Most of incomplete multi-view clustering (IMVC) methods typically choose to ignore the missing samples and only utilize observed unpaired samples to construct bipartite similarity. Moreover, they employ a single quantity of prototypes to extract the information of $\textbf{all}$ views. To eliminate these drawbacks, we present a simple yet effective IMVC approach, SIIHPC, in this work. It firstly transforms partial bipartition learning into original sample form by virtue of reconstruction concept to split out of observed similarity, and then loosens traditional non-negative constraints via regularizing samples to more freely characterize the similarity. Subsequently, it learns to recover the incomplete parts by utilizing the connection built between the similarity exclusive on respective view and the consensus graph shared for all views. On this foundation, it further introduces a group of hybrid prototype quantities for each individual view to flexibly extract the data features belonging to each view itself. Accordingly, the resulting graphs are with various scales and describe the overall similarity more comprehensively. It is worth mentioning that these all are optimized in one unified learning framework, which makes it possible for them to reciprocally promote. Then, to effectively solve the formulated optimization problem, we design an ingenious auxiliary function that is with theoretically proven monotonic-increasing properties. Finally, the clustering results are obtained by implementing spectral grouping action on the eigenvectors of stacked multi-scale consensus similarity. Experimental results confirm the effectiveness of SIIHPC.

Few-shot classification aims to adapt to new tasks with limited labeled examples. Recent methods have explored various techniques for measuring the similarity between query and support images, along with meta-training and pre-training strategies, to leverage visual features more effectively. However, the potential of multi-modality information remains unexplored, presenting a promising avenue for improvement in few-shot classification. In this paper, we propose a Language-guided Prototypical Network (LPN) for few-shot classification without image-level captions. LPN leverages the complementarity of vision and language modalities through two parallel branches with pre-fusion and post-fusion. Firstly, we introduce the language modality by utilizing a pre-trained text encoder to extract class-level text features from class names. In the visual branch, we process images using a conventional image encoder and leverage the class-level features to align the visual features, effectively capturing more class-relevant visual information. In the text branch, we combine the class-level text features with the visual features using a language-guided decoder. This decoder generates image-specific text features for the pre-fusion step. Additionally, we utilize these class-level text features to refine the prototypical head, creating robust prototypes for subsequent measurements. Finally, to enhance overall performance, we aggregate the visual and text logits, adjusting for discrepancies between the modalities during the post-fusion process. Extensive experiments demonstrate that LPN outperforms several state-of-the-art methods on benchmark datasets, showcasing its effectiveness and robustness.

In this study, we tackle the critical challenge of sea-land segmentation for enhancing ship detection in remote sensing imagery. By focusing the search area, we significantly reduce the false alarm rate in ship detection. To overcome the limitations of scarce training data and annotation complexity, we introduce a novel zero-shot sea-land segmentation framework. This framework is integrated with a robust image segmentation model and employs an automatic prompt point generation strategy to facilitate sea-land discrimination. Our method is structured around three core components: image preprocessing, image block classification, and prompt point generation. The preprocessing module generates an edge feature map using downsampling and edge detection techniques. The classification module segments land and sea areas through a rasterization and classification process. The prompt point generation module leverages edge point clustering to create prompts on the land image block background. These prompts are then utilized by the image segmentation model to achieve precise sea segmentation. Our extensive experiments on public land-sea segmentation datasets show that our approach is robust across various parameter settings and outperforms current state-of-the-art methods.

Ship classification in remote sensing images holds paramount significance for surveillance and defense applications. However, the intricate nature of ship classes poses a challenge in accurately discriminating among diverse ship types. This challenge is exacerbated by the long-tailed data distribution, where certain classes are underrepresented by insufficient samples. Furthermore, the limited visual information available from single-perspective remote sensing imaging complicates the extraction of discriminative features. To address these challenges, we propose the Text-Guided Feature Mining Network (TGFMN). This approach aims to exploit strong textual knowledge to construct discriminative image features. We employ a unified classifier for pre-training to classify features from both modalities, ensuring that the dual modal features are integrated into a cohesive feature space, thereby maximizing the efficacy of textual information. The text-guided strategy is employed to enhance attention regions within the shallow spatial dimensions of visual features, facilitating the extraction of highly discriminative visual features during the fine-tuning process. The experimental results demonstrate the effectiveness of our method, achieving state-of-the-art performance on two benchmark datasets for fine-grained ship classification in remote sensing: FGSC-23 and FGSCR-42.

