Feature dynamics have emerged as a critical topic about open-environment learning due to the instability of feature availability. While traditional feature evolution targets single-label tasks, multi-label learning is essential to accommodate the exploding annotation spaces. However, multi-label classification with incremental and decremental features is a crucial yet underexplored problem, which poses the challenge of preserving feature representations and label correlations from historical instances and simultaneously adapting to newly arriving streaming data. To address these issues, we propose a two-stage, one-pass learning approach termed MLID. It attempts to compress the informative content of vanished features into the domain of survived ones, facilitate the propagation of label dependencies via low-rank regularization of the classifier, and incorporate augmented features to construct an adaptive classification mechanism. Besides, we design optimization strategies for each stage and provide theoretical guarantees of convergence. Moreover, we establish the generalization error bound of MLID and demonstrate that the compactness of the trace norm and the reuse of models based on effective features can enhance the generalization performance. Finally, we extend it to multi-shot case and extensive experimental results validate the superiority of our MLID.

Partial Label Learning (PLL) aims to train multi-class classifiers from examples where each instance is associated with a set of candidate labels, among which the ground-truth label is assumed to be included. While most existing studies assume that partial labels are both instance-independent and reliable, such assumptions often break down in real-world scenarios, where candidate sets may depend on instance-specific features and even exclude the ground-truth label. In this work, we investigate a more realistic setting termed Unreliable Instance-Dependent Partial Label Learning (UIDPLL). To address the challenges in UIDPLL, we propose a novel framework named Neighborhood-guided Label Augmentation and Pruning (NLAP). NLAP exploits the structural consistency among neighboring instances to progressively refine candidate label sets and integrates classifier feedback to disambiguate labels during training. This progressive mechanism improves classification performance by tackling ambiguity caused by noise and instance dependency in partial labels. Furthermore, we provide theoretical guarantees for the proposed NLAP framework, demonstrating that label ambiguity can be effectively reduced through appropriate refinement and pruning procedures. Extensive experiments on both benchmark and real-world datasets demonstrate the robustness and effectiveness of the proposed method.

Transfer subspace learning plays a critical role in unsupervised domain adaptation by establishing a shared embedding space where source domain data can be linearly reconstructed to match target domain distribution. While existing methods exploit the low-rank structures of reconstruction matrix, they frequently overlook the alignment of cross-domain joint probability distributions in the learned low-dimensional subspace. To address these challenges, we propose a novel non-convex transfer learning method named DATSL, which employs embedded distribution alignment. Our DATSL incorporates a non-convex regularizer to approximate low-rank constraints, capturing the complex characteristics of the rank function by minimizing top $k$ smallest singular values of reconstruction matrix. To align the joint distributions across domains, a category-aware joint distribution alignment mechanism extracts more discriminative representations and enhances subspace discriminability through label-informed covariance matching. Besides, DATSL is extended to a graph-based variant GDATSL, which incorporates manifold-preserving constraints via Laplacian regularization to maintain intrinsic data topology during knowledge transfer. Furthermore, we develop an efficient iterative optimization algorithm to solve our formulated nonconvex minimization problems with proved convergence. Extensive experimental results on several public datasets demonstrate the effectiveness of our proposed methods in comparison to other state-of-the-art approaches.

Imbalance in multi-domain multi-modal settings remains a significant challenge in real-world applications, such as fake news detection. Although existing methods have enhanced semantic representations and employed complex architectures to improve recognition performance, most of them focus on domain heterogeneity and modality sensitivity. However, these methods neglect the class imbalance, which severely impacts model robustness and generalization in open-world scenarios. Learning for such imbalanced multi-domain multi-modal data is crucial but rarely studied, particularly when the domain and modal of samples are imbalanced. To address these challenges, we propose a novel Imbalanced multi-domain multi-modal learning method with Expert Collaboration and Dynamic Fusion, named IECDF. Specifically, to alleviate inter-domain imbalance, we design an expert collaboration module with a domain-shared specific embedding structure and an improved gating strategy to enhance the discriminative power of the cross-domain features. Besides, a dynamic fusion mechanism based on Mamba-Former is designed to learn adaptive weights for each modality. Moreover, to tackle the intra-class imbalance problem, we adopt asymmetric re-weighted loss—DLINEX—to increase the contributions of minority class samples and learn the unbiased decision boundary. Extensive experimental results on various datasets validate the superiority of our proposed IECDF compared to state-of-the-art methods. Our code will be available at https://github.com/Yuchen-zh/IECDF .

Multi-view multi-label learning has become a research focus for describing objects with rich expressions and annotations. However, real-world data often contains numerous unlabeled instances, due to the high cost and technical limitations of manual labeling. This crucial problem involves three main challenges: i) How to extract advanced semantics from available views? ii) How to build a refined classification framework with limited labeled space? iii) How to provide more high-quality supervisory information? To address these problems, we propose a Semi-Supervised Multi-View Multi-Label Learning Method with View-Specific Transformer and Enhanced Pseudo-Label named SMVTEP. Specifically, Generative Adversarial Networks are employed to extract informative shared and specific representations and their consistency and distinctiveness are ensured through the adversarial mechanism and information theory based contrastive learning. Then we build specific classifiers for each extracted feature and apply instance-level manifold constraints to reduce bias across classifiers. Moreover, we design a transformer-style fusion approach that simultaneously captures the imbalance of expressive power among views, mapping effects on specific labels, and label dependencies by incorporating confidence scores and category semantics into the self-attention mechanism. Furthermore, after using Mixup for data augmentation, category-enhanced pseudo-labels are leveraged to improve the reliability of additional annotations by aligning the label distribution of unlabeled samples with the true distribution. Finally, extensive experimental results validate the effectiveness of SMVTEP against state-of-the-art methods.

Label shift, which investigates the adaptation of label distributions between the fixed source and target domains, has attracted significant research interests and broad applications in offline settings. In real-world scenarios, however, data often arrives as a continuous stream. Addressing label shift in online learning settings is paramount. Existing strategies, which tailor traditional offline label shift techniques to online settings, have degraded performance due to the inconsistent estimation of label distributions and violation of convex assumption for theoretical guarantee. In this paper, we propose a novel method to ensure consistent adaptation to online label shift. We construct a new convex risk estimator that is pivotal for both online optimization and theoretical analysis. Furthermore, we enhance an optimistic online algorithm as the base learner and refine the classifier using an ensemble method. Theoretically, we derive a universal dynamic regret which achieves minimax optimal. Extensive experiments on both real-world datasets and human motion task demonstrate the superiority of our method comparing existing methods.

In open-environment applications, data are often collected from heterogeneous modalities with distinct encodings, resulting in feature space heterogeneity. This heterogeneity inherently induces label shift, making cross-modal knowledge transfer particularly challenging when the source and target data exhibit simultaneous heterogeneous feature spaces and shifted label distributions. Existing studies address only partial aspects of this issue, leaving the broader problem unresolved. To bridge this gap, we introduce a new concept of Heterogeneous Label Shift (HLS), targeting this critical but underexplored challenge. We first analyze the impact of heterogeneous feature spaces and label distribution shifts on model generalization and introduce a novel error decomposition theorem. Based on these insights, we propose a bound minimization HLS framework that decouples and tackles feature heterogeneity and label shift accordingly. Extensive experiments on various benchmarks for cross-modal classification validate the effectiveness and practical relevance of the proposed approach.

In many real applications, the data attributes are incremental and the samples are stored with accumulated feature spaces gradually. Although there are several elegant approaches to tackling this problem, the theoretical analysis is still limited. There exist at least two challenges and fundamental questions. 1) How to derive the generalization bounds of these approaches? 2) Under what conditions do these approaches have a strong generalization guarantee? To solve these crucial but rarely studied problems, we provide a comprehensive theoretical analysis in this paper. We begin by summarizing and refining four strategies for addressing feature incremental data. Subsequently, we derive their generalization bounds, providing rigorous and quantitative insights. The theoretical findings highlight the key factors influencing the generalization abilities of different strategies. In tackling the above two fundamental problems, we also provide valuable guidance for exploring other learning challenges in dynamic environments. Finally, the comprehensive experimental and theoretical results mutually validate each other, underscoring the reliability of our conclusions.

