Low-Rank Preserving Projection Via Graph Regularized Reconstruction

Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds

Low-Rank Representation (LRR) methods integrate low-rank constraints and projection operators to model the mapping from the sample space to low-dimensional manifolds. Nonetheless, existing approaches typically apply Euclidean algorithms directly to manifold data in the original input space, leading to suboptimal classification accuracy. To mitigate this limitation, we introduce an unsupervised low-rank projection learning method named Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds (LRR-EKM). LRR-EKM leverages an empirical kernel mapping to project samples into the Reproduced Kernel Hilbert Space (RKHS), enabling the linear separability of non-linearly structured samples and facilitating improved low-dimensional manifold representations through Euclidean distance metrics. By incorporating a row sparsity constraint on the projection matrix, LRR-EKM not only identifies discriminative features and removes redundancies but also enhances the interpretability of the learned subspace. Additionally, we introduce a manifold structure preserving constraint to retain the original representation and distance information of the samples during projection. Comprehensive experimental evaluations across various real-world datasets validate the superior performance of our proposed method compared to the state-of-the-art methods. The code is publicly available at https://github.com/ff-raw-war/LRR-EKM.

Learning the Optimal Discriminant SVM With Feature Extraction

Subspace learning and Support Vector Machine (SVM) are two critical techniques in pattern recognition, playing pivotal roles in feature extraction and classification. However, how to learn the optimal subspace such that the SVM classifier can perform the best is still a challenging problem due to the difficulty in optimization, computation, and algorithm convergence. To address these problems, this paper develops a novel method named Optimal Discriminant Support Vector Machine (ODSVM), which integrates support vector classification with discriminative subspace learning in a seamless framework. As a result, the most discriminative subspace and the corresponding optimal SVM are obtained simultaneously to pursue the best classification performance. The efficient optimization framework is designed for binary and multi-class ODSVM. Moreover, a fast sequential minimization optimization (SMO) algorithm with pruning is proposed to accelerate the computation in multi-class ODSVM. Unlike other related methods, ODSVM has a strong theoretical guarantee of global convergence, highlighting its superiority and stability. Numerical experiments are conducted on thirteen datasets and the results demonstrate that ODSVM outperforms existing methods with statistical significance.

Joint Structured Bipartite Graph and Row-Sparse Projection for Large-Scale Feature Selection

Feature selection plays an important role in data analysis, yet traditional graph-based methods often produce suboptimal results. These methods typically follow a two-stage process: constructing a graph with data-to-data affinities or a bipartite graph with data-to-anchor affinities and independently selecting features based on their scores. In this article, a large-scale feature selection approach based on structured bipartite graph and row-sparse projection (RS2BLFS) is proposed to overcome this limitation. RS2BLFS integrates the construction of a structured bipartite graph consisting of c connected components into row-sparse projection learning with k nonzero rows. This integration allows for the joint selection of an optimal feature subset in an unsupervised manner. Notably, the c connected components of the structured bipartite graph correspond to c clusters, each with multiple subcluster centers. This feature makes RS2BLFS particularly effective for feature selection and clustering on nonspherical large-scale data. An algorithm with theoretical analysis is developed to solve the optimization problem involved in RS2BLFS. Experimental results on synthetic and real-world datasets confirm its effectiveness in feature selection tasks.

On-the-move heterogeneous face recognition in frequency and spatial domain using sparse representation

Heterogeneity of a probe image is one of the most complex challenges faced by researchers and implementers of current surveillance systems. This is due to existence of multiple cameras working in different spectral ranges in a single surveillance setup. This paper proposes two different approaches including spatial sparse representations (SSR) and frequency sparse representation (FSR) to recognize on-the-move heterogeneous face images with database of single sample per person (SSPP). SCface database, with five visual and two Infrared (IR) cameras, is taken as a benchmark for experiments, which is further confirmed using CASIA NIR-VIS 2.0 face database with 17580 visual and IR images. Similarity, comparison is performed for different scenarios such as, variation of distances from a camera and variation in sizes of face images and various visual and infrared (IR) modalities. Least square minimization based approach for finding the solution is used to match face images as it makes the recognition process simpler. A side by side comparison of both the proposed approaches with the state-of-the-art, classical, principal component analysis (PCA), kernel fisher analysis (KFA) and coupled kernel embedding (CKE) methods, along with modern low-rank preserving projection via graph regularized reconstruction (LRPP-GRR) method, is also presented. Experimental results suggest that the proposed approaches achieve superior performance.