Vision Transformer (ViT) models have recently emerged as powerful and versatile tools for various visual tasks. In this article, we investigate ViT in a more challenging scenario within the context of few-shot conditions. Recent work has achieved promising results in few-shot image classification by utilizing pre-trained vision transformer models. However, this work employs full fine-tuning for the downstream tasks, leading to significant overfitting and storage issues, especially in the remote sensing domain. In order to tackle these issues, we turn to the recently proposed Parameter-Efficient Tuning (PETuning) methods, which update only the newly added parameters while keeping the pre-trained backbone frozen. Inspired by these methods, we propose the Meta Visual Prompt Tuning (MVP) method. Specifically, we integrate the prompt-tuning-based PETuning method into the meta-learning framework and tailor it for remote sensing datasets, resulting in an efficient framework for Few-Shot Remote Sensing Scene Classification (FS-RSSC). Moreover, we introduce a novel data augmentation scheme that exploits patch embedding recombination to enhance the data diversity and quantity. This scheme is generalizable to any network that employs the ViT architecture as its backbone. Experimental results on the FS-RSSC benchmark demonstrate the superior performance of the proposed MVP over existing methods in various settings, including various-way-various-shot, various-way-one-shot, and cross-domain adaptation.

The recent advance has shown that few-shot learning may be a promising way to alleviate the data reliance of remote sensing image scene classification. However, most existing works focus on extracting distinguishable features only from visual modality, while the problem of learning knowledge from multiple modalities has barely been visited. In this work, we propose a text-aware framework for few-shot remote sensing image scene classification (TeAw). Specifically, TeAw converts the class names to more detailed text descriptions and extracts text features using a pre-trained text encoder. Mean-while, TeAw obtains image features via an image encoder. Then we compute the correlation between the text and the image features, which helps the model grasp the core concept of the input image. Finally, TeAw calculates the similarity of local features between supports and queries to get the predictions. Extensive experiments show the outperformance of our TeAw compared with other SOTA methods.

Large-scale pre-trained transformers have recently achieved remarkable success in several computer vision tasks. However, it remains highly challenging to fully fine-tune models for downstream tasks, due to the expensive computational and storage cost. Recently, Parameter-Efficient Tuning (PETuning) techniques, e.g., Visual Prompt Tuning (VPT), have significantly reduced the computation cost by inserting lightweight prompt modules including prompt tokens or adapter layers, into the pre-trained models and tuning these prompt modules with a small number of trainable parameters, while keeping the transformer backbone freeze. Although encouraging results were achieved, existing PETuning methods cannot perform well under the few-shot learning settings (i.e., extremely limited training data, with only 1 or 2 shots per class), due to the scarce supervision signal. To this end, we first empirically identify the poor performance is mainly due to the inappropriate way of initializing prompt modules, which has also been verified in the pre-trained language models. Next, we propose a Visual Pre-trained Prompt Tuning framework (VPPT), which pre-trains the prompt modules first and then leverages the pre-trained modules along with the pre-trained transformer backbone to perform prompt tuning on downstream tasks. Extensive experiments show that our VPPT framework achieves 16.08% average accuracy absolute improvement under 1 shot setting on five fine-grained visual classification datasets, compared with the previous PETuning techniques, e.g., VPT, in few-shot image classification.

Few-shot learning has received widespread attention in remote sensing image scene classification. Many existing methods address this challenge by utilizing meta-learning and metric learning, which focus on developing feature extractors that can quickly adapt to novel few-shot scene classification (FSSC) tasks. However, these methods are often insufficient for real-world datasets with class confusion, where there is high inter-class compactness and intra-class diversity. To overcome this issue, we investigate efficient strategies, i.e., meta-learning-based transferable feature representation and contrastive-based prototypical regularization for learning task-adaptive class boundaries for FSSC. Specifically, we designed a combination of Query-vs-Prototype contrastive loss and Prototype-vs-Prototype contrastive loss to normalize the prototypical representation to be more discriminative in a novel FSSC task. Our proposed model is named the Hybrid Contrastive Prototypical Network (HCP-Net). Experiment results on three popular datasets under two standard benchmarks, i.e., general few-shot classification and few-shot domain generalization, indicate the effectiveness of the proposed method.

Big models, large datasets, and self-supervised learning (SSL) have recently gained substantial research interest due to their potential to alleviate our reliance on annotations. Considering the current high generalization ability of self-supervised models in literature, we explore in the letter how helpful SSL can be for a crucial task in remote sensing (RS), image scene classification, when forced to rely on only a few labeled samples. We proposed a simple prototype-based classification procedure without training and fine-tuning, which uses open self-supervised features from the contrastive language-image pre-training (CLIP). We test our method by exploiting ready-to-use open features on four diversified benchmark datasets, including red-green-blue (RGB) and multispectral (MS) images. Highly competitive accuracy has been obtained compared to work with similar settings, i.e., based on an exceedingly small number of labels. To the best of our knowledge, our model is the first to achieve such high accuracy in austere label conditions. We further analyze our approach from different perspectives, including its advantages and limitations, reasons for its astonishing performance, potential applications, and future improvements.

