sparse unmixing separates the pixel of hyperspectral images into a collection of pure spectral signatures and the associated fractional coefficients with a complete spectral library as a priori, avoiding the drawback of inaccurate extraction of endmember information from the original hyperspectral image. As a state-of-the-art sparse unmixing method, fast multiscale spatial regularization unmixing algorithm (MUA) consists of two procedures, concerning on the approximation image domain and the original domain, respectively. However, it ignores the inter-superpixel correlation of the original domain that each superpixel only involves a small number of spectral signatures, and ignores the spectral variability of the approximate image domain. We address these two issues by introducing two different weighting factors to enhance the unmixing result. The effectiveness of our proposed algorithm is demonstrated by the experimental results on both synthetic and real hyperspectral data. The code and datasets of this letter can be found at https://github.com/wangtaowei11/Unmixing-Algorithm.

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of variables. Inspired by ensemble clustering that aims to seek a better clustering result from a set of clustering results, we propose self-supervised SNMF (S3NMF), which is capable of boosting clustering performance progressively by taking advantage of the sensitivity to initialization characteristic of SNMF, without relying on any additional information. Specifically, we first perform SNMF repeatedly with a random positive matrix for initialization each time, leading to multiple decomposed matrices. Then, we rank the quality of the resulting matrices with adaptively learned weights, from which a new similarity matrix that is expected to be more discriminative is reconstructed for SNMF again. These two steps are iterated until the stopping criterion/maximum number of iterations is achieved. We mathematically formulate S3NMF as a constrained optimization problem, and provide an alternative optimization algorithm to solve it with the theoretical convergence guaranteed. Extensive experimental results on 10 commonly used benchmark datasets demonstrate the significant advantage of our S3NMF over 14 state-of-the-art methods in terms of 5 quantitative metrics. The source code is publicly available athttps://github.com/jyh-learning/SSSNMF.

This paper explores the problem of recovering the discriminative representation of a hyperspectral remote sensing image (HRSI), which suffers from spectral variations, to boost its classification accuracy. To tackle this challenge, we propose a new method, namely local-global balanced low-rank approximation (GLB-LRA), which can increase the similarity between pixels belonging to an identical category while promoting the discriminability between pixels of different categories. Specifically, by taking advantage of the particular structural spatial information of HRSIs, we exploit the low-rankness of an HRSI robustly in both spatial and spectral domains from the perspective of local and global balance. We mathematically formulate GLB-LRA as an explicit optimization problem and propose an iterative algorithm to solve it efficiently. Experimental results over three commonly-used benchmark datasets demonstrate the significant superiority of our method over state-of-the-art methods.

In this paper, we propose a new semi-supervised graph construction method, which is capable of adaptively learning the similarity relationship between data samples by fully exploiting the potential of pairwise constraints, a kind of weakly supervisory information. Specifically, to adaptively learn the similarity relationship, we linearly approximate each sample with others under the regularization of the low-rankness of the matrix formed by the approximation coefficient vectors of all the samples. In the meanwhile, by taking advantage of the underlying local geometric structure of data samples that is empirically obtained, we enhance the dissimilarity information of the available pairwise constraints via propagation. We seamlessly combine the two adversarial learning processes to achieve mutual guidance. We cast our method as a constrained optimization problem and provide an efficient alternating iterative algorithm to solve it. Experimental results on five commonly-used benchmark datasets demonstrate that our method produces much higher classification accuracy than state-of-the-art methods, while running faster.

Deep subspace clustering networks have attracted much attention in subspace clustering, in which an auto-encoder non-linearly maps the input data into a latent space, and a fully connected layer named self-expressiveness module is introduced to learn the affinity matrix via a typical regularization term (e.g., sparse or low-rank). However, the adopted regularization terms ignore the connectivity within each subspace, limiting their clustering performance. In addition, the adopted framework suffers from the coupling issue between the auto-encoder module and the self-expressiveness module, making the network training non-trivial. To tackle these two issues, we propose a novel deep subspace clustering method named Maximum Entropy Subspace Clustering Network (MESC-Net). Specifically, MESC-Net maximizes the entropy of the affinity matrix to promote the connectivity within each subspace, in which its elements corresponding to the same subspace are uniformly and densely distributed. Meanwhile, we design a novel framework to explicitly decouple the auto-encoder module and the self-expressiveness module. Besides, we also theoretically prove that the learned affinity matrix satisfies the block-diagonal property under the assumption of independent subspaces. Extensive quantitative and qualitative results on commonly used benchmark datasets validate MESC-Net significantly outperforms state-of-the-art methods. The code is publicly available athttps://github.com/ZhihaoPENG-CityU/MESC.