Projective Incomplete Multi-View Clustering

Due to the rapid development of multimedia technology and sensor technology, multi-view clustering (MVC) has become a research hotspot in machine learning, data mining, and other fields and has been developed significantly in the past decades. Compared with single-view clustering, MVC improves clustering performance by exploiting complementary and consistent information among different views. Such methods are all based on the assumption of complete views, which means that all the views of all the samples exist. It limits the application of MVC, because there are always missing views in practical situations. In recent years, many methods have been proposed to solve the incomplete MVC (IMVC) problem and a kind of popular method is based on matrix factorization (MF). However, such methods generally cannot deal with new samples and do not take into account the imbalance of information between different views. To address these two issues, we propose a new IMVC method, in which a novel and simple graph regularized projective consensus representation learning model is formulated for incomplete multi-view data clustering task. Compared with the existing methods, our method not only can obtain a set of projections to handle new samples but also can explore information of multiple views in a balanced way by learning the consensus representation in a unified low-dimensional subspace. In addition, a graph constraint is imposed on the consensus representation to mine the structural information inside the data. Experimental results on four datasets show that our method successfully accomplishes the IMVC task and obtain the best clustering performance most of the time. Our implementation is available at https://github.com/Dshijie/PIMVC.

Low-Rank Graph Completion-Based Incomplete Multiview Clustering

In order to reduce the negative effect of missing data on clustering, incomplete multiview clustering (IMVC) has become an important research content in machine learning. At present, graph-based methods are widely used in IMVC, but these methods still have some defects. First, some of the methods overlook potential relationships across views. Second, most of the methods depend on local structure information and ignore the global structure information. Third, most of the methods cannot use both global structure information and potential information across views to adaptively recover the incomplete relationship structure. To address the above issues, we propose a unified optimization framework to learn reasonable affinity relationships, called low-rank graph completion-based IMVC (LRGR_IMVC). 1) Our method introduces adaptive graph embedding to effectively explore the potential relationship among views; 2) we append a low-rank constraint to adequately exploit the global structure information among views; and 3) this method unites related information within views, potential information across views, and global structure information to adaptively recover the incomplete graph structure and obtain complete affinity relationships. Experimental results on several commonly used datasets show that the proposed method achieves better clustering performance significantly than some of the most advanced methods.

Fuzzy Graph Subspace Convolutional Network

Graph convolutional networks (GCNs) are a popular approach to learn the feature embedding of graph-structured data, which has shown to be highly effective as well as efficient in performing node classification in an inductive way. However, with massive nongraph-organized data existing in application scenarios nowadays, it is critical to exploit the relationships behind the given groups of data, which makes better use of GCN and broadens the application field. In this article, we propose the f uzzy g raph s ubspace c onvolutional n etwork (FGSCN) to provide a brand-new paradigm for feature embedding and node classification with graph convolution (GC) when given an arbitrary collection of data. The FGSCN performs GC on the f uzzy s ubspace ( F -space), which simultaneously learns from the underlying subspace information in the low-dimensional space as well as its neighborliness information in the high-dimensional space. In particular, we construct the fuzzy homogenous graph GF on the F -space by fusing the homogenous graph of neighborliness GN and homogenous graph of subspace GS (defined by the affinity matrix of the low-rank representation). Here, it is proven that the GC on F -space will propagate both the local and global information through fuzzy set theory. We evaluated FGSCN on 15 unique datasets with different tasks (e.g., feature embedding, visual recognition, etc.). The experimental results showed that the proposed FGSCN has significant superiority compared with current state-of-the-art methods.