Ship detection in large-scale synthetic aperture radar (SAR) images has essential value in both military and civilian applications. However, due to the complexity of the background and the simplicity of the texture, ship detection in large-scale SAR images is prone to false alarms, such as similar-shaped reefs, islands, sea clutter, and inland buildings. This article proposes a multisize inference fusion framework to eliminate false alarms and improve the overall performance of ship detection in large-scale SAR images. In this framework, a multisize slicer is proposed to expand the scale range of image expression. Then, a detection model library is built to keep various types of models for different task scenarios and requirements. Finally, two subapproaches are proposed for false alarm elimination, namely, pixel feature filtering (FAE-pff) and multisource fusion (FAE-msf), to reduce false detection results in the output of the detection model. FAE-pff calculates how obvious each target is relative to the background and eliminates less obvious results. FAE-msf obtains bounding boxes and corresponding confidences from multiple inference sources and fuses them through weighting and updating them to achieve complementation and enhancement of information. Various experiments were conducted to evaluate the performance of each module qualitatively and quantitatively. It proves the effectiveness of the proposed framework, which can achieve more correct detections while greatly reducing erroneous detections.

Zero-shot learning (ZSL), with the assistance of the seen class image and additional semantic knowledge, generalizes its classification ability to the unseen class by aligning the visual-semantic space embeddings. Few previous methods have researched whether discriminative visual features are helpful to recognize different classes while neglecting the rich semantic information from the surrounding background. This paper proposes a channel-wise mix-fusion ZSL model (CMFZ) to contextualize the ZSL classifier's discriminative information by incorporating much richer visual semantic information from both objects and their semantic surrounding environments. In particular, the channel-wise connection module (CCM) learns to construct the relationship between the object and its surroundings. A collaborative channel-wise activation module (CAM) is adopted to learn from a more delicate scale image attained from the cropping module. It highlights the most distinct channels representing the object’s discriminative regions to eliminate inadvertently introduced background noise. Furthermore, the representation ability of the learned mapping is enhanced by integrating the visual semantic features processed by CCM and CAM. Experimental results show that CMFZ outperforms the state-of-the-art ZSL methods and verifies the effectiveness of incorporating visual semantic information.

Recently, Multi-Target Multi-Camera Tracking (MTMCT) has gained more and more attention. It is a challenging task with major problems including occlusion, background clutter, poses and camera point of view variations. Compared to single camera tracking, which takes advantage of location information and strict time constraints, good appearance features are more important to MTMCT. This drives us to extract robust and discriminative features for MTMCT. We propose MTMCT\_HS which uses human body part semantic features to overcome the above challenges. We use a two-stream deep neural network to extract the global appearance features and human body part semantic maps separately, and employ aggregation operations to generate final features. We argue that these features are more suitable for affinity measurement, which can be seen as the average of appearance similarity weighted by the corresponding human body part similarity. Next, our tracker adopts a hierarchical correlation clustering algorithm, which combines targets' appearance feature similarity with motion correlation for data association. We validate the effectiveness of our MTMCT\_HS method by demonstrating its superiority over the state-of-the-art method on DukeMTMC benchmark. Experiments show that the extracted features with human body part semantics are more effective for MTMCT compared with the methods solely employing global appearance features.

Trajectory prediction can aid in target tracking, automatic system navigation, social behavior prediction, analysis and other computer vision tasks. When people walk in crowded spaces such as sidewalks, subway and airports, etc., they naturally adjust their walking style according to the scene context and follow common social etiquette, such as maintaining separation and avoiding collisions. Accurate prediction of trajectories is a big challenge in a crowded scenario where interaction between targets may cause complex societal dynamics. Unlike the prediction of a single person trajectory, it is difficult to capture the real motion of multiple people by only considering the historical positions of each individual separately. Benefit from the recent success of graph neural networks, we propose a model called GNN-TP for pedestrian trajectory prediction. GNN-TP is a purely data-driven model that simultaneously infers the interactions between pedestrians in an unsupervised way and predicts their future trajectories jointly in crowded scenes. On the one hand, GNN-TP infers the interactions employing the observed historical trajectories. We transfer pedestrians' information on the graph-structured data and classify the interaction type based on edges' features. On the other hand, it learns the dynamical model and predicts future trajectories based on the inferred interactions and the observations. Extensive experiments show that our trajectory prediction model achieves efficient and state-of-the-art performance on several public datasets.