This article explores the problem of semisupervised affinity matrix learning, that is, learning an affinity matrix of data samples under the supervision of a small number of pairwise constraints (PCs). By observing that both the matrix encoding PCs, called pairwise constraint matrix (PCM) and the empirically constructed affinity matrix (EAM), express the similarity between samples, we assume that both of them are generated from a latent affinity matrix (LAM) that can depict the ideal pairwise relation between samples. Specifically, the PCM can be thought of as a partial observation of the LAM, while the EAM is a fully observed one but corrupted with noise/outliers. To this end, we innovatively cast the semisupervised affinity matrix learning as the recovery of the LAM guided by the PCM and EAM, which is technically formulated as a convex optimization problem. We also provide an efficient algorithm for solving the resulting model numerically. Extensive experiments on benchmark datasets demonstrate the significant superiority of our method over state-of-the-art ones when used for constrained clustering and dimensionality reduction. The code is publicly available at https://github.com/jyh-learning/LAM.

Deep self-expressiveness-based subspace clustering methods have demonstrated effectiveness. However, existing works only consider the attribute information to conduct the self-expressiveness, limiting the clustering performance. In this paper, we propose a novel adaptive attribute and structure subspace clustering network (AASSC-Net) to simultaneously consider the attribute and structure information in an adaptive graph fusion manner. Specifically, we first exploit an auto-encoder to represent input data samples with latent features for the construction of an attribute matrix. We also construct a mixed signed and symmetric structure matrix to capture the local geometric structure underlying data samples. Then, we perform self-expressiveness on the constructed attribute and structure matrices to learn their affinity graphs separately. Finally, we design a novel attention-based fusion module to adaptively leverage these two affinity graphs to construct a more discriminative affinity graph. Extensive experimental results on commonly used benchmark datasets demonstrate that our AASSC-Net significantly outperforms state-of-the-art methods. In addition, we conduct comprehensive ablation studies to discuss the effectiveness of the designed modules. The code is publicly available at https://github.com/ZhihaoPENG-CityU/AASSC-Net.

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a co-association matrix, which indicates the pairwise similarity between samples, as the weighted linear combination of the connective matrices from different base clusterings, and the resulting co-association matrix is then adopted as the input of an off-the-shelf clustering algorithm, e.g., spectral clustering. However, the co-association matrix may be dominated by poor base clusterings, resulting in inferior performance. In this paper, we propose a novel low-rank tensor approximation based method to solve the problem from a global perspective. Specifically, by inspecting whether two samples are clustered to an identical cluster under different base clusterings, we derive a coherent-link matrix, which contains limited but highly reliable relationships between samples. We then stack the coherent-link matrix and the co-association matrix to form a three-dimensional tensor, the low-rankness property of which is further explored to propagate the information of the coherent-link matrix to the co-association matrix, producing a refined co-association matrix. We formulate the proposed method as a convex constrained optimization problem and solve it efficiently. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods. To the best of our knowledge, this is the first work to explore the potential of low-rank tensor on clustering ensemble, which is fundamentally different from previous approaches. Last but not least, our method only contains one parameter, which can be easily tuned.

The combination of the traditional convolutional network (i.e., an auto-encoder) and the graph convolutional network has attracted much attention in clustering, in which the auto-encoder extracts the node attribute feature and the graph convolutional network captures the topological graph feature. However, the existing works (i) lack a flexible combination mechanism to adaptively fuse those two kinds of features for learning the discriminative representation and (ii) overlook the multi-scale information embedded at different layers for subsequent cluster assignment, leading to inferior clustering results. To this end, we propose a novel deep clustering method named Attention-driven Graph Clustering Network (AGCN). Specifically, AGCN exploits a heterogeneity-wise fusion module to dynamically fuse the node attribute feature and the topological graph feature. Moreover, AGCN develops a scale-wise fusion module to adaptively aggregate the multi-scale features embedded at different layers. Based on a unified optimization framework, AGCN can jointly perform feature learning and cluster assignment in an unsupervised fashion. Compared with the existing deep clustering methods, our method is more flexible and effective since it comprehensively considers the numerous and discriminative information embedded in the network and directly produces the clustering results. Extensive quantitative and qualitative results on commonly used benchmark datasets validate that our AGCN consistently outperforms state-of-the-art methods.