Discriminative Regression With Adaptive Graph Diffusion

In this article, we propose a new linear regression (LR)-based multiclass classification method, called discriminative regression with adaptive graph diffusion (DRAGD). Different from existing graph embedding-based LR methods, DRAGD introduces a new graph learning and embedding term, which explores the high-order structure information between four tuples, rather than conventional sample pairs to learn an intrinsic graph. Moreover, DRAGD provides a new way to simultaneously capture the local geometric structure and representation structure of data in one term. To enhance the discriminability of the transformation matrix, a retargeted learning approach is introduced. As a result of combining the above-mentioned techniques, DRAGD can flexibly explore more unsupervised information underlying the data and the label information to obtain the most discriminative transformation matrix for multiclass classification tasks. Experimental results on six well-known real-world databases and a synthetic database demonstrate that DRAGD is superior to the state-of-the-art LR methods.

Latent Low-Rank Representation With Weighted Distance Penalty for Clustering

Latent low-rank representation (LatLRR) is a critical self-representation technique that improves low-rank representation (LRR) by using observed and unobserved samples. It can simultaneously learn the low-dimensional structure embedded in the data space and capture the salient features. However, LatLRR ignores the local geometry structure and can be affected by the noise and redundancy in the original data space. To solve the above problems, we propose a latent LRR with weighted distance penalty (LLRRWD) for clustering in this article. First, a weighted distance is proposed to enhance the original Euclidean distance by enlarging the distance among the unconnected samples, which can enhance the discriminitation of the distance among the samples. By leveraging on the weighted distance, a weighted distance penalty is introduced to the LatLRR model to enable the method to preserve both the local geometric information and global information, improving discrimination of the learned affinity matrix. Moreover, a weight matrix is imposed on the sparse error norm to reduce the effect of noise and redundancy. Experimental results based on several benchmark databases show the effectiveness of our method in clustering.

ARGLRR: A Sparse Low-Rank Representation Single-Cell RNA-Sequencing Data Clustering Method Combined with a New Graph Regularization

The development of single-cell transcriptome sequencing technologies has opened new ways to study biological phenomena at the cellular level. A key application of such technologies involves the employment of single-cell RNA sequencing (scRNA-seq) data to identify distinct cell types through clustering, which in turn provides evidence for revealing heterogeneity. Despite the promise of this approach, the inherent characteristics of scRNA-seq data, such as higher noise levels and lower coverage, pose major challenges to existing clustering methods and compromise their accuracy. In this study, we propose a method called Adjusted Random walk Graph regularization Sparse Low-Rank Representation (ARGLRR), a practical sparse subspace clustering method, to identify cell types. The fundamental low-rank representation (LRR) model is concerned with the global structure of data. To address the limited ability of the LRR method to capture local structure, we introduced adjusted random walk graph regularization in its framework. ARGLRR allows for the capture of both local and global structures in scRNA-seq data. Additionally, the imposition of similarity constraints into the LRR framework further improves the ability of the proposed model to estimate cell-to-cell similarity and capture global structural relationships between cells. ARGLRR surpasses other advanced comparison approaches on nine known scRNA-seq data sets judging by the results. In the normalized mutual information and Adjusted Rand Index metrics on the scRNA-seq data sets clustering experiments, ARGLRR outperforms the best-performing comparative method by 6.99% and 5.85%, respectively. In addition, we visualize the result using Uniform Manifold Approximation and Projection. Visualization results show that the usage of ARGLRR enhances the separation of different cell types within the similarity matrix.

Robust Dimensionality Reduction via Low-rank Laplacian Graph Learning

Manifold learning is a widely used technique for dimensionality reduction as it can reveal the intrinsic geometric structure of data. However, its performance decreases drastically when data samples are contaminated by heavy noise or occlusions, which leads to unsatisfying data processing performance. We propose a novel robust dimensionality reduction method via low-rank Laplacian graph learning for classification and clustering tasks to solve the above problem. First, we construct a low-rank Laplacian graph by combining manifold learning and subspace learning. This graph can capture both global and local structural information of the data. And we introduce rank constraints for the Laplacian graph to make it more discriminative. Second, we put the learning of projection matrix and sample affinity graph into a unified framework. The projection matrix is embedded into a robust low-rank Laplacian graph so that the low-dimensional mapping of data can maintain the structural information in the graph well. Finally, we add a regularization term to the projection matrix to make it have the ability of both feature extraction and feature selection. Therefore, the proposed model can resist the interference of noise or data damage to learn the optimal projection to achieve better performance in dimensionality reduction through such a data dimensionality reduction joint framework. Comprehensive experiments on various benchmark datasets with varying degrees of occlusions or corruptions are carried out to evaluate the performance of the proposed method. Compared with the state-of-the-art dimensionality reduction methods in the literature, the experimental results are inspiring, showing our method’s effectiveness and robustness in classification and clustering, especially in object recognition scenarios with noise or occlusions.