Non-negative matrix factorization (NMF) minimizes the euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated CauchyNMF loss that handle outliers by truncating large errors, and develop a Truncated CauchyNMF to robustly learn the subspace on noisy datasets contaminated by outliers. We theoretically analyze the robustness of Truncated CauchyNMF comparing with the competing models and theoretically prove that Truncated CauchyNMF has a generalization bound which converges at a rate of order , where is the sample size. We evaluate Truncated CauchyNMF by image clustering on both simulated and real datasets. The experimental results on the datasets containing gross corruptions validate the effectiveness and robustness of Truncated CauchyNMF for learning robust subspaces.

Domain adaptation (DA) attempts to enhance the generalization capability of classifier through narrowing the gap of the distributions across domains. This paper focuses on unsupervised domain adaptation where labels are not available in target domain. Most existing approaches explore the domain-invariant features shared by domains but ignore the discriminative information of source domain. To address this issue, we propose a discriminative domain adaptation method (DDA) to reduce domain shift by seeking a common latent subspace jointly using supervised sparse coding (SSC) and discriminative regularization term. Particularly, DDA adapts SSC to yield discriminative coefficients of target data and further unites with discriminative regularization term to induce a common latent subspace across domains. We show that both strategies can boost the ability of transferring knowledge from source to target domain. Experiments on two real world datasets demonstrate the effectiveness of our proposed method over several existing state-of-the-art domain adaptation methods.

Non-negative matrix factorization (NMF) has attracted great attentions in speech separation as it can preserve the non-negativity property of the magnitude spectrogram of speech signal. However, NMF sometimes performs poorly because it cannot extract the non-linear features in speech. In this paper, we propose a deep transductive NMF model (DTNMF) which incorporates a multi-layer structure into NMF and learns a shared dictionary on source signal of each speaker and the mixture signal to be separated. Since the multi-layer structure enables DTNMF to learn more precise presentation of source signal with the non-linear features extracted, DTNMF significantly enhances the performance of speech separation. Experimental results on Non-negative matrix factorization (NMF) has attracted great attentions in speech separation as it can preserve the non-negativity property of the magnitude spectrogram of speech signal. However, NMF sometimes performs poorly because it cannot extract the non-linear features in speech. In this paper, we propose a deep transductive NMF model (DTNMF) which incorporates a multi-layer structure into NMF and learns a shared dictionary on source signal of each speaker and the mixture signal to be separated. Since the multi-layer structure enables DTNMF to learn more precise presentation of source signal with the non-linear features extracted, DTNMF significantly enhances the performance of speech separation. Experimental results on the popular LibriSpeech dataset show that DTNMF outperforms the representative NMF models for separating the mixture of single-channel speech signals.

Studies on nowadays human-machine interface have demonstrated that visual information can enhance speech recognition accuracy especially in noisy environments. Deep learning has been widely used to tackle such audio visual speech recognition (AVSR) problem due to its astonishing achievements in both speech recognition and image recognition. Although existing deep learning models succeed to incorporate visual information into speech recognition, none of them simultaneously considers sequential characteristics of both audio and visual modalities. To overcome this deficiency, we proposed a multimodal recurrent neural network (multimodal RNN) model to take into account the sequential characteristics of both audio and visual modalities for AVSR. In particular, multimodal RNN includes three components, i.e., audio part, visual part, and fusion part, where the audio part and visual part capture the sequential characteristics of audio and visual modalities, respectively, and the fusion part combines the outputs of both modalities. Here we modelled the audio modality by using a LSTM RNN, and modelled the visual modality by using a convolutional neural network (CNN) plus a LSTM RNN, and combined both models by a multimodal layer in the fusion part. We validated the effectiveness of the proposed multimodal RNN model on a multi-speaker AVSR benchmark dataset termed AVletters. The experimental results show the performance improvements comparing to the known highest audio visual recognition accuracies on AVletters, and confirm the robustness of our multimodal RNN model.

Genome-wide expression data consists of millions of measurements towards large number of genes, and thus it is challenging for human beings to directly analyze such large-scale data. Clustering provides a more convenient way to analyze gene expression data because it can subdivide raw data into comprehensive classes. However, the number of probed genes is rather greater than the number of samples, and this makes conventional clustering methods perform unsatisfactorily. In this paper, we propose a Gauss-Seidel based non-negative matrix factorization (GSNMF) method to overcome such imbalance deficiency between features and samples. In particular, GSNMF it-eratively projects gene expression data onto the learned subspace followed by adaptively updating the cluster centroids based on the projected data. Since this data projection strategy significantly reduces the influence of imbalance between the number of samples and the number of genes, GSNMF performs better than traditional clustering methods in gene expression clustering. Since GSNMF updates each factor matrix by solution of a linear system obtained by the Gauss-Seidel method, it converges rapidly without neither complex line search nor matrix inverse operators. Experimental results on several cancer expression datasets confirm both efficiency and effectiveness of GSNMF comparing with the representative NMF methods and conventional clustering methods.