Label shift is a prevalent phenomenon encountered in open environments, characterized by a notable discrepancy in the label distributions between the source (training) and target (test) domains, whereas the conditional distributions given the labels remain invariant. Existing label shift methods adopt a two-step strategy: initially computing the importance weight and subsequently utilizing it to calibrate the target outputs. However, this conventional strategy overlooks the intricate interplay between output adjustment and weight estimation. In this paper, we introduce a novel approach termed as One-step Label Shift Adaptation (OLSA). Our methodology jointly learns the predictive model and the corresponding weights through a bi-level optimization framework, with the objective of minimizing an upper bound on the target risk. To enhance the robustness of our proposed model, we incorporate a debiasing term into the upper-level classifier training and devise a regularization term for the lower-level weight estimation. Furthermore, we present theoretical analyses about the generalization bounds, offering guarantees for the model's performance. Extensive experimental results substantiate the efficacy of our proposal.

Second-order Online Kernel Learning (OKL) has attracted considerable research interest due to its promising predictive performance in streaming environments. However, existing second-order OKL approaches suffer from at least quadratic time complexity with respect to the pre-set budget, rendering them unsuitable for large-scale datasets. Moreover, the singular value decomposition required to obtain explicit feature mapping is computationally expensive due to the complete decomposition process. To address these issues, we propose FORKS, a fast incremental matrix sketching and decomposition approach tailored for second-order OKL. FORKS constructs an incremental maintenance paradigm for second-order kernelized gradient descent, which includes incremental matrix sketching for kernel approximation and incremental matrix decomposition for explicit feature mapping construction. Theoretical analysis demonstrates that FORKS achieves a logarithmic regret guarantee on par with other second-order approaches while maintaining a linear time complexity w.r.t. the budget, significantly enhancing efficiency over existing methods. We validate the performance of our method through extensive experiments conducted on real-world datasets, demonstrating its superior scalability and robustness against adversarial attacks.

Label distribution learning (LDL) has large practical application potentials due to its superiority in dealing with ambiguous label information. Most existing LDL methods are designed in a closed environment, wherein all the elements, e.g., feature and label space, are fixed. Nevertheless, in reality, data are dynamically acquired in the open environment, wherein the feature space can accumulate over time and the label space can be further enriched and refined accordingly with the accumulated feature space. Conducting LDL for such simultaneous augmentation of feature and label is crucial but rarely studied, particularly when the labeled samples with full observations are limited. In this paper, we propose a novel Incremental Label Distribution Learning (ILDL) method to tackle this brand new LDL problem by continuously transiting discriminative information from the previous model to the current one. Concretely, a prior compensation regularization is designed for such discriminative information transitivity. In this manner, the current model has the capacity to reuse the previous model to guide its own training. Furthermore, we present the theoretical analyses about the generalization bound, which provides guarantees for model inheritance. Comprehensive experimental studies validate the effectiveness of our proposal.

Traditional multi-view clustering methods rely on the cross-view sample alignment presumption to explore consistent and complementary information from multiple views. However, in real-world scenarios, sensor heterogeneity and decentralized data storage and processing frequently make this presumption violated, leading to the Unaligned Multi-view Clustering (UMC) problem. Although existing works have promoted the development of UMC, they have at least one of the following limitations, i.e., high computational complexity, inadequate use of high-order correlation and two-stage clustering. To address these limitations, we propose a Joint High-order Correlation Learning (JHCL) framework for scalable one-step unaligned multi-view clustering. Specifically, multi-order bipartite graphs are utilized to make fully use of intra-view high-order correlations. Then, based on a tensorial bipartite graph alignment and fusion model, inter-view high-order correlations are exploited simultaneously. In such manner, the learned consistent bipartite graph retains adequate structural information for accurate and fast clustering in one step. Extensive experiments on real-world datasets validate the superiority of JHCL in both clustering performance and computational efficiency. Code available: https://github.com/revolution6575/JHCL.git.

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when adapting to new tasks. Recently, approaches leveraging pre-trained models have gained increasing popularity in mitigating this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address this limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of the gradients. CoSO updates the model by projecting gradients onto these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspace of each task is constrained to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions for the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.

Multi-view multi-label learning typically suffers from dual data incompleteness due to limitations in feature storage and annotation costs. The interplay of hetero geneous features, numerous labels, and missing information significantly degrades model performance. To tackle the complex yet highly practical challenges, we propose a Theory-Driven Label-Specific Representation (TDLSR) framework. Through constructing the view-specific sample topology and prototype association graph, we develop the proximity-aware imputation mechanism, while deriving class representatives that capture the label correlation semantics. To obtain semantically distinct view representations, we introduce principles of information shift, inter action and orthogonality, which promotes the disentanglement of representation information, and mitigates message distortion and redundancy. Besides, label semantic-guided feature learning is employed to identify the discriminative shared and specific representations and refine the label preference across views. Moreover, we theoretically investigate the characteristics of representation learning and the generalization performance. Finally, extensive experiments on public datasets and real-world applications validate the effectiveness of TDLSR.

Multi-view subspace clustering, which aims to partition a set of multi-source data into a common space, has recently attracted wide attention in the field of data analysis and machine learning. Traditional algorithms may face the problem of high complexity in calculating the self-expression matrix and in turning parameter. This paper proposes a novel multi-view subspace clustering model termed as Low-rank Multi-view Subspace Clustering via Adaptive Weight (LMSCAW). LMSCAW decomposes the self-expression matrix into the product of two low-rank representation matrices and thus can fix the rank of the self-expression matrix of each view to increase the stability of the algorithm. In addition, in order to learn the common representation matrix better, LMSCAW fuses the self-expression matrices among multiple views and implicitly weights each view by the Frobenius norm without additional parameters. Extensive experimental results on multiple benchmark datasets are provided to show the effectiveness of the proposed algorithm and its superior performance over other state-of-the-art methods.

Applying current machine learning algorithms in complex and open environments remains challenging, especially when different changing elements are coupled and the training data is scarce. For example, in the activity recognition task, the motion sensors may change position or fall off due to the intensity of the activity, leading to changes in feature space and finally resulting in label noise. Learning from such a problem where the dynamic features are coupled with noisy labels is crucial but rarely studied, particularly when the noisy samples in new feature space are limited. In this paper, we tackle the above problem by proposing a novel two-stage algorithm, called Adaptive Learning for Dynamic features and Noisy labels (ALDN). Specifically, optimal transport is first modified to map the previously learned heterogeneous model to the prior model of the current stage. Then, to fully reuse the mapped prior model, we add a simple yet efficient regularizer as the consistency constraint to assist both the estimation of the noise transition matrix and the model training in the current stage. Finally, two implementations with direct (ALDN-D) and indirect (ALDN-ID) constraints are illustrated for better investigation. More importantly, we provide theoretical guarantees for risk minimization of ALDN-D and ALDN-ID. Extensive experiments validate the effectiveness of the proposed algorithms.

Traditional classification problems assume that features and labels are fixed. However, this assumption is easily violated in open environments. For example, the exponential growth of web pages leads to an expanding feature space with the accumulation of keywords. At the same time, rapid refresh makes it difficult to obtain accurate labels for web pages, often resulting in rough annotations containing potentially correct labels, i.e., partial label set. In such cases, the coupling between the incremental feature space and the partial label set introduces more complex real-world challenges, which deserve attention but have not been fully explored. In this paper, we address this issue by introducing a novel incremental learning approach with Simultaneous Incremental Feature and Partial Label (SIFPL). SIFPL models the data evolution in dynamic and open environments in a two-stage way, consisting of a previous stage and an adapting stage, to deal with the associated challenges. Specifically, to ensure the reusability of the model during adaptation, we impose classifier consistency constraints to enhance the stability of the current model. This constraint leverages historical information from the previous stage to improve the generalization ability of the current model, providing a reliable foundation for further refining the model with new features. Regarding label disambiguation, we filter out incorrect candidate labels based on the principle of minimizing classifier loss, ensuring that the new features and labels effectively support the model's adaptation to the incremental feature space, thereby further refining its performance. Furthermore, we also provide a solid theoretical analysis of the model's generalization bounds, which can validate the efficiency of model inheritance. Experiments on benchmark and real-world datasets validate that the proposed method achieves better accuracy performance than the baseline methods in most cases.