Graph Regularized Structured Output SVM for Early Expression Detection With Online Extension

In this study, a graph regularized algorithm for early expression detection (EED), called GraphEED, is proposed. EED is aimed at detecting the specified expression in the early stage of a video. Existing EED detectors fail to explicitly exploit the local geometrical structure of the data distribution, which may affect the prediction performance significantly. According to manifold learning, the data in real-world applications are likely to reside on a low-dimensional submanifold embedded in the high-dimensional ambient space. The proposed graph Laplacian consists of two parts: 1) a k -nearest neighbor graph is first constructed to encode the geometrical information under the manifold assumption and 2) the entire expressions are regarded as the must-link constraints since they all contain the complete duration information and it is shown that this can also be formulated as a graph regularization. GraphEED is to have a detection function representing these graph structures. Even with the inclusion of the graph Laplacian, the proposed GraphEED has the same computational complexity as that of the max-margin EED, which is a well-known learning-based EED, but the detection performance has been largely improved. To further make the model appropriate in large-scale applications, with the technique of online learning, the proposed GraphEED is extended to the so-called online GraphEED (OGraphEED). In OGraphEED, the buffering technique is employed to make the optimization practical by reducing the computation and storage cost. Extensive experiments on three video-based datasets have demonstrated the superiority of the proposed methods in terms of both effectiveness and efficiency.

Self-Supervision-Augmented Deep Autoencoder for Unsupervised Visual Anomaly Detection

Deep autoencoder (AE) has demonstrated promising performances in visual anomaly detection (VAD). Learning normal patterns on normal data, deep AE is expected to yield larger reconstruction errors for anomalous samples, which is utilized as the criterion for detecting anomalies. However, this hypothesis cannot be always tenable since the deep AE usually captures the low-level shared features between normal and abnormal data, which leads to similar reconstruction errors for them. To tackle this problem, we propose a self-supervised representation-augmented deep AE for unsupervised VAD, which can enlarge the gap of anomaly scores between normal and abnormal samples by introducing autoencoding transformation (AT). Essentially, AT is introduced to facilitate AE to learn the high-level visual semantic features of normal images by introducing a self-supervision task (transformation reconstruction). In particular, our model inputs the original and transformed images into the encoder for obtaining latent representations; afterward, they are fed to the decoder for reconstructing both the original image and applied transformation. In this way, our model can utilize both image and transformation reconstruction errors to detect anomaly. Extensive experiments indicate that the proposed method outperforms other state-of-the-art methods, which demonstrates the validity and advancement of our model.

Average Approximate Hashing-Based Double Projections Learning for Cross-Modal Retrieval

Cross-modal retrieval has attracted considerable attention for searching in large-scale multimedia databases because of its efficiency and effectiveness. As a powerful tool of data analysis, matrix factorization is commonly used to learn hash codes for cross-modal retrieval, but there are still many shortcomings. First, most of these methods only focus on preserving locality of data but they ignore other factors such as preserving reconstruction residual of data during matrix factorization. Second, the energy loss of data is not considered when the data of cross-modal are projected into a common semantic space. Third, the data of cross-modal are directly projected into a unified semantic space which is not reasonable since the data from different modalities have different properties. This article proposes a novel method called average approximate hashing (AAH) to address these problems by: 1) integrating the locality and residual preservation into a graph embedding framework by using the label information; 2) projecting data from different modalities into different semantic spaces and then making the two spaces approximate to each other so that a unified hash code can be obtained; and 3) introducing a principal component analysis (PCA)-like projection matrix into the graph embedding framework to guarantee that the projected data can preserve the main energy of data. AAH obtains the final hash codes by using an average approximate strategy, that is, using the mean of projected data of different modalities as the hash codes. Experiments on standard databases show that the proposed AAH outperforms several state-of-the-art cross-modal hashing methods.