Graph regularized non-negative matrix factorization (GNMF) decomposes a high-dimensional non-negative data matrix into two low-dimensional matrices with the non-negativity property kept and the geometric structure preserved. Due to its effectiveness, GNMF has been widely used in many fields such as computer vision and data mining. However, GNMF cannot process large-scale datasets on distributed system because the gradient of the graph regularization term costs huge amount of communication overheads among computing nodes. In this paper, we proposed a distributed GNMF (DGNMF) algorithm to overcome this deficiency. Particularly, DGNMF reformulates the graph regularization term to avoid multiplying graph Laplacian by factor matrix through introducing an auxiliary variable and incorporating an equality constraint over it. We optimize DGNMF by using greedy coordinate descent method in the frame of augmented Lagrange method and implement this algorithm on a distributed system. Since DGNMF requires quite few communication overheads among computing nodes, it can be applied to large scale dataset. The preliminary results illustrate efficiency, scalability, and effectiveness of DGNMF.

Semi-supervised learning (SSL) utilizes plenty of unlabeled examples to boost the performance of learning from limited labeled examples. Due to its great discriminant power, SSL has been widely applied to various real-world tasks such as information retrieval, pattern recognition, and speech separa- tion. Label propagation (LP) is a popular SSL method which propagates labels through the dataset along high density areas defined by unlabeled examples, LP assumes nearby examples should share the same label, thus, it unavoidably pushes the labels to the wrong examples, especially when different la- beled examples are not strictly separated. Seed K-means uses labeled examples to initialize class centers, and avoid getting stuck in poor local optima comparing to traditional K-means, however the hard constraint of each example's membership makes Seed K-means failed in many real world applications. This paper proposes a novel label walking nonnegative matrix factorization method (LWNMF) to handle labeled examples in SSL based on the framework of NMF. LWNMF decomposes the whole dataset into the product of a basis matrix and a coefficient matrix, and to travel labels to unlabeled examples, LWNMF regards the class indicators of labeled examples as their coefficients and iteratively updates both basis matrix and coefficients of unlabeled examples. Since LWNMF learns comprehensive class centroids, labels iteratively walk to unlabeled examples through these significant centroids.

Non-negative matrix factorization (NMF) decomposes any non-negative matrix into the product of two low dimensional non-negative matrices. Since NMF learns effective parts-based representation, it has been widely applied in computer vision and data mining. However, traditional NMF has the risk learning rank-deficient basis on high-dimensional dataset with few examples especially when some examples are heavily corrupted by outliers. In this paper, we propose a Logdet divergence based sparse NMF method (LDS-NMF) to deal with the rank-deficiency problem. In particular, LDS-NMF reduces the risk of rank deficiency by minimizing the Logdet divergence between the product of basis matrix with its transpose and the identity matrix, meanwhile penalizing the density of the coefficients. Since the objective function of LDS-NMF is nonconvex, it is difficult to optimize. In this paper, we develop a multiplicative update rule to optimize LDS-NMF in the frame of block coordinate descent, and theoretically prove its convergence. Experimental results on popular datasets show that LDS-NMF can learn more stable representations than those learned by representative NMF methods.

Non-negative matrix factorization (NMF) decomposes a group of non-negative examples into both lower-rank factors including the basis and coefficients. It still suffers from the following deficiencies: 1) it does not always ensure the decomposed factors to be sparse theoretically, and 2) the learned basis often stays away from original examples, and thus lacks enough representative capacity. This paper proposes a local coordinate projective NMF (LCPNMF) to overcome the above deficiencies. Particularly, LCPNMF induces sparse coefficients by relaxing the original PNMF model meanwhile encouraging the basis to be close to original examples with the local coordinate constraint. Benefitting from both strategies, LCPNMF can significantly boost the representation ability of the PNMF. Then, we developed the multiplicative update rule to optimize LCPNMF and theoretically proved its convergence. Experimental results on three popular frontal face image datasets verify the effectiveness of LCPNMF comparing to the representative methods.

This paper formulates multi-label learning as a constrained projective non-negative matrix factorization (CPNMF) problem which concentrates on a variant of the original projective NMF (PNMF) and explicitly introduces an auxiliary basis to learn the semantic subspace and boosts its discriminating ability by exploiting labeled and unlabeled examples together. Particularly, it propagates labels of the labeled examples to the unlabeled ones by enforcing coefficients of examples sharing identical semantic contents to be identical based on a hard constraint, i.e., embedding the class indicator of labeled examples into their coefficients. CPNMF preserves the geometrical structure of dataset via manifold regularization meanwhile captures the inherent structure of labels by using label correlations. We developed a multiplicative update rule (MUR) based algorithm to optimize CPNMF and proved its convergence. Experiments of image annotation on Corel dataset, text categorization on Rcv1v2 dataset, and text clustering on two popular text corpuses suggest the effectiveness of CPNMF.