This paper explores the problem of multi-view spectral clustering (MVSC) based on tensor low-rank modeling. Unlike the existing methods that all adopt an off-the-shelf tensor low-rank norm without considering the special characteristics of the tensor in MVSC, we design a novel structured tensor low-rank norm tailored to MVSC. Specifically, we explicitly impose a symmetric low-rank constraint and a structured sparse low-rank constraint on the frontal and horizontal slices of the tensor to characterize the intra-view and inter-view relationships, respectively. Moreover, the two constraints could be jointly optimized to achieve mutual refinement. On basis of the novel tensor low-rank norm, we formulate MVSC as a convex low-rank tensor recovery problem, which is then efficiently solved with an augmented Lagrange multiplier-based method iteratively. Extensive experimental results on seven commonly used benchmark datasets show that the proposed method outperforms state-of-the-art methods to a significant extent. Impressively, our method is able to produce perfect clustering. In addition, the parameters of our method can be easily tuned, and the proposed model is robust to different datasets, demonstrating its potential in practice. The code is available athttps://github.com/jyh-learning/MVSC-TLRR.

Positive label is often used as the supervisory information in the learning scenario, which refers to the category that a sample is assigned to. However, another side information lying in the labels, which describes the categories that a sample is exclusive of, have been largely ignored. In this paper, we propose a nonnegative matrix factorization (NMF) based classification method leveraging both positive and negative label information, which is termed as positive and negative label-driven NMF (PNLD-NMF). The proposed scheme concurrently accomplishes data representation and classification in a joint manner. Owing to the complementary characteristics between positive and negative labels, we further design a new regularization framework to take advantage of these two label types. Extensive experiments on six image classification benchmark datasets show that the proposed scheme is able to consistently deliver better classification accuracy.

As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose. However, the similarity matrix in the traditional SymNMF methods is usually predefined, resulting in limited clustering performance. Considering that the quality of the similarity graph is crucial to the final clustering performance, we propose a new semisupervised model, which is able to simultaneously learn the similarity matrix with supervisory information and generate the clustering results, such that the mutual enhancement effect of the two tasks can produce better clustering performance. Our model fully utilizes the supervisory information in the form of pairwise constraints to propagate it for obtaining an informative similarity matrix. The proposed model is finally formulated as a non-negativity-constrained optimization problem. Also, we propose an iterative method to solve it with the convergence theoretically proven. Extensive experiments validate the superiority of the proposed model when compared with nine state-of-the-art NMF models.

Superpixel segmentation aims at dividing the input image into some representative regions containing pixels with similar and consistent intrinsic properties, without any prior knowledge about the shape and size of each superpixel. In this article, to alleviate the limitation of superpixel segmentation applied in practical industrial tasks that detailed boundaries are difficult to be kept, we regard each representative region with independent semantic information as a subspace, and correspondingly formulate superpixel segmentation as a subspace clustering problem to preserve more detailed content boundaries. We show that a simple integration of superpixel segmentation with the conventional subspace clustering does not effectively work due to the spatial correlation of the pixels within a superpixel, which may lead to boundary confusion and segmentation error when the correlation is ignored. Consequently, we devise a spatial regularization and propose a novel convex locality-constrained subspace clustering model that is able to constrain the spatial adjacent pixels with similar attributes to be clustered into a superpixel and generate the content-aware superpixels with more detailed boundaries. Finally, the proposed model is solved by an efficient alternating direction method of multipliers solver. Experiments on different standard datasets demonstrate that the proposed method achieves superior performance both quantitatively and qualitatively compared with some state-of-the-art methods.