Unsupervised Adaptive Embedding for Dimensionality Reduction

High-dimensional data are highly correlative and redundant, making it difficult to explore and analyze. Amount of unsupervised dimensionality reduction (DR) methods has been proposed, in which constructing a neighborhood graph is the primary step of DR methods. However, there exist two problems: 1) the construction of graph is usually separate from the selection of projection direction and 2) the original data are inevitably noisy. In this article, we propose an unsupervised adaptive embedding (UAE) method for DR to solve these challenges, which is a linear graph-embedding method. First, an adaptive allocation method of neighbors is proposed to construct the affinity graph. Second, the construction of affinity graph and calculation of projection matrix are integrated together. It considers the local relationship between samples and global characteristic of high-dimensional data, in which the cleaned data matrix is originally proposed to remove noise in subspace. The relationship between our method and local preserving projections (LPPs) is also explored. Finally, an alternative iteration optimization algorithm is derived to solve our model, the convergence and computational complexity of which are also analyzed. Comprehensive experiments on synthetic and benchmark datasets illustrate the superiority of our method.

Fast Unsupervised Projection for Large-Scale Data

Dimensionality reduction (DR) technique has been frequently used to alleviate information redundancy and reduce computational complexity. Traditional DR methods generally are inability to deal with nonlinear data and have high computational complexity. To cope with the problems, we propose a fast unsupervised projection (FUP) method. The simplified graph of FUP is constructed by samples and representative points, where the number of the representative points selected through iterative optimization is less than that of samples. By generating the presented graph, it is proved that large-scale data can be projected faster in numerous scenarios. Thereafter, the orthogonality FUP (OFUP) method is proposed to ensure the orthogonality of projection matrix. Specifically, the OFUP method is proved to be equivalent to PCA upon certain parameter setting. Experimental results on benchmark data sets show the effectiveness in retaining the essential information.

Relaxed Block-Diagonal Dictionary Pair Learning With Locality Constraint for Image Recognition

We propose a novel structured analysis-synthesis dictionary pair learning method for efficient representation and image classification, referred to as relaxed block-diagonal dictionary pair learning with a locality constraint (RBD-DPL). RBD-DPL aims to learn relaxed block-diagonal representations of the input data to enhance the discriminability of both analysis and synthesis dictionaries by dynamically optimizing the block-diagonal components of representation, while the off-block-diagonal counterparts are set to zero. In this way, the learned synthesis subdictionary is allowed to be more flexible in reconstructing the samples from the same class, and the analysis dictionary effectively transforms the original samples into a relaxed coefficient subspace, which is closely associated with the label information. Besides, we incorporate a locality-constraint term as a complement of the relaxation learning to enhance the locality of the analytical encoding so that the learned representation exhibits high intraclass similarity. A linear classifier is trained in the learned relaxed representation space for consistent classification. RBD-DPL is computationally efficient because it avoids both the use of class-specific complementary data matrices to learn discriminative analysis dictionary, as well as the time-consuming l₁/l₀ -norm sparse reconstruction process. The experimental results demonstrate that our RBD-DPL achieves at least comparable or better recognition performance than the state-of-the-art algorithms. Moreover, both the training and testing time are significantly reduced, which verifies the efficiency of our method. The MATLAB code of the proposed RBD-DPL is available at https://github.com/chenzhe207/RBD-DPL.

A supervised discriminant data representation: application to pattern classification

The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing frameworks and data transformations able to support effective machine learning. The method proposed in this work consists of a hybrid linear feature extraction scheme to be used in supervised multi-class classification problems. Inspired by two recent linear discriminant methods: robust sparse linear discriminant analysis (RSLDA) and inter-class sparsity-based discriminative least square regression (ICS_DLSR), we propose a unifying criterion that is able to retain the advantages of these two powerful methods. The resulting transformation relies on sparsity-promoting techniques both to select the features that most accurately represent the data and to preserve the row-sparsity consistency property of samples from the same class. The linear transformation and the orthogonal matrix are estimated using an iterative alternating minimization scheme based on steepest descent gradient method and different initialization schemes. The proposed framework is generic in the sense that it allows the combination and tuning of other linear discriminant embedding methods. According to the experiments conducted on several datasets including faces, objects, and digits, the proposed method was able to outperform competing methods in most cases.