Classification tasks have long been a central concern in the field of machine learning. Although deep neural network-based approaches offer a novel, versatile and highly precise solution for classification tasks, the intrinsic ambiguity and uncertainty present in the data continue to pose a significant challenge, impeding the potential for further advancements in classification accuracy. To address this issue, we propose a Fuzzy neurAl SupporT vEctor machiNe (FASTEN) which mitigates the fuzziness and uncertainty inherent in the data and enhances the classification performance. FASTEN mainly consists of two parts: the fuzzy feature extraction unit and the multi-path classifier aggregation unit. The fuzzy feature extraction unit is designed to precisely capture the fuzzy features of the uncertainty data by embedding membership functions and fuzzy rules within the neural network. In this process, fuzzy parameters are dynamically updated on a task-driven basis, ensuring that the model can adaptively handle data with different degrees of fuzziness. The multi-path classifier aggregation unit is designed to integrate the outputs of multiple neural network classifiers through dynamic linear combination. Meanwhile, we introduce the maximum margin theory of support vector machines to optimize the feature representation and improve classification accuracy. Our experimental results show that FASTEN can improve the classification performance on image and signal datasets. Through ablation experiments, the contributions of each unit to performance enhancement have been further validated, thereby establishing a foundation for subsequent model optimization.

In many image processing tasks, e.g., 3D reconstruction of dynamic scenes, different types of descriptions, a.k.a., views, of an object are emerging in a streaming way. Streaming view learning provides an effective solution to this dynamic view problem. In this paradigm, existing streaming view learning methods typically assume that all labels are accurate. However, in many real-world applications, the initial views may be not good enough for characterizing, leading to noisy labels that degrade classification performance. How to learn a model for simultaneous view evolving and label ambiguity is critical yet unexplored. In this paper, we propose a novel method called Streaming View Classification with Noisy Label (SVCNL). We calibrate noisy labels according to the emerging of new views, thereby reflecting the dynamic changes in the data more accurately. Leveraging the sequential and non-revisitable nature of views, the method tunes existing models to inherit information from previous stages by utilizing current-stage data. It reconstructs noisy labels through a label transition matrix and establishes relationships between true labels and samples using a graph embedding strategy, progressively correcting noisy labels. Together with the theoretical analyses about generalization bounds, extensive experiments demonstrate the effectiveness of the proposed approach.

Learning from data streams collected sequentially over time are widely spread in real-world applications. Previous methods typically assume that the data stream has a feature space with a fixed or clearly defined evolution pattern, as well as a balanced class distribution. However, in many practical scenarios, such as environmental monitoring systems, the frequency of anomalous events is significantly imbalanced compared to normal ones and the feature space dynamically changes due to ecological evolution and sensor lifespan. To alleviate this important but rarely studied problem, we propose the Adaptive Learning in Imbalace data streams with Unpredictable feature evolution (ALIU) algorithm. As data streams with imbalanced class distribution arrive, ALIU first mitigates the model's bias for the majority class by reweighting the adaptive gradient descent magnitudes between different classes. Then, a new loss function is proposed that simultaneously focuses on misclassifications and maintains model robustness. Further, when imbalanced data streams arrive with feature evolutions, we reuse the previously learned model and update the incomplete and augmented features by adopting the adaptive gradient strategy and ensemble method, respectively. Finally, we utilize the projected technique to build a sparse yet efficient model. Based on a few common and mild assumptions, we theoretically analyze that the ALIU satisfies a sub-linear regret bound under both convex and strong convex loss functions and the performance of model can be improved with the assistance of old features. Besides, extensive experimental results further demonstrate the effectiveness of our proposed algorithm.

Pairwise constrained clustering, which employs the pairwise constraints to boost clustering performance, has been widely used in many applications such as face clustering and image retrieval. Due to the prevalence of multi-view data, pairwise constrained multi-view clustering has attracted increasing attention. Nevertheless, existing methods suffer from at least one of the three issues, i.e., expensive time consumption, two-stage clustering and inadequate use of pairwise constraints. To address the above issues, this paper proposes a Pairwise Constrained Bipartite Graph (PCBG) learning method for efficient one-step pairwise constrained multi-view clustering. Concretely, to encode must-link constraints, a novel comprehensive bipartite graph is elegantly designed. Meanwhile, a cannot-link regularization is derived and imposed on the comprehensive bipartite graph, which enforces cannot-link constraints to be realized with theoretically provable guarantees. Moreover, the comprehensive bipartite graph is constrained to exhibit explicit clustering partition by its connected components. Then, an efficient and convergent algorithm with theoretically proved accelerating techniques is derived for optimization, which has linear time complexity to the sample size. Extensive experimental results demonstrate the advantages of PCBG in both clustering performance and time complexity compared with state-of-the-art baselines.

Positive and unlabeled (PU) learning, which trains binary classifiers using only PU data, has gained vast attentions in recent years. Traditional PU learning often assumes that all the positive samples are labeled accurately. Nevertheless, due to the reasons such as sample ambiguity and insufficient algorithms, label noise is almost unavoidable in this scenario. Current PU algorithms neglect the label noise issue in the positive set, which is often biased toward certain instances rather than being uniformly distributed in practical applications. We define this important but understudied problem as PU learning with instance-dependent label noise (PUIDN). To eliminate the adverse impact of IDN, we leverage confidence scores for each instance in the positive set, which establish the connection between samples and labels without any assumption on noise distribution. Then, we propose an unbiased estimator for classification risk considering both label and confidence information, which can be computed immediately from PUIDN data along with their confidence scores. Moreover, our classification framework integrates an optimization strategy of alternating iteration based on the correlation between different confidence information, thereby alleviating the additional requirement for training data. Theoretically, we derive a generalization error bound for our proposed method. Experimentally, the effectiveness of our approach is demonstrated through various types of numerical results.

The bagging method has received much application and attention in recent years due to its good performance and simple framework. It has facilitated the advanced random forest method and accuracy-diversity ensemble theory. Bagging is an ensemble method based on simple random sampling (SRS) method with replacement. However, SRS is the most foundation sampling method in the field of statistics, where exists some other advanced sampling methods for probability density estimation. In imbalanced ensemble learning, down-sampling, over-sampling, and SMOTE methods have been proposed for generating base training set. However, these methods aim at changing the underlying distribution of data rather than simulating it better. The ranked set sampling (RSS) method uses auxiliary information to get more effective samples. The purpose of this article is to propose a bagging ensemble method based on RSS, which uses the ordering of objects related to the class to obtain more effective training sets. To explain its performance, we give a generalization bound of ensemble from the perspective of posterior probability estimation and Fisher information. On the basis of RSS sample having a higher Fisher information than SRS sample, the presented bound theoretically explains the better performance of RSS-Bagging. The experiments on 12 benchmark datasets demonstrate that RSS-Bagging statistically performs better than SRS-Bagging when the base classifiers are multinomial logistic regression (MLR) and support vector machine (SVM).

Due to the timeliness and uncertainty of data acquisition, label shift, which assumes that the source (training) and target (test) label distributions differ, occurs with the changing environment and reduces the generalization ability of traditional models. To correct the label shift, existing methods estimate the true label distribution by prediction of target data from a source classifier, which results in high variance, especially with large label shift. In this paper, we tackle this problem by proposing a novel approach termed as Label Shift Correction via Bidirectional Marginal Distribution Matching (BMDM). Our approach matchs the label and feature marginal distributions simultaneously to ensure the stability of estimated class proportions. We prove theoretically that there is a unique optimal solution, i.e., true target label distribution, for our approach under mild conditions, and an efficient optimization strategy is also proposed. On this basis, in multi-shot scenario where label distribution changes continuously, we extend BMDM by designing a new distribution matching mechanism and constructing a regularization term that constrains the direction of label distribution change. Extensive experimental results validate the effectiveness of our approach over existing state-of-the-arts methods.

Multi-instance multi-label learning (MIML), which deals with objects with complex structures and multiple semantics, plays a crucial role in various fields. In practice, the naturally skewed label distribution and label dependence contribute to the issue of label imbalance in MIML, which is crucial but rarely studied. Most existing MIML methods often produce biased models due to the ignorance of inter-class variations in imbalanced data. To address this issue, we propose a novel imbalanced multi-instance multi-label learning method named IMIMLC, based on the error-correcting coding ensemble and an adaptive threshold strategy. Specifically, we design a feature embedding method to extract the structural information of each object via Fisher vectors and eliminate inexact supervision. Subsequently, to alleviate the disturbance caused by the imbalanced distribution, a novel ensemble model is constructed by concatenating the error-correcting codes of randomly selected subtasks. Meanwhile, IMIMLC trains binary base classifiers on small-scale data blocks partitioned by our codes to enhance their diversity and then learns more reliable results to improve model robustness for the imbalance issue. Furthermore, IMIMLC adaptively learns thresholds for each individual label by margin maximization, preventing inaccurate predictions caused by the semantic discrepancy across many labels and their unbalanced ratios. Finally, extensive experimental results on various datasets validate the effectiveness of IMIMLC against state-of-the-art approaches.