Modern understanding of microbiology largely lays foundation in the biological characterization of microorganisms. However, the landscape relationships of host transcriptional response (HTR) to different bacterial pathogens have not yet been systematically explored. Here, we established the first generation of HTR network (HTRN) according to the HTR similarities among 21 different human pathogenic bacterial species by integrating 258 pairs of host cellular gene expression profiles upon infections. Further, the network was dissected into five bacterial communities of more consensus internal HTR. Interestingly, analysis of signature genes across different communities revealed that distinct community signatures (CS) present differential gene expression patterns. Functional annotation suggested a common feature of host cell response to bacterial infections that specific functional gene clusters (BPs and/or signaling pathways) were preferentially elicited or subverted by community bacterial pathogens. Notably, community signatures (especially key associators participating dissimilar functional profiles) were highly enriched of GWAS disease-related genes, which associated bacterial infections with common and specific non-infectious human disease(s). About 40% of the associations were confirmed by literature investigation that further indicated possible/potential association directionality. Our characterization and analysis were the first to feature differential community HTRs upon bacterial pathogen infections and suggested new perspective of understanding infection-disease associations and underlying pathogenesis.

Non-negative matrix factorization (NMF) is a powerful dimension reduction method and has been widely used in many pattern recognition and computer vision problems. However, conventional NMF methods are neither robust enough as their loss functions are sensitive to outliers, nor discriminative because they completely ignore labels in a dataset. In this paper, we proposed a correntropy supervised NMF (CSNMF) to simultaneously overcome aforementioned deficiencies. In particular, CSNMF maximizes the correntropy between the data matrix and its reconstruction in low-dimensional space to inhibit outliers during learning the subspace, and narrows the minimizes the distances between coefficients of any two samples with the same class labels to enhance the subsequent classification performance. To solve CSNMF, we developed a multiplicative update rules and theoretically proved its convergence. Experimental results on popular face image datasets verify the effectiveness of CSNMF comparing with NMF, its supervised variants, and its robustified variants.

Non-negative matric factorization (NMF) decomposes a given data matrix X into the product of two lower dimensional non-negative matrices U and V. It has been widely applied in pattern recognition and computer vision because of its simplicity and effectiveness. However, existing NMF methods often fail to learn the sparse representation on high-dimensional dataset, especially when some examples are heavily corrupted. In this paper, we propose a robust local coordinate NMF method (RLCNMF) by using the maximum correntropy criteria to overcome such deficiency. Particularly, RLCNMF induces sparse coefficients by imposing the local coordinate constraint over both factors. To solve RLCNMF, we developed a multiplicative update rules and theoretically proved its convergence. Experimental results on popular image datasets verify the effectiveness of RLCNMF comparing with the representative methods.

Nonnegative matrix factorization (NMF) is a powerful technique for dimensionality reduction. Conventional NMF algorithms usually keep the matrices W and H nonnegative while iterating. However, to get the NMF of a matrix, it's unnecessary to force the temporary solutions in iterations nonnegative. In this paper, we propose a two-staged approach for NMF. At the relaxation stage, the nonnegative constraint of temporary solutions is relaxed and a real valued matrix factorization is generated. At the constraint stage, the real valued matrix factorization is transformed to a nonnegative matrix factorization by an invertible linear transformation. Based on this approach, we study on exact nonnegative matrix factorization when rank=2. We proved that, given two real valued matrices of rank=2, there exists an invertible linear transformation which can transform the real valued matrices to nonnegative matrices with their product stable. We propose an algorithm to find out the transformation. When rank is higher than 2, this kind of transformation may not exist. In the experiments, it's showed that this approach can reach a nonnegative matrix factorization with lower reconstruction error than conventional methods, and the technique for rank=2 exact NMF works well.

Partitioning links rather than nodes is effective in overlapping community detection (OCD) on complex networks. However, it consumes high CPU and memory overheads because the volume of links is huge especially when the network is rather complex. In this paper, we proposes a symmetric non-negative matrix factorization (SNMF) based link partition method called SNMF-Link to overcome this deficiency. In particular, SNMF-Link represents data in a lower-dimensional space spanned by the node-link incidence matrix. By solving a lighter SNMF problem, SNMF-Link learns the clustering indicators of each links. Since traditional multiplicative update rule (MUR) based optimization algorithm for SNMF suffers from slow convergence, we applied the augmented Lagrangian method (ALM) to efficiently optimize SNMF. Experimental results show that SNMF-Link is much more efficient than the representative clustering algorithms without reducing the OCD performance.