Joint Optimal Transport With Convex Regularization for Robust Image Classification

The critical step of learning the robust regression model from high-dimensional visual data is how to characterize the error term. The existing methods mainly employ the nuclear norm to describe the error term, which are robust against structure noises (e.g., illumination changes and occlusions). Although the nuclear norm can describe the structure property of the error term, global distribution information is ignored in most of these methods. It is known that optimal transport (OT) is a robust distribution metric scheme due to that it can handle correspondences between different elements in the two distributions. Leveraging this property, this article presents a novel robust regression scheme by integrating OT with convex regularization. The OT-based regression with L₂ norm regularization (OTR) is first proposed to perform image classification. The alternating direction method of multipliers is developed to handle the model. To further address the occlusion problem in image classification, the extended OTR (EOTR) model is then presented by integrating the nuclear norm error term with an OTR model. In addition, we apply the alternating direction method of multipliers with Gaussian back substitution to solve EOTR and also provide the complexity and convergence analysis of our algorithms. Experiments were conducted on five benchmark datasets, including illumination changes and various occlusions. The experimental results demonstrate the performance of our robust regression model on biometric image classification against several state-of-the-art regression-based classification methods.

Research on Real-Time Face Key Point Detection Algorithm Based on Attention Mechanism

The existing face detection methods were affected by the network model structure used. Most of the face recognition methods had low recognition rate of face key point features due to many parameters and large amount of calculation. In order to improve the recognition accuracy and detection speed of face key points, a real-time face key point detection algorithm based on attention mechanism was proposed in this paper. Due to the multiscale characteristics of face key point features, the deep convolution network model was adopted, the attention module was added to the VGG network structure, the feature enhancement module and feature fusion module were combined to improve the shallow feature representation ability of VGG, and the cascade attention mechanism was used to improve the deep feature representation ability. Experiments showed that the proposed algorithm not only can effectively realize face key point recognition but also has better recognition accuracy and detection speed than other similar methods. This method can provide some theoretical basis and technical support for face detection in complex environment.

Research on Face Image Digital Processing and Recognition Based on Data Dimensionality Reduction Algorithm

Because face recognition is greatly affected by external environmental factors and the partial lack of face information challenges the robustness of face recognition algorithm, while the existing methods have poor robustness and low accuracy in face image recognition, this paper proposes a face image digital processing and recognition based on data dimensionality reduction algorithm. Based on the analysis of the existing data dimensionality reduction and face recognition methods, according to the face image input, feature composition, and external environmental factors, the face recognition and processing technology flow is given, and the face feature extraction method is proposed based on nonparametric subspace analysis (NSA). Finally, different methods are used to carry out comparative experiments in different face databases. The results show that the method proposed in this paper has a higher correct recognition rate than the existing methods and has an obvious effect on the XM2VTS face database. This method not only improves the shortcomings of existing methods in dealing with complex face images but also provides a certain reference for face image feature extraction and recognition in complex environment.

Protein Fold Recognition Based on Auto-Weighted Multi-View Graph Embedding Learning Model

Protein fold recognition is critical for studies of the protein structure prediction and drug design. Several methods have been proposed to obtain discriminative features from the protein sequences for fold recognition. However, the ensemble methods that combine the various features to improve predictive performance remain the challenge problems. In this study, we proposed two novel algorithms: AWMG and EMfold. AWMG used a novel predictor based on the multi-view learning framework for fold recognition. Each view was treated as the intermediate representation of the corresponding data source of proteins, including the evolutionary information and the retrieval information. AWMG calculated the auto-weight for each view respectively and constructed the latent subspace which contains the common information shared by different views. The marginalized constraint was employed to enlarge the margins between different folds, improving the predictive performance of AWMG. Furthermore, we proposed a novel ensemble method called EMfold, which combines two complementary methods AWMG and DeepSS. The later method was a template-based algorithm using the SPARKS-X and DeepFR programs. EMfold integrated the advantages of template-based assignment and machine learning classifier. Experimental results on the two widely datasets (LE and YK) showed that the proposed methods outperformed some state-of-the-art methods, indicating that AWMG and EMfold are useful tools for protein fold recognition.