Visual speech, referring to the visual domain of speech, has attracted increasing attention due to its wide applications, such as public security, medical treatment, military defense, and film entertainment. As a powerful AI strategy, deep learning techniques have extensively promoted the development of visual speech learning. Over the past five years, numerous deep learning based methods have been proposed to address various problems in this area, especially automatic visual speech recognition and generation. To push forward future research on visual speech, this paper will present a comprehensive review of recent progress in deep learning methods on visual speech analysis. We cover different aspects of visual speech, including fundamental problems, challenges, benchmark datasets, a taxonomy of existing methods, and state-of-the-art performance. Besides, we also identify gaps in current research and discuss inspiring future research directions.

With the advent of vast data collection ways, data are often with multiple modalities or coming from multiple sources. Traditional multiview learning often assumes that each example of data appears in all views. However, this assumption is too strict in some real applications such as multisensor surveillance system, where every view suffers from some data absent. In this article, we focus on how to classify such incomplete multiview data in semisupervised scenario and a method called absent multiview semisupervised classification (AMSC) has been proposed. Specifically, partial graph matrices are constructed independently by anchor strategy to measure the relationships among between each pair of present samples on each view. And to obtain unambiguous classification results for all unlabeled data points, AMSC learns view-specific label matrices and a common label matrix simultaneously. AMSC measures the similarity between pair of view-specific label vectors on each view by partial graph matrices, and consider the similarity between view-specific label vectors and class indicator vectors based on the common label matrix. To characterize the contributions of different views, the p th root integration strategy is adopted to incorporate the losses of different views. By further analyzing the relation between the p th root integration strategy and exponential decay integration strategy, we develop an efficient algorithm with proved convergence to solve the proposed nonconvex problem. To validate the effectiveness of AMSC, comparisons are made with some benchmark methods on real-world datasets and in the document classification scenario as well. The experimental results demonstrate the advantages of our proposed approach.

Clustering is a fundamental and important step in many image processing tasks, such as face recognition and image segmentation. The performance of clustering can be largely enhanced if relevant weak supervision information is appropriately exploited. To achieve this goal, in this paper, we propose the Compound Weakly Supervised Clustering (CSWC) method. Concretely, CSWC incorporates two types of widely available and easily accessed weak supervision information from the label and feature aspects, respectively. To be specific, at the label level, the pairwise constraints are utilized as a kind of typical weak label supervision information. At the feature level, the partial instances collected from multiple perspectives have internal consistency and they are regarded as weak structure supervision information. To achieve a more confident clustering partition, we learn a unified graph with its similarity matrix to incorporate the above two types of weak supervision. On one hand, this similarity matrix is constructed by self-expression across the partial instances collected from multiple perspectives. On the other hand, the pairwise constraints, i.e., must-links and cannot-links, are considered by formulating a regularizer on the similarity matrix. Finally, the clustering results can be directly obtained according to the learned graph, without performing additional clustering techniques. Besides evaluating CSWC on 7 benchmark datasets, we also apply it to the application of face clustering in video data since it has vast application potentiality. Experimental results demonstrate the effectiveness of our algorithm in both incorporating compound weak supervision and identifying faces in real applications.

Multi-instance Learning (MIL) is a popular learning paradigm arising from many real applications. It assigns a label to a set of instances, which is called a bag, and the bag’s label is determined by the instances within it. A bag is positive if and only if it has at least one positive instance. Since labeling bags is more complicated than labeling each instance, we will often face the mislabeling problem in MIL. Furthermore, it is more common that a negative bag has been mislabeled to a positive one, since one mislabeled instance will lead to the change of the whole bag label. This is an important problem that originated from real applications, e.g., web mining and image classification, but little research has concentrated on it as far as we know. In this article, we focus on this MIL problem with one side label noise that the negative bags are mislabeled as positive ones. To address this challenging problem, we propose, to the best our our knowledge, a novel multi-instance learning method with one side label noise. We design a new double weighting approach under traditional framework to characterize the “faithfulness” of each instance and each bag in learning the classifier. Briefly, on the instance level, we employ a sparse weighting method to select the key instances, and the MIL problem with one size label noise is converted to a mislabeled supervised learning scenario. On the bag level, the weights of bags, together with the selected key instances, will be utilized to identify the real positive bags. In addition, we have solved our proposed model by an alternative iteration method with proved convergence behavior. Empirical studies on various datasets have validated the effectiveness of our method.

In many real-world applications, data may dynamically expand over time in both volume and feature dimensions. Besides, they are often collected in batches (also called blocks). We refer this kind of data whose volume and features increase in blocks as blocky trapezoidal data streams. Current works either assume that the feature space of data streams is fixed or stipulate that the algorithm receives only one instance at a time, and none of them can effectively handle the blocky trapezoidal data streams. In this article, we propose a novel algorithm to learn a classification model from blocky trapezoidal data streams, called learning with incremental instances and features (IIF). We attempt to design highly dynamic model update strategies that can learn from increasing training data with an expanding feature space. Specifically, we first divide the data streams obtained on each round and construct the corresponding classifiers for these different divided parts. Then, to realize the effective interaction of information between each classifier, we utilize a single global loss function to capture their relationship. Finally, we use the idea of ensemble to achieve the final classification model. Furthermore, to make this method more applicable, we directly transform it into the kernel method. Both theoretical analysis and empirical analysis validate the effectiveness of our algorithm.

With the evolution of data collection ways, label ambiguity has arisen from various applications. How to reduce its uncertainty and leverage its effectiveness is still a challenging task. As two types of representative label ambiguities, Label Distribution Learning (LDL), which annotates each instance with a label distribution, and Emerging New Class (ENC), which focuses on model reusing with new classes, have attached extensive attentions. Nevertheless, in many applications, such as emotion distribution recognition and facial age estimation, we may face a more complicated label ambiguity scenario, i.e., label distribution changing with sample space expanding owing to the new class. To solve this crucial but rarely studied problem, we propose a new framework named as Label Distribution Changing Learning (LDCL) in this paper, together with its theoretical guarantee with generalization error bound. Our approach expands the sample space by re-scaling previous distribution and then estimates the emerging label value via scaling constraint factor. For demonstration, we present two special cases within the framework, together with their optimizations and convergence analyses. Besides evaluating LDCL on most of the existing 13 data sets, we also apply it in the application of emotion distribution recognition. Experimental results demonstrate the effectiveness of our approach in both tackling label ambiguity problem and estimating facial emotion

In many dynamic environment applications, with the evolution of data collection ways, the data attributes are incremental and the samples are stored with accumulated feature spaces gradually. For instance, in the neuroimaging-based diagnosis of neuropsychiatric disorders, with emerging of diverse testing ways, we get more brain image features over time. The accumulation of different types of features will unavoidably bring difficulties in manipulating the high-dimensional data. It is challenging to design an algorithm to select valuable features in this feature incremental scenario. To address this important but rarely studied problem, we propose a novel Adaptive Feature Selection method (AFS). It enables the reusability of the feature selection model trained on previous features and adapts it to fit the feature selection requirements on all features automatically. Besides, an ideal$\ell _{0}$-norm sparse constraint for feature selection is imposed with a proposed effective solving strategy. We present the theoretical analyses about the generalization bound and convergence behavior. After tackling this problem in a one-shot case, we extend it to the multi-shot scenario. Plenty of experimental results demonstrate the effectiveness of reusing previous features and the superior of$\ell _{0}$-norm constraint in various aspects, together with its effectiveness in discriminating schizophrenic patients from healthy controls.