In this article, we propose a novel model for constrained clustering, namely, the dissimilarity propagation-guided graph-Laplacian principal component analysis (DP-GLPCA). By fully utilizing a limited number of weakly supervisory information in the form of pairwise constraints, the proposed DP-GLPCA is capable of capturing both the local and global structures of input samples to exploit their characteristics for excellent clustering. More specifically, we first formulate a convex semisupervised low-dimensional embedding model by incorporating a new dissimilarity regularizer into GLPCA (i.e., an unsupervised dimensionality reduction model), in which both the similarity and dissimilarity between low-dimensional representations are enforced with the constraints to improve their discriminability. An efficient iterative algorithm based on the inexact augmented Lagrange multiplier is designed to solve it with the global convergence guaranteed. Furthermore, we innovatively propose to propagate the cannot-link constraints (i.e., dissimilarity) to refine the dissimilarity regularizer to be more informative. The resulting DP model is iteratively solved, and we also prove that it can converge to a Karush-Kuhn-Tucker point. Extensive experimental results over nine commonly used benchmark data sets show that the proposed DP-GLPCA can produce much higher clustering accuracy than state-of-the-art constrained clustering methods. Besides, the effectiveness and advantage of the proposed DP model are experimentally verified. To the best of our knowledge, it is the first time to investigate DP, which is contrast to existing pairwise constraint propagation that propagates similarity. The code is publicly available at https://github.com/jyh-learning/DP-GLPCA.

Constrained spectral clustering (SC) based on pairwise constraint propagation has attracted much attention due to the good performance. All the existing methods could be generally cast as the following two steps, i.e., a small number of pairwise constraints are first propagated to the whole data under the guidance of a predefined affinity matrix, and the affinity matrix is then refined in accordance with the resulting propagation and finally adopted for SC. Such a stepwise manner, however, overlooks the fact that the two steps indeed depend on each other, i.e., the two steps form a "chicken-egg" problem, leading to suboptimal performance. To this end, we propose a joint PCP model for constrained SC by simultaneously learning a propagation matrix and an affinity matrix. Especially, it is formulated as a bounded symmetric graph regularized low-rank matrix completion problem. We also show that the optimized affinity matrix by our model exhibits an ideal appearance under some conditions. Extensive experimental results in terms of constrained SC, semisupervised classification, and propagation behavior validate the superior performance of our model compared with state-of-the-art methods.

In this letter, we propose a new sparse representation (SR)-based method for hyperspectral image (HSI) classification, namely SR with incremental dictionaries (SRID). Our SRID boosts existing SR-based HSI classification methods significantly, especially when used for the task with extremely limited training samples. Specifically, by exploiting unlabeled pixels with spatial information and multiple-feature-based SR classifiers, we select and add some of them to dictionaries in an iterative manner, such that the representation abilities of the dictionaries are progressively augmented, and likewise more discriminative representations. In addition, to deal with large-scale data sets, we use a certainty sampling strategy to control the sizes of the dictionaries, such that the computational complexity is well balanced. Experiments over two benchmark data sets show that our proposed method achieves higher classification accuracy than the state-of-the-art methods, i.e., the overall classification accuracy can improve more than 4%.

In this letter, we propose a novel transfer learning approach, which simultaneously exploits the intra-domain differentiation and inter-domain correlation to comprehensively solve the drawbacks many existing transfer learning methods suffer from, i.e., they either are unable to handle the negative samples or have strict assumptions on the distribution. Specifically, the sample selection strategy is introduced to handle negative samples by using the local geometry structure and the label information of source samples. Furthermore, the pseudo target label is imposed to slack the assumption on the inter-domain distribution for considering the inter-domain correlation. Then, an efficient alternating iterative algorithm is proposed to solve the formulated optimization problem with multiple constraints. The extensive experiments conducted on eleven real-world datasets show the superiority of our method over state-of-the-art approaches, i.e., our method achieves 11.23% improvement on the MNIST dataset.

In this article, we propose a semi-supervised non-negative matrix factorization (NMF) model by means of elegantly modeling the label information. The proposed model is capable of generating discriminable low-dimensional representations to improve clustering performance. Specifically, a pair of complementary regularizers, i.e., similarity and dissimilarity regularizers, is incorporated into the conventional NMF to guide the factorization. And, they impose restrictions on both the similarity and dissimilarity of the low-dimensional representations of data samples with labels as well as a small number of unlabeled ones. The proposed model is formulated as a well-posed constrained optimization problem and further solved with an efficient alternating iterative algorithm. Moreover, we theoretically prove that the proposed algorithm can converge to a limiting point that meets the Karush-Kuhn-Tucker conditions. Extensive experiments as well as comprehensive analysis demonstrate that the proposed model outperforms the state-of-the-art NMF methods to a large extent over five benchmark data sets, i.e., the clustering accuracy increases to 82.2% from 57.0%.