Regarding the non-negativity property of the magnitude spectrogram of speech signals, nonnegative matrix factorization (NMF) has obtained promising performance for speech separation by independently learning a dictionary on the speech signals of each known speaker. However, traditional NM-F fails to represent the mixture signals accurately because the dictionaries for speakers are learned in the absence of mixture signals. In this paper, we propose a new transductive NMF algorithm (TNMF) to jointly learn a dictionary on both speech signals of each speaker and the mixture signals to be separated. Since TNMF learns a more descriptive dictionary by encoding the mixture signals than that learned by NMF, it significantly boosts the separation performance. Experiments results on a popular TIMIT dataset show that the proposed TNMF-based methods outperform traditional NMF-based methods for separating the monophonic mixtures of speech signals of known speakers.

Semi-supervised clustering aims at boosting the clustering performance on unlabeled samples by using labels from a few labeled samples. Constrained NMF (CNMF) is one of the most significant semi-supervised clustering methods, and it factorizes the whole dataset by NMF and constrains those labeled samples from the same class to have identical encodings. In this paper, we propose a novel soft-constrained NMF (SCNMF) method by softening the hard constraint in CNMF. Particularly, SCNMF factorizes the whole dataset into two lower-dimensional factor matrices by using multiplicative update rule (MUR). To utilize the labels of labeled samples, SCNMF iteratively normalizes both factor matrices after updating them with MURs to make encodings of labeled samples close to their label vectors. It is therefore reasonable to believe that encodings of unlabeled samples are also close to their corresponding label vectors. Such strategy significantly boosts the clustering performance even when the labeled samples are rather limited, e.g., each class owns only a single labeled sample. Since the normalization procedure never increases the computational complexity of MUR, SCNMF is quite efficient and effective in practices. Experimental results on face image datasets illustrate both efficiency and effectiveness of SCNMF compared with both NMF and CNMF.

Projective non-negative matrix factorization (P-NMF) projects a set of examples onto a subspace spanned by a non-negative basis whose transpose is regarded as the projection matrix. Since PNMF learns a natural parts-based representation, it has been successfully used in text mining and pattern recognition. However, it is non-trivial to analyze the convergence of the optimization algorithms for PNMF because its objective function is non-convex. In this paper, we propose a Box-constrained PNMF (BPNMF) method to overcome this deficiency of PNMF. In particular, BPNMF introduces an auxiliary variable, i.e., the coefficients of examples, and incorporates the following two types of constraints: 1) each entry of the basis is non-negative and upper-bounded, i.e., box-constrained, and 2) the coefficients equal to the projected points of the examples. The first box constraint makes the basis to be bound and the second equality constraint keeps its equivalence to PNMF. Similar to PNMF, BPNMF is difficult because the objective function is non-convex. To solve BPNMF, we developed an efficient algorithm in the frame of augmented Lagrangian multiplier (ALM) method and proved that the ALM-based algorithm converges to local minima. Experimental results on two face image datasets demonstrate the effectiveness of BPNMF compared with the representative methods.

Non-negative matrix factorization (NMF) reconstructs the original samples in a lower dimensional space and has been widely used in pattern recognition and data mining because it usually yields sparse representation. Since NMF leads to unsatisfactory reconstruction for the datasets that contain translations of large magnitude, it is required to develop translation NMF (TNMF) to first remove the translation and then conduct a decomposition. However, existing multiplicative update rule based algorithm for TNMF is not efficient enough. In this paper, we reformulate TNMF and show that it can be efficiently solved by using the state-of-the-art solvers such as NeNMF. Experimental results on face image datasets confirm both efficiency and effectiveness of the reformulated TNMF.

Nonnegative matrix factorization (NMF) decomposes a nonnegative dataset X into two low-rank nonnegative factor matrices, i.e., W and H, by minimizing either Kullback-Leibler (KL) divergence or Euclidean distance between X and WH. NMF has been widely used in pattern recognition, data mining and computer vision because the non-negativity constraints on both W and H usually yield intuitive parts-based representation. However, NMF suffers from two problems: 1) it ignores geometric structure of dataset, and 2) it does not explicitly guarantee parts-based representation on any datasets. In this paper, we propose an orthogonal nonnegative locally linear embedding (ONLLE) method to overcome aforementioned problems. ONLLE assumes that each example embeds in its nearest neighbors and keeps such relationship in the learned subspace to preserve geometric structure of a dataset. For the purpose of learning parts-based representation, ONLLE explicitly incorporates an orthogonality constraint on the learned basis to keep its spatial locality. To optimize ONLLE, we applied an efficient fast gradient descent (FGD) method on Stiefel manifold which accelerates the popular multiplicative update rule (MUR). The experimental results on real-world datasets show that FGD converges much faster than MUR. To evaluate the effectiveness of ONLLE, we conduct both face recognition and image clustering on real-world datasets by comparing with the representative NMF methods.