With the emergence of new data collection ways in many dynamic environment applications, the samples are gathered gradually in the accumulated feature spaces. With the incorporation of new type features, it may result in the augmentation of class numbers. For instance, in activity recognition, using the old features during warm-up, we can separate different warm-up exercises. With the accumulation of new attributes obtained from newly added sensors, we can better separate the newly appeared formal exercises. Learning for such simultaneous augmentation of feature and class is crucial but rarely studied, particularly when the labeled samples with full observations are limited. In this paper, we tackle this problem by proposing a novel incremental learning method for Simultaneous Augmentation of Feature and Class (SAFC) in a two-stage way. To guarantee the reusability of the model trained on previous data, we add a regularizer in the current model, which can provide solid prior in training the new classifier. We also present the theoretical analyses about the generalization bound, which can validate the efficiency of model inheritance. After solving the one-shot problem, we also extend it to multi-shot. Experimental results demonstrate the effectiveness of our approaches, together with their effectiveness in activity recognition applications.

Insufficient annotated data and minor lung lesions pose big challenges for computed tomography (CT)-aided automatic COVID-19 diagnosis at an early outbreak stage. To address this issue, we propose a Semi-Supervised Tri-Branch Network (SS-TBN). First, we develop a joint TBN model for dual-task application scenarios of image segmentation and classification such as CT-based COVID-19 diagnosis, in which pixel-level lesion segmentation and slice-level infection classification branches are simultaneously trained via lesion attention, and individual-level diagnosis branch aggregates slice-level outputs for COVID-19 screening. Second, we propose a novel hybrid semi-supervised learning method to make full use of unlabeled data, combining a new double-threshold pseudo labeling method specifically designed to the joint model and a new inter-slice consistency regularization method specifically tailored to CT images. Besides two publicly available external datasets, we collect internal and our own external datasets including 210,395 images (1,420 cases versus 498 controls) from ten hospitals. Experimental results show that the proposed method achieves state-of-the-art performance in COVID-19 classification with limited annotated data even if lesions are subtle, and that segmentation results promote interpretability for diagnosis, suggesting the potential of the SS-TBN in early screening in insufficient labeled data situations at the early stage of a pandemic outbreak like COVID-19.

In image processing, images are usually composed of partial views due to the uncertainty of collection and how to efficiently process these images, which is called incomplete multi-view learning, has attracted widespread attention. The incompleteness and diversity of multi-view data enlarges the difficulty of annotation, resulting in the divergence of label distribution between the training and testing data, named as label shift. However, existing incomplete multi-view methods generally assume that the label distribution is consistent and rarely consider the label shift scenario. To address this new but important challenge, we propose a novel framework termed as Incomplete Multi-view Learning under Label Shift (IMLLS). In this framework, we first give the formal definitions of IMLLS and the bidirectional complete representation which describes the intrinsic and common structure. Then, a multilayer perceptron which combines the reconstruction and classification loss is employed to learn the latent representation, whose existence, consistency and universality are proved with the theoretical satisfaction of label shift assumption. After that, to align the label distribution, the learned representation and trained source classifier are used to estimate the importance weight by designing a new estimation scheme which balances the error generated by finite samples in theory. Finally, the trained classifier reweighted by the estimated weight is fine-tuned to reduce the gap between the source and target representations. Extensive experimental results validate the effectiveness of our algorithm over existing state-of-the-arts methods in various aspects, together with its effectiveness in discriminating schizophrenic patients from healthy controls.

Online learning is a fundamental paradigm for learning from continuous data stream. Tradition online learning approaches usually assume that the feature space of data stream is fixed and the incoming instance can always get the true label after making its prediction. However, in many real-world applications, such as the personalized recommender systems, the feature space may keep expanding due to the accumulation of user behaviors. Besides, we may only get bandit feedback, i.e., we only know whether the prediction is correct or not. To solve this important but rarely studied problem, we propose a novel algorithm LIFBF, together with its two variants LIFBF-I and LIFBF-II, to learn from data stream with incremental feature space and bandit feedback. Specifically, when an instance arrives with augmented features, we first utilize the exploration-exploitation strategy to guess its best label, then, a new loss function considering both bandit feedback and guessed label is proposed. Finally, we design a highly dynamic multi-class classifier, which updates the shared and augmented features by adopting the passive-aggressive rule and structural risk minimization principle, respectively. We theoretically analyze the cumulative loss bound of LIFBF. Besides, empirical studies on various datasets further validate the effectiveness of our proposed algorithms.

The scarcity of labels is common and great challenge in traditional supervised learning. Semi-supervised learning (SSL) leverages unlabeled samples to alleviate the absence of label information. Similar with annotation, label proportion is another type of prior information and plays a significant role in classification tasks. Compared with the acquisition of labels, label proportion can be obtained more easily. For example, only a small number of patients have been diagnosed with or not with cancers in hospital database, while the proportion with cancer can be generally estimated by historical records. How to incorporate such prior information of label proportion is crucial but rarely studied in literature. Traditional SSL methods often ignore this prior information and will lead to performance degradation inevitably. To solve this problem, we propose a novel SSL with Label Proportion (SSLLP). Our approach encourages to preserve label consistency and label proportion by imposing the cardinality bound constraints. Our formulated problem equals to a mixed-integer constrained submodular minimization and it is difficult to be solved directly. Therefore, we transformed the original problem into a convex one by Lov$\acute{\text{a}}$sz extension and designed an efficient solving algorithm. Extensive experimental results present the improved performance of our method over several state-of-the-art methods.

Imbalanced clustering, where the number of samples varies in different clusters, has arisen from many real data mining applications. It has gained increasing attention. Nevertheless, due to its unsupervised nature, imbalanced clustering is more challenging than its supervised counterpart, i.e., imbalanced classification. Furthermore, existing imbalanced clustering methods are empirically designed and they often lack solid theoretical guarantees, e.g., the excess risk estimation. To solve these important but rarely studied problems, we first propose a novel$k$-Means algorithm for imbalanced clustering problem with Adaptive Cluster Weight (MACW), together with its excess clustering risk bound analysis. Inspired by this theoretical result, we further propose an improved algorithm called Imbalanced Clustering with Theoretical Learning Bounds (ICTLB). It refines the weights and encourages the optimal trade-off among per-cluster weights by optimizing the excess clustering risk bound. A theoretically-principled justification of ICTLB is provided for verification. Comprehensive experiments on many imbalanced datasets verify the effectiveness of ICTLB in solving cluster imbalanced problems.

Multiple Instance Learning (MIL) is a widely studied learning paradigm which arises from real applications. Existing MIL methods have achieved prominent performances under the premise of plenty annotation data. Nevertheless, sufficient labeled data is often unattainable due to the high labeling cost. For example, the task in web image identification is to find similar samples among a large size of unlabeled dataset through a small number of provided target pictures. This leads to a particular scenario of Multiple Instance Learning with insufficient Positive and superabundant Unlabeled data (PU-MIL), which is a hot research topic in MIL recently. In this paper, we propose a novel method called Multiple Instance Learning with Bi-level Embedding (MILBLE) to tackle PU-MIL problem. Unlike other PU-MIL method using only simple single-level mapping, the bi-level embedding strategy are designed to customize specific mapping for positive and unlabeled data. It ensures the characteristics of key instance are not erased. Moreover, the weighting measure adopted in positive data can extracts the uncontaminated information of true positive instances without interference from negative ones. Finally, we minimize the classification error loss of mapped examples based on class-prior probability to train the optimal classifier. Experimental results show that our method has better performance than other state-of-the-art methods.

Recently, learning and mining from data streams with incremental feature spaces have attracted extensive attention, where data may dynamically expand over time in both volume and feature dimensions. Existing approaches usually assume that the incoming instances can always receive true labels. However, in many real-world applications, e.g., environment monitoring, acquiring the true labels is costly due to the need of human effort in annotating the data. To tackle this problem, we propose a novel incremental Feature spaces Learning with Label Scarcity (FLLS) algorithm, together with its two variants. When data streams arrive with augmented features, we first leverage the margin-based online active learning to select valuable instances to be labeled and thus build superior predictive models with minimal supervision. After receiving the labels, we combine the online passive-aggressive update rule and margin-maximum principle to jointly update the dynamic classifier in the shared and augmented feature space. Finally, we use the projected truncation technique to build a sparse but efficient model. We theoretically analyze the error bounds of FLLS and its two variants. Also, we conduct experiments on synthetic data and real-world applications to further validate the effectiveness of our proposed algorithms.