Pairwise constraints (PCs) composed of must-links (MLs) and cannot-links (CLs) are widely used in many semisupervised tasks. Due to the limited number of PCs, pairwise constraint propagation (PCP) has been proposed to augment them. However, the existing PCP algorithms only adopt a single matrix to contain all the information, which overlooks the differences between the two types of links such that the discriminability of the propagated PCs is compromised. To this end, this article proposes a novel PCP model via dual adversarial manifold regularization to fully explore the potential of the limited initial PCs. Specifically, we propagate MLs and CLs with two separated variables, called similarity and dissimilarity matrices, under the guidance of the graph structure constructed from data samples. At the same time, the adversarial relationship between the two matrices is taken into consideration. The proposed model is formulated as a nonnegative constrained minimization problem, which can be efficiently solved with convergence theoretically guaranteed. We conduct extensive experiments to evaluate the proposed model, including propagation effectiveness and applications on constrained clustering and metric learning, all of which validate the superior performance of our model to state-of-the-art PCP models.

The learning algorithm of an extreme learning machine (ELM) has two fundamental steps: 1) random nonlinear feature transformation and 2) least squares learning. Since the probabilistic interpretation for a sample by the least squares method follows a Gaussian distribution, there are two limitations in ELM caused by the second step: 1) it may be inaccurate to handle binary classification problems, since the output of a binary dataset has a distribution far from Gaussian and 2) it may have difficulties in dealing with nontraditional data types (such as count data, ordinal data, etc.), which also do not follow Gaussian distribution. In order to solve the above-mentioned problems, this paper proposes a generalized ELM (GELM) framework by applying the exponential family distribution (EFD) to the output layer node of ELM. It simplifies the design of ELM models for task-specific output domains with different data types. We propose a unified learning paradigm for all the models under this GELM framework with different distributions in EFD, and prove that traditional ELM is a special instance of GELM by setting the output distribution as a Gaussian distribution (GELM-Gaussian). We also prove that the training of GELM-Gaussian can be finished in one iteration, in this case, GELM-Gaussian does not slow down the training speed of traditional ELM. Besides, we propose the kernel version of GELM, which can also be concretized to different models by applying different EFDs. Experimental comparisons demonstrate that GELM can give more accurate probabilistic interpretation to binary classification and GELM has a great potential in dealing with a broader range of machine learning tasks.

Pairwise constraint propagation (PCP) aims to propagate a limited number of initial pairwise constraints (PCs, including must-link and cannot-link constraints) from the constrained data samples to the unconstrained ones to boost subsequent PC-based applications. The existing PCP approaches always suffer from the imbalance characteristic of PCs, which limits their performance significantly. To this end, we propose a novel imbalance-aware PCP method, by comprehensively and theoretically exploring the intrinsic structures of the underlying PCs. Specifically, different from the existing methods that adopt a single representation, we propose to use two separate carriers to represent the two types of links. And the propagation is driven by the structure embedded in data samples and the regularization of the local, global, and complementary structures of the two carries. Our method is elegantly cast as a well-posed constrained optimization model, which can be efficiently solved. Experimental results demonstrate that the proposed PCP method is capable of generating more high-fidelity PCs than the recent PCP algorithms. In addition, the augmented PCs by our method produce higher accuracy than state-of-the-art semi-supervised clustering methods when applied to constrained clustering. To the best of our knowledge, this is the first PCP method taking the imbalance property of PCs into account.

In this paper, we introduce a closed-form sparse Bayesian kernel Poisson regression (SBKPR) model for count data regression problems based on the sparse Bayesian learning (SBL) approach. In Bayesian setting, a Gaussian prior is given to the model parameter, which is not the conjugate distribution of Poisson regression. Hence, the model parameters cannot be integrated analytically, which leads to the inference intractable problem. In this paper, the log-gamma Gaussian approximation method is proposed to solve this analytically intractable problem, which can give out the closed-form solutions. Furthermore, an individual Gaussian prior is given to the model parameters, which can enhance the flexibility of the proposed method. Finally, sparse solutions can be obtained by applying SBL, which can benefit the learning efficiency and reduce the computational time in practical applications. Experimental results demonstrate that the proposed SBKPR model can outperform some state-of-the-art count data regression models on both toy data and real-world data.