Non-negative matrix factorization (NMF) approximates a non-negative matrix by the product of two low-rank matrices and achieves good performance in clustering. Recently, semi-supervised NMF (SS-NMF) further improves the performance by incorporating part of the labels of few samples into NMF. In this paper, we proposed a novel graph based SS-NMF (GSS-NMF). For each sample, GSS-NMF minimizes its distances to the same labeled samples and maximizes the distances against different labeled samples to incorporate the discriminative information. Since both labeled and unlabeled samples are embedded in the same reduced dimensional space, the discriminative information from the labeled samples is successfully transferred to the unlabeled samples, and thus it greatly improves the clustering performance. Since the traditional multiplicative update rule converges slowly, we applied the well-known projected gradient method to optimizing GSS-NMF and the proposed algorithm can be applied to optimizing other manifold regularized NMF efficiently. Experimental results on two popular document datasets, i.e., Reuters21578 and TDT-2, show that GSS-NMF outperforms the representative SS-NMF algorithms.

Canonical correlation analysis (CCA) has been widely used in pattern recognition and machine learning. However, both CCA and its extensions sometimes cannot give satisfactory results. In this paper, we propose a new CCA-type method termed sparse representation based discriminative CCA (SPDCCA) by incorporating sparse representation and discriminative information simultaneously into traditional CCA. In particular, SPDCCA not only preserves the sparse reconstruction relationship within data based on sparse representation, but also preserves the maximum-margin based discriminative information, and thus it further enhances the classification performance. Experimental results on Yale, Extended Yale B, and ORL datasets show that SPDCCA outperforms both CCA and its extensions including KCCA, LPCCA and LDCCA in face recognition.

Non-negative matrix factorization (NMF) learns the latent semantic space more direct and reliable than the latent semantic indexing (LSI) and the spectral clustering methods, thus performs well in document clustering. Recently, semi-supervised NMF such as N2S2L, CNMF and unsupervised method such as GNMF significantly improve the face recognition performance, but they are designed for classification. In this paper, we combine both geometric structure and label information with NMF under the non-negative patch alignment framework (NPAF) to form SS-NPAF. Due to this combination, it greatly improves the clustering performance. To optimize SS-NPAF, we apply the well-known projected gradient method to overcome the slow convergence problem of the mostly used multiplicative update rule. Experimental results on two popular document datasets, i.e., Reuters21578 and TDT-2, show that SS-NPAF outperforms the representative SS-NMF algorithms.

Nonnegative matrix factorization (NMF) has become a popular dimension-reduction method and has been widely applied to image processing and pattern recognition problems. However, conventional NMF learning methods require the entire dataset to reside in the memory and thus cannot be applied to large-scale or streaming datasets. In this paper, we propose an efficient online RSA-NMF algorithm (OR-NMF) that learns NMF in an incremental fashion and thus solves this problem. In particular, OR-NMF receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation. Benefitting from the smartly chosen learning rate and averaging technique, OR-NMF converges at the rate of in each update of the bases. Furthermore, we prove that OR-NMF almost surely converges to a local optimal solution by using the quasi-martingale. By using a buffering strategy, we keep both the time and space complexities of one step of the OR-NMF constant and make OR-NMF suitable for large-scale or streaming datasets. Preliminary experimental results on real-world datasets show that OR-NMF outperforms the existing online NMF (ONMF) algorithms in terms of efficiency. Experimental results of face recognition and image annotation on public datasets confirm the effectiveness of OR-NMF compared with the existing ONMF algorithms.

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

In this paper, we present a non-negative patch alignment framework (NPAF) to unify popular non-negative matrix factorization (NMF) related dimension reduction algorithms. It offers a new viewpoint to better understand the common property of different NMF algorithms. Although multiplicative update rule (MUR) can solve NPAF and is easy to implement, it converges slowly. Thus, we propose a fast gradient descent (FGD) to overcome the aforementioned problem. FGD uses the Newton method to search the optimal step size, and thus converges faster than MUR. Experiments on synthetic and real-world datasets confirm the efficiency of FGD compared with MUR for optimizing NPAF. Based on NPAF, we develop non-negative discriminative locality alignment (NDLA). Experiments on face image and handwritten datasets suggest the effectiveness of NDLA in classification tasks and its robustness to image occlusions, compared with representative NMF-related dimension reduction algorithms.