Partial multi-view clustering has attracted various attentions from diverse fields. Most existing methods adopt separate steps to obtain unified representations and extract clustering indicators. This separate manner prevents two learning processes to negotiate to achieve optimal performance. In this paper, we propose the Joint Representation Learning and Clustering (JRLC) framework to address this issue. The JRLC framework employs representation matrices to extract view-specific clustering information directly from the presence of partial similarity matrices, and rotates them to learn a common probability label matrix simultaneously, which connects representation learning and clustering seamlessly to achieve better clustering performance. Under the guidance of JRLC framework, several new incomplete multi-view clustering methods can be developed by extending existing single-view graph-based representation learning methods. For illustration, within the framework, we propose two specific methods, JRLC with spectral embedding (JRLC-SE) and JRLC via integrating nonnegative embedding and spectral embedding (JRLC-NS). Two iterative algorithms with guaranteed convergence are designed to solve the resultant optimization problems of JRLC-SE and JRLC-NS. Experimental results on various datasets and news topic clustering application demonstrate the effectiveness of the proposed algorithms.

In real-world applications, not all instances in the multiview data are fully represented. To deal with incomplete data, incomplete multiview learning (IML) rises. In this article, we propose the joint embedding learning and low-rank approximation (JELLA) framework for IML. The JELLA framework approximates the incomplete data by a set of low-rank matrices and learns a full and common embedding by linear transformation. Several existing IML methods can be unified as special cases of the framework. More interestingly, some linear transformation-based complete multiview methods can be adapted to IML directly with the guidance of the framework. Thus, the JELLA framework improves the efficiency of processing incomplete multiview data, and bridges the gap between complete multiview learning and IML. Moreover, the JELLA framework can provide guidance for developing new algorithms. For illustration, within the framework, we propose the IML with the block-diagonal representation (IML-BDR) method. Assuming that the sampled examples have an approximate linear subspace structure, IML-BDR uses the block-diagonal structure prior to learning the full embedding, which would lead to more correct clustering. A convergent alternating iterative algorithm with the successive over-relaxation optimization technique is devised for optimization. The experimental results on various datasets demonstrate the effectiveness of IML-BDR.

Multi-instance learning (MIL) has been extensively applied to various real tasks involving objects with bags of instances, such as in drugs and images. Previous studies on MIL assume that data are entirely complete. However, in many real tasks, the instance is fragmentary. In this article, we present probably the first study on multi-instance classification with fragmentary data. In our proposed framework, called fragmentary multi-instance classification (FIC), the fragmentary data are completed and the multi-instance classifier is learned jointly. To facilitate the integration between the completion and classifier learning, FIC establishes the weighting mechanism to measure the importance levels of different instances. To validate the compatibility of our framework, four typical MIL methods, including multi-instance support vector machine (MI-SVM), expectation maximization diverse density (EM-DD), citation- K nearest neighbors (Citation-KNNs), and MIL with discriminative bag mapping (MILDM), are embedded into the framework to obtain the corresponding FIC versions. As an illustration, an efficient solving algorithm is developed to address the problem for MI-SVM, together with the proof of convergence behavior. The experimental results on various types of real-world datasets demonstrate the effectiveness.

Different views of multiview data share certain common information (consensus) and also contain some complementary information (complementarity). Both consensus and complementarity are of significant importance to the success of multiview learning. In this paper, we explicitly formulate both of them for multiview classification. On the one hand, a cohesion-increasing loss term with a learnable label-adjusting matrix is designed to facilitate consensus among views in the training stage. With this kind of loss, the learned classifiers of all views are more likely to obtain the correct classification, thereby maximizing the agreement among views. On the other hand, an independence measurement is adopted as the diversity-promoting regularization to encourage classifiers to be diverse such that more complementary information can be captured by these "diversified" classifiers. Overall, the resultant model is capable of achieving more comprehensive and accurate classification by exploring and exploiting the common and complementary information across multiple views more thoroughly. An iterative optimization algorithm with proved convergence is proposed for training the model. Extensive experimental results on various datasets have demonstrated the efficacy of the proposed method.

Multi-view subspace clustering has been applied to applications such as image processing and video surveillance, and has attracted increasing attention. Most existing methods learn view-specific self-representation matrices, and construct a combined affinity matrix from multiple views. The affinity construction process is time-consuming, and the combined affinity matrix is not guaranteed to reflect the whole true subspace structure. To overcome these issues, the Latent Complete Row Space Recovery (LCRSR) method is proposed. Concretely, LCRSR is based on the assumption that the multi-view observations are generated from an underlying latent representation, which is further assumed to collect the authentic samples drawn exactly from multiple subspaces. LCRSR is able to recover the row space of the latent representation, which not only carries complete information from multiple views but also determines the subspace membership under certain conditions. LCRSR does not involve the graph construction procedure and is solved with an efficient and convergent algorithm, thereby being more scalable to large-scale datasets. The effectiveness and efficiency of LCRSR are validated by clustering various kinds of multi-view data and illustrated in the background subtraction task.

Learning Partial Differential Equations (LPDEs) from training data for particular tasks has been successfully applied to many image processing problems. In this paper, we aim to learn compact Partial Differential Equations (LCPDEs) for color image tasks by proposing a more effective algorithm. The LCPDEs system is formulated as a linear combination of fundamental differential invariants and simplified by omitting the PDE which works as an indicate function. We replace L2-norm with Ll-norm to regularize the coefficients with respect to the invariants. As the objective function is non-smooth, we resort to proximal algorithm to optimize it, which ensures convergence in an at least sub-linear rate. Experiments demonstrate the advantages of the proposed method over other PDE-based methods in terms of both quality and efficiency.

Incomplete multi-view clustering has attracted various attentions from diverse fields. Most existing methods factorize data to learn a unified representation linearly. Their performance may degrade when the relations between the unified representation and data of different views are nonlinear. Moreover, they need post-processing on the unified representations to extract the clustering indicators, which separates the consensus learning and subsequent clustering. To address these issues, in this paper, we propose a Simultaneous Representation Learning and Clustering (SRLC) method. Concretely, SRLC constructs similarity matrices to measure the relations between pair of instances, and learns low-dimensional representations of present instances on each view and a common probability label matrix simultaneously. Thus, the nonlinear information can be reflected by these representations and the clustering results can obtained from label matrix directly. An efficient iterative algorithm with guaranteed convergence is presented for optimization. Experiments on several datasets demonstrate the advantages of the proposed approach.

With the evolution of data collection methods, it is possible to produce abundant data described by multiple feature sets. Previous studies show that including more features does not necessarily bring positive effects. How to prevent the augmented features from worsening classification performance is crucial but rarely studied. In this paper, we study this challenging problem by proposing a safe classification approach, whose accuracy is never degenerated when exploiting augmented features. We propose two ways to achieve the safeness of our method named as SAfe Classification (SAC). First, to leverage augmented features, we learn various types of classifiers and adapt them by employing a specially designed robust loss. It provides various candidate classifiers to meet the assumption of safeness operation. Second, we search for a safe prediction by integrating all candidate classifiers. Under a mild assumption, the integrated classifier has theoretical safeness guarantee. Several new optimization methods have been developed to accommodate the problems with proved convergence. Besides evaluating SAC on 16 data sets, we also apply SAC in the application of diagnostic classification of schizophrenia since it has vast application potentiality. Experimental results demonstrate the effectiveness of SAC in both tackling safeness problem and discriminating schizophrenic patients from healthy controls.

High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample's importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data.

Data recycling, which reuses the historical data to assist the present data to achieve better performance, is an emerging and important research topic. A common case is that historical examples only have features from one source while presently have more data collection ways and extract different types of features simultaneously for new examples. Previous studies assume that either historical data appear in all sources, or at least there is one type of representations for all data. In this paper, we study the challenging problem in the above common case and propose a novel semisupervised approach by leveraging nonoverlapping historical features (NHFs). It learns full representations of both historical features and present features in a latent subspace. We utilize the intrinsic geometrical structure of all data and add the label information of historical data as a hard constraint to discover a latent subspace. Then, the classification will be performed with these new representations. Moreover, we provide an efficient algorithm to solve the formulated optimization problem with proved convergence behavior, together with some insightful discussions about parameter determination. Experimental results on real-world data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all demonstrate the effectiveness of our proposed approach on recycling NHFs.