Nonnegative matrix factorization (NMF) is a well-known paradigm for data representation. Traditional NMF-based classification methods first perform NMF or one of its variants on input data samples to obtain their low-dimensional representations, which are successively classified by means of a typical classifier [e.g., k -nearest neighbors (KNN) and support vector machine (SVM)]. Such a stepwise manner may overlook the dependency between the two processes, resulting in the compromise of the classification accuracy. In this paper, we elegantly unify the two processes by formulating a novel constrained optimization model, namely dual embedding regularized NMF (DENMF), which is semi-supervised. Our DENMF solution simultaneously finds the low-dimensional representations and assignment matrix via joint optimization for better classification. Specifically, input data samples are projected onto a couple of low-dimensional spaces (i.e., feature and label spaces), and locally linear embedding is employed to preserve the identical local geometric structure in different spaces. Moreover, we propose an alternating iteration algorithm to solve the resulting DENMF, whose convergence is theoretically proven. Experimental results over five benchmark datasets demonstrate that DENMF can achieve higher classification accuracy than state-of-the-art algorithms.

Superpixel segmentation aims at grouping discretizing pixels into high-level correlative units and reducing the complexity of subsequent tasks, e.g., saliency detection and object tracking. Existing superpixel segmentation algorithms mainly focus on maintaining the geometrical information, while neglecting the irregular structure of superpixels. In this paper, a superpixel segmentation method is proposed to generate approximately structural superpixels with sharp boundary adherence and comprehensive semantic information. The superpixel segmentation is formulated as a square-wise asymmetric partition problem, where the semantic perceptual superpixels are recorded in a square level to preserve abundant semantic information and save storage simultaneously. Moreover, in order to achieve regular-shape superpixel units to better adhere to image boundaries and contours, a combinatorial optimization strategy is devised to achieve an optimal combination of squares and isolated pixels. Experimental comparisons with some state-of-the-art superpixel segmentation methods on the public benchmarks demonstrate the effectiveness of the proposed method quantitatively and qualitatively. In addition, we have applied the method to brain tissue segmentation to illustrate superior performance.

For solving multi-label classification problems, traditional random K-labelsets method has two main drawbacks: 1) the randomly selected label set may result in highly imbalanced data for single-label multi-class learning, and 2) the dependency relations among different labels in the same label set may cause serious information redundancy and overlap. Both of these two drawbacks can affect the generalization capability of the multi-label learner. In order to overcome these two problems, in this paper, we propose a K-labelsets ensemble method based on mutual information and joint entropy. First, the mutual information and joint entropy are adopted to evaluate the redundancy level and imbalance level of each K-labelset. Then, disjoint sampling is performed iteratively, where during each iteration, a number of K-labelsets with low mutual information are retained to be the candidates, and the one with the highest joint entropy is selected. Afterwards, for each selected K-labelset, the label powerset method is employed and a multi-class classification model is constructed. Finally, the multi-class models on different K-labelsets are integrated, and a voting based ensemble model is generated to perform the predictions for unseen samples. We conduct extensive experiments on real-world multi-label data sets. Experimental results demonstrate the effectiveness of the proposed method.

In this paper, we propose a new algorithm for constrained clustering, in which a new regularizer elegantly incorporates a small amount of weakly supervisory information in the form of pair-wise constraints to regularize the similarity between the low-dimensional representations of a set of data samples. By exploring both the local and global structures of the data samples with the guidance of the supervisory information, the proposed algorithm is capable of learning the low-dimensional representations with strong separability. Technically, the proposed algorithm is formulated and relaxed as a convex optimization model, which is further efficiently solved with the global convergence guaranteed. Experimental results on multiple benchmark data sets show that our proposed model can produce higher clustering accuracy than state-of-the-art algorithms.

Spectral clustering (SC) is one of the most widely used clustering methods. In this letter, we extend the traditional SC with a semi-supervised manner. Specifically, with the guidance of small amount of supervisory information, we build a matrix with anti-block-diagonal appearance, which is further utilized to regularize the product of the low-dimensional embedding and its transpose. Technically, we formulate the proposed model as a constrained optimization problem. Then, we relax it as a convex problem, which can be efficiently solved with the global convergence guaranteed via the inexact augmented Lagrangian multiplier method. Experimental results over four real-world datasets demonstrate that higher accuracy and normalized mutual information are achieved when compared with state-of-the-art methods.

As a variant of nonnegative matrix factorization (NMF), symmetric NMF (SNMF) has shown to be effective for capturing the cluster structure embedded in the graph representation. In contrast to the existing SNMF-based clustering methods that empirically construct the similarity matrix and rigidly introduce the supervisory information to the assignment matrix, in this paper, we propose a novel SNMF-based semisupervised clustering method, namely, pairwise constraint propagation-induced SNMF (PCPSNMF). By formulating a single-constrained optimization problem, PCPSNMF is capable of learning the similarity and assignment matrices adaptively and simultaneously, in which a small amount of supervisory information in the form of pairwise constraints is introduced in a flexible way to guide the construction of the similarity matrix, and the two matrices communicate with each other to achieve mutual refinement until convergence. In addition, we propose an efficient alternating iterative algorithm to solve the optimization problem, whose convergence is theoretically proven. Experimental results over several benchmark image data sets demonstrate that PCPSNMF is less sensitive to initialization and produces higher clustering performance, compared with the state-of-the-art methods.

By transforming a multi-objective optimization problem into a number of single-objective optimization problems and optimizing them simultaneously, decomposition-based evolutionary multi-objective optimization algorithms have attracted much attention in the field of multi-objective optimization. In decomposition-based algorithms, the population diversity is maintained using a set of predefined weight vectors, which are often evenly sampled on a unit simplex. However, when the Pareto front of the problem is not a hyperplane but more complex, the distribution of the final solution set will not be that uniform. In this paper, we propose an adaptive method to periodically regenerate the weight vectors for decomposition-based multi-objective algorithms according to the geometry of the estimated Pareto front. In particular, the Pareto front is estimated via Gaussian process regression. Thereafter, the weight vectors are reconstructed by sampling a set of points evenly distributed on the estimated Pareto front. Experimental studies on a set of multi-objective optimization problems with different Pareto front geometries verify the effectiveness of the proposed adaptive weights generation method.

MOTIVATION: The exponential growth of biological network database has increasingly rendered the global network similarity search (NSS) computationally intensive. Given a query network and a network database, it aims to find out the top similar networks in the database against the query network based on a topological similarity measure of interest. With the advent of big network data, the existing search methods may become unsuitable since some of them could render queries unsuccessful by returning empty answers or arbitrary query restrictions. Therefore, the design of NSS algorithm remains challenging under the dilemma between accuracy and efficiency. RESULTS: We propose a global NSS method based on regression, denotated as NSSRF, which boosts the search speed without any significant sacrifice in practical performance. As motivated from the nature, subgraph signatures are heavily involved. Two phases are proposed in NSSRF: offline model building phase and similarity query phase. In the offline model building phase, the subgraph signatures and cosine similarity scores are used for efficient random forest regression (RFR) model training. In the similarity query phase, the trained regression model is queried to return similar networks. We have extensively validated NSSRF on biological pathways and molecular structures; NSSRF demonstrates competitive performance over the state-of-the-arts. Remarkably, NSSRF works especially well for large networks, which indicates that the proposed approach can be promising in the era of big data. Case studies have proven the efficiencies and uniqueness of NSSRF which could be missed by the existing state-of-the-arts. AVAILABILITY AND IMPLEMENTATION: The source code of two versions of NSSRF are freely available for downloading at https://github.com/zhangjiaobxy/nssrfBinary and https://github.com/zhangjiaobxy/nssrfPackage . CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In this paper, a joint machine learning and game theory modeling (MLGT) framework is proposed for inter frame coding tree unit (CTU) level bit allocation and rate control (RC) optimization in high efficiency video coding (HEVC). First, a support vector machine-based multi-classification scheme is proposed to improve the prediction accuracy of CTU-level rate-distortion (R-D) model. The legacy "chicken-and-egg" dilemma in video coding is proposed to be overcome by the learning-based R-D model. Second, a mixed R-D model-based cooperative bargaining game theory is proposed for bit allocation optimization, where the convexity of the mixed R-D model-based utility function is proved, and Nash bargaining solution is achieved by the proposed iterative solution search method. The minimum utility is adjusted by the reference coding distortion and frame-level quantization parameter (QP) change. Finally, intra frame QP and inter frame adaptive bit ratios are adjusted to make inter frames have more bit resources to maintain smooth quality and bit consumption in the bargaining game optimization. Experimental results demonstrate that the proposed MLGT-based RC method can achieve much better R-D performances, quality smoothness, bit rate accuracy, buffer control results, and subjective visual quality than the other state-of-the-art one-pass RC methods, and the achieved R-D performances are very close to the performance limits from the FixedQP method.