With the advent of multi-view data, multi-view learning (MVL) has become an important research direction in machine learning. It is usually expected that multi-view algorithms can obtain better performance than that of merely using a single view. However, previous researches have pointed out that sometimes the utilization of multiple views may even deteriorate the performance. This will be a stumbling block for the practical use of MVL in real applications, especially for tasks requiring high dependability. Thus, it is eager to design reliable multi-view approaches, such that their performance is never degenerated by exploiting multiple views.This issue is vital but rarely studied. In this paper, we focus on clustering and propose the Reliable Multi-View Clustering (RMVC) method. Based on several candidate multi-view clusterings, RMVC maximizes the worst-case performance gain against the best single view clustering, which is equivalently expressed as no label information available. Specifically, employing the squared χ2 distance for clustering comparison makes the formulation of RMVC easy to solve, and an efficient strategy is proposed for optimization. Theoretically, it can be proved that the performance of RMVC will never be significantly decreased under some assumption. Experimental results on a number of data sets demonstrate that the proposed method can effectively improve the reliability of multi-view clustering.

Multi-label classification has attracted significant interests in various domains. In many applications, only partial labels are available and the others are missing or not provided. How to design an accurate multi-label classifier with such partial labeled data is a challenging problem. In this paper, we propose a Low Rank multi-label classification with Missing Label method (LRML), which joints label matrix recovery and multi-label classifier learning to address the classification problem. The proposed algorithm recover the missing labels via laplacian manifold regularization derived from the feature space. By utilizing the low-rank mapping, the proposed algorithm can efficiently exploit the label correlations and analyze the high-dimensional data in the discriminant subspace simultaneously. Besides, the proposed algorithm is formulated as a convex but not smooth optimization problem. An effective algorithm which divides the problem into multiple convex and smooth sub-problems is developed, together with some theoretical analyses. Experimental results validate that our method leads to a significant improvement in performance and robustness to missing labels over other well-established algorithms.

In many real tasks the features are evolving, with some features vanished and some other features being augmented. For example, in environment monitoring some sensors expired whereas some new ones were deployed; in mobile game recommendation some games dropped whereas some new ones were added. Learning with such incremental and decremental features is crucial but rarely studied, particularly when the data comes like a stream and thus it is infeasible to keep the whole data for optimization. In this paper, we study this challenging problem and present the OPID approach. Our approach attempts to compress important information of vanished features into functions of survived features, and then expand to include the augmented features. It is an one-pass learning approach, which only needs to scan each instance once and does not need to store the whole data, and thus satisfies the evolving streaming data nature. After tackling this problem in one-shot scenario, we then extend it to multi-shot case. Empirical study on a broad range of data sets shows that our approach can address this problem effectively.

Feature selection plays a significant role in dealing with high-dimensional data to avoid the curse of dimensionality. In many real applications, like video semantic recognition, handling few labeled and large unlabeled data samples from the same population is a recently addressed challenge in feature selection. To solve this problem, we propose a novel semi-supervised feature selection method via insensitive sparse regression (ISR). Specifically, we compute the soft label matrix by the special label propagation, which can predict the labels of the unlabeled data. To guarantee the robustness of ISR to the false labeled instances or outliers, we propose Insensitive Regression Model (IRM) by capped$l_2$-$l_p$-norm loss. The soft label is imposed as the weights of IRM to fully utilize the label information. Meanwhile, to perform feature selection, we incorporate$l_{2,q}$-norm regularizer with IRM as the structural sparsity constraint when$0 < q\leq 1$. Moreover, we put forward an effective approach for solving the formulated non-convex optimization problem. We analyze the performance of convergence rigorously and discuss the parameter determination problem. Extensive experimental results on several public data sets verify the effectiveness of our proposed algorithm in comparison with the state-of-art feature selection methods. Finally, we apply our method to video semantic recognition successfully.

Multi-view clustering, which aims to improve the clustering performance by exploring the data’s multiple representations, has become an important research direction. Graph based methods have been widely studied and achieve promising performance for multi-view clustering. However, most existing multi-view graph based methods perform clustering on the fixed input graphs, and the results are dependent on the quality of input graphs. In this paper, instead of fixing the input graphs, we propose Multi-view clustering with Adaptively Learned Graph (MALG), learning a new common similarity matrix. In our model, we not only consider the importance of multiple graphs from view level, but also focus on the performance of similarities within a view from sample-pair level. Sample-pair-specific weights are introduced to exploit the connection across views in more depth. In addition, the obtained optimal graph can be partitioned into specific clusters directly, according to its connected components. Experimental results on toy and real-world datasets demonstrate the efficacy of the proposed algorithm.

For many image processing and computer vision problems, data points are in matrix form. Traditional methods often convert a matrix into a vector and then use vector-based approaches. They will ignore the location of matrix elements and the converted vector often has high dimensionality. How to select features for 2D matrix data directly is still an uninvestigated important issue. In this paper, we propose an algorithm named sparse matrix regression (SMR) for direct feature selection on matrix data. It employs the matrix regression model to accept matrix as input and bridges each matrix to its label. Based on the intrinsic property of regression coefficients, we design some sparse constraints on the coefficients to perform feature selection. An effective optimization method with provable convergence behavior is also proposed. We reveal that the number of regression vectors can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. To examine the effectiveness of SMR, we have compared it with several vector-based approaches on some benchmark data sets. Furthermore, we have also evaluated SMR in the application of scene classification. They all validate the effectiveness of our method.

With the advent of multi-view data, multi-view learning has become an important research direction in machine learning and image processing. Considering the difficulty of obtaining labeled data in many machine learning applications, we focus on the multi-view semi-supervised classification problem. In this paper, we propose an algorithm named multi-view semi-supervised classification via adaptive regression (MVAR) to address this problem. Specifically, regression-based loss functions with ℓ2,1matrix norm are adopted for each view and the final objective function is formulated as the linear weighted combination of all the loss functions. An efficient algorithm with proved convergence is developed to solve the non-smooth ℓ2,1-norm minimization problem. Regressing to class labels directly makes the proposed algorithm efficient in calculation and can be applied to large-scale data sets. The adaptively optimized weight coefficients balance the contributions of different views automatically, which makes the performance robust against the existence of low-quality views. With the learned projection matrices and bias vectors, predictions for out-of-sample data can be easily made. To validate the effectiveness of MVAR, comparisons are made with some benchmark methods on realworld data sets and in the scene classification scenario as well. The experimental results demonstrate the effectiveness of our proposed algorithm.

With the advent of multi-view data, multi-view learning has become an important research direction in both machine learning and data mining. Considering the difficulty of obtaining labeled data in many real applications, we focus on the multi-view unsupervised feature selection problem. Traditional approaches all characterize the similarity by fixed and pre-defined graph Laplacian in each view separately and ignore the underlying common structures across different views. In this paper, we propose an algorithm named Multi-view Unsupervised Feature Selection with Adaptive Similarity and View Weight (ASVW) to overcome the above mentioned problems. Specifically, by leveraging the learning mechanism to characterize the common structures adaptively, we formulate the objective function by a common graph Laplacian across different views, together with the sparse ℓ2,p-norm constraint designed for feature selection. We develop an efficient algorithm to address the non-smooth minimization problem and prove that the algorithm will converge. To validate the effectiveness of ASVW, comparisons are made with some benchmark methods on real-world datasets. We also evaluate our method in the real sports action recognition task. The experimental results demonstrate the effectiveness of our proposed algorithm.

Many feature extraction methods reduce the dimensionality of data based on the input graph matrix. The graph construction which reflects relationships among raw data points is crucial to the quality of resulting low-dimensional representations. To improve the quality of graph and make it more suitable for feature extraction tasks, we incorporate a new graph learning mechanism into feature extraction and add an interaction between the learned graph and the low-dimensional representations. Based on this learning mechanism, we propose a novel framework, termed as unsupervised single view feature extraction with structured graph (FESG), which learns both a transformation matrix and an ideal structured graph containing the clustering information. Moreover, we propose a novel way to extend FESG framework for multi-view learning tasks. The extension is named as unsupervised multiple views feature extraction with structured graph (MFESG), which learns an optimal weight for each view automatically without requiring an additional parameter. To show the effectiveness of the framework, we design two concrete formulations within FESG and MFESG, together with two efficient solving algorithms. Promising experimental results on plenty of real-world datasets have validated the effectiveness of our proposed algorithms.

Vanishing Component Analysis (VCA) is a recently proposed prominent work in machine learning. It narrows the gap between tools and computational algebra: the vanishing ideal and its applications to classification problem. In this paper, we will analyze VCA in the kernel view, which is also another important research direction in machine learning. Under a very weak assumption, we provide a different point of view to VCA and make the kernel trick on VCA become possible. We demonstrate that the projection matrix derived by VCA is located in the same space as that of Kernel Principal Component Analysis (KPCA) with a polynomial kernel. Two groups of projections can express each other by linear transformation. Furthermore, we prove that KPCA and VCA have identical discriminative power, provided that the ratio trace criteria is employed as the measurement. We also show that the kernel formulated by the inner products of VCA's projections can be expressed by the KPCA's kernel linearly. Based on the analysis above, we proposed a novel Discriminative Vanishing Component Analysis (DVCA) approach. Experimental results are provided for demonstration.

Multi-label data with high dimensionality arise frequently in data mining and machine learning. It is not only time consuming but also computationally unreliable when we use high-dimensional data directly. Supervised dimensionality reduction approaches are based on the assumption that there are large amounts of labeled data. It is infeasible to label a large number of training samples in practice especially in multi-label learning. To address these challenges, we propose a novel algorithm, namely Semi-Supervised Multi-Label Dimensionality Reduction (SSMLDR), which can utilize the information from both labeled data and unlabeled data in an effective way. First, the proposed algorithm enlarges the multi-label information from the labeled data to the unlabeled data through a special designed label propagation method. It then learns a transformation matrix to perform dimensionality reduction by incorporating the enlarged multi-label information. Extensive experiments on a broad range of datasets validate the effectiveness of our approach against other well-established algorithms.

Feature extraction, one kind of dimensionality reduction methodology, has aroused considerable research interests during the last few decades. Traditional graph embedding methods construct a fixed graph with original data to fulfill the aim of feature extraction. The lack of the graph learning mechanism leaves room for the improvement of their performances. In this paper, we propose a novel framework, termed as unsupervised feature extraction using a learned graph with clustering structure (LGCS), in which a graph learning mechanism has been presented. To be specific, the proposed LGCS learns both a transformation matrix and an ideal structured graph which incorporates clustering information. To show the effectiveness of the framework, we present a concrete method within our framework, and an iteration algorithm has been designed to solve the corresponding optimizing problem. Promising experimental results on real-world datasets have validated the effectiveness of our proposed algorithm.

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation-based dimensionality reduction method linear discriminant analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through l2,1-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the l2,p-norm regularized case, which is more likely to offer better sparsity when 0 < p < 1. Thus, the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the l2,p-norm-based optimization problem and it is proved that the algorithm converges when 0 < p ≤ 2. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm.

In many real applications of machine learning and data mining, we are often confronted with high-dimensional data. How to cluster high-dimensional data is still a challenging problem due to the curse of dimensionality. In this paper, we try to address this problem using joint dimensionality reduction and clustering. Different from traditional approaches that conduct dimensionality reduction and clustering in sequence, we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively. Within this framework, we are able not only to view several traditional approaches and reveal their intrinsic relationships, but also to be stimulated to develop a new method. We also propose an effective approach for solving the formulated nonconvex optimization problem. Comprehensive analyses, including convergence behavior, parameter determination, and computational complexity, together with the relationship to other related approaches, are also presented. Plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state-of-the-art clustering approaches and existing joint dimensionality reduction and clustering methods.

Feature selection has aroused considerable research interests during the last few decades. Traditional learning-based feature selection methods separate embedding learning and feature ranking. In this paper, we propose a novel unsupervised feature selection framework, termed as the joint embedding learning and sparse regression (JELSR), in which the embedding learning and sparse regression are jointly performed. Specifically, the proposed JELSR joins embedding learning with sparse regression to perform feature selection. To show the effectiveness of the proposed framework, we also provide a method using the weight via local linear approximation and adding the l2,1 -norm regularization, and design an effective algorithm to solve the corresponding optimization problem. Furthermore, we also conduct some insightful discussion on the proposed feature selection approach, including the convergence analysis, computational complexity, and parameter determination. In all, the proposed framework not only provides a new perspective to view traditional methods but also evokes some other deep researches for feature selection. Compared with traditional unsupervised feature selection methods, our approach could integrate the merits of embedding learning and sparse regression. Promising experimental results on different kinds of data sets, including image, voice data and biological data, have validated the effectiveness of our proposed algorithm.

In real world applications, we often have to deal with some high-dimensional, sparse and noisy data. In this paper, we aim to handle this kind of complex data by a Robust Non-negative Matrix Factorization via joint Sparse and Graph regularization model (RSGNMF). We provide a novel efficient and elegant iterative updating algorithm with rigorous convergence analysis for RSGNMF model. Experimental results on image data sets demonstrate that our RSGNMF model outperforms existing start-of-art methods.

Learning an optimal kernel plays a pivotal role in kernel-based methods. Recently, an approach called optimal neighborhood kernel learning (ONKL) has been proposed, showing promising classification performance. It assumes that the optimal kernel will reside in the neighborhood of a "pre-specified" kernel. Nevertheless, how to specify such a kernel in a principled way remains unclear. To solve this issue, this paper treats the pre-specified kernel as an extra variable and jointly learns it with the optimal neighborhood kernel and the structure parameters of support vector machines. To avoid trivial solutions, we constrain the pre-specified kernel with a parameterized model. We first discuss the characteristics of our approach and in particular highlight its adaptivity. After that, two instantiations are demonstrated by modeling the pre-specified kernel as a common Gaussian radial basis function kernel and a linear combination of a set of base kernels in the way of multiple kernel learning (MKL), respectively. We show that the optimization in our approach is a min-max problem and can be efficiently solved by employing the extended level method and Nesterov's method. Also, we give the probabilistic interpretation for our approach and apply it to explain the existing kernel learning methods, providing another perspective for their commonness and differences. Comprehensive experimental results on 13 UCI data sets and another two real-world data sets show that via the joint learning process, our approach not only adaptively identifies the pre-specified kernel, but also achieves superior classification performance to the original ONKL and the related MKL algorithms.

The problem of image classification has aroused considerable research interest in the field of image processing. Traditional methods often convert an image to a vector and then use a vector-based classifier. In this paper, a novel multiple rank regression model (MRR) for matrix data classification is proposed. Unlike traditional vector-based methods, we employ multiple-rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category. The convergence behavior, initialization, computational complexity, and parameter determination are also analyzed. Compared with vector-based regression methods, MRR achieves higher accuracy and has lower computational complexity. Compared with traditional supervised tensor-based methods, MRR performs better for matrix data classification. Promising experimental results on face, object, and hand-written digit image classification tasks are provided to show the effectiveness of our method.

The problem of semisupervised learning has aroused considerable research interests in the past few years. Most of these methods aim to learn from a partially labeled dataset, i.e., they assume that the exact labels of some data are already known. In this paper, we propose to use a novel type of supervision information to guide the process of semisupervised learning, which indicates whether a point does not belong to a specific category. We call this kind of information negative label (NL) and propose a novel approach called NL propagation (NLP) to efficiently make use of this type of information to assist the process of semisupervised learning. Specifically, NLP assumes that nearby points should have similar class indicators. The data labels are propagated under the guidance of NL information and the geometric structure revealed by both labeled and unlabeled points, by employing some specified initialization and parameter matrices. The convergence analysis, out-of-sample extension, parameter determination, computational complexity, and relations to other approaches are presented. We also interpret the proposed approach within the framework of regularization. Promising experimental results on image, digit, spoken letter, and text classification tasks are provided to show the effectiveness of our method.

The recent years have witnessed a surge of interests of learning a subspace for image classification, which has aroused considerable researches from the pattern recognition and signal processing fields. However, for image classification, the accuracies of previous methods are not so high since they neglect some particular characters of the image data. In this paper, we propose a new subspace learning method. It constrains that the transformation basis is orthonormal and the derived coefficients are spatially smooth. Classification is then performed in the image subspace. The proposed method can not only represent the intrinsic structure of the image data, but also avoid over-fitting. More importantly, it can be considered as a general framework, within which the performances of other subspace learning methods can be improved in the same way. Some related analyses of the proposed approach are presented. Promising experimental results on different kinds of real images demonstrate the effectiveness of our algorithm for image classification.