Visualization and Analysis of Single cell RNA-seq Data by Maximizing Correntropy based Non-negative Low Rank Representation

The exploration of single cell RNA-sequencing (scRNA-seq) technology generates a new perspective to analyze biological problems. One of the major applications of scRNA-seq data is to discover subtypes of cells by cell clustering. Nevertheless, it is challengeable for traditional methods to handle scRNA-seq data with high level of technical noise and notorious dropouts. To better analyze single cell data, a novel scRNA-seq data analysis model called Maximum correntropy criterion based Non-negative and Low Rank Representation (MccNLRR) is introduced. Specifically, the maximum correntropy criterion, as an effective loss function, is more robust to the high noise and large outliers existed in the data. Moreover, the low rank representation is proven to be a powerful tool for capturing the global and local structures of data. Therefore, some important information, such as the similarity of cells in the subspace, is also extracted by it. Then, an iterative algorithm on the basis of the half-quadratic optimization and alternating direction method is developed to settle the complex optimization problem. Before the experiment, we also analyze the convergence and robustness of MccNLRR. At last, the results of cell clustering, visualization analysis, and gene markers selection on scRNA-seq data reveal that MccNLRR method can distinguish cell subtypes accurately and robustly.

Uniform Distribution Non-Negative Matrix Factorization for Multiview Clustering

Multiview data processing has attracted sustained attention as it can provide more information for clustering. To integrate this information, one often utilizes the non-negative matrix factorization (NMF) scheme which can reduce the data from different views into the subspace with the same dimension. Motivated by the clustering performance being affected by the distribution of the data in the learned subspace, a tri-factorization-based NMF model with an embedding matrix is proposed in this article. This model tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative. As a result, the obtained consensus matrix can be a better representative of the multiview data in the subspace, leading to higher clustering performance. Also, a new lemma is proposed to provide the formulas about the partial derivation of the trace function with respect to an inner matrix, together with its theoretical proof. Based on this lemma, a gradient-based algorithm is developed to solve the proposed model, and its convergence and computational complexity are analyzed. Experiments on six real-world datasets are performed to show the advantages of the proposed algorithm, with comparison to the existing baseline methods.

Shared Linear Encoder-Based Multikernel Gaussian Process Latent Variable Model for Visual Classification

Multiview learning has been widely studied in various fields and achieved outstanding performances in comparison to many single-view-based approaches. In this paper, a novel multiview learning method based on the Gaussian process latent variable model (GPLVM) is proposed. In contrast to existing GPLVM methods which only assume that there are transformations from the latent variable to the multiple observed inputs, our proposed method simultaneously takes a back constraint into account, encoding multiple observations to the latent variable by enjoying the Gaussian process (GP) prior. Particularly, to overcome the difficulty of the covariance matrix calculation in the encoder, a linear projection is designed to map different observations to a consistent subspace first. The obtained variable in this subspace is then projected to the latent variable in the manifold space with the GP prior. Furthermore, different from most GPLVM methods which strongly assume that the covariance matrices follow a certain kernel function, for example, radial basis function (RBF), we introduce a multikernel strategy to design the covariance matrix, being more reasonable and adaptive for the data representation. In order to apply the presented approach to the classification, a discriminative prior is also embedded to the learned latent variables to encourage samples belonging to the same category to be close and those belonging to different categories to be far. Experimental results on three real-world databases substantiate the effectiveness and superiority of the proposed method compared with state-of-the-art approaches.

Generalized Incomplete Multiview Clustering With Flexible Locality Structure Diffusion

An important underlying assumption that guides the success of the existing multiview learning algorithms is the full observation of the multiview data. However, such rigorous precondition clearly violates the common-sense knowledge in practical applications, where in most cases, only incomplete fractions of the multiview data are given. The presence of the incomplete settings generally disables the conventional multiview clustering methods. In this article, we propose a simple but effective incomplete multiview clustering (IMC) framework, which simultaneously considers the local geometric information and the unbalanced discriminating powers of these incomplete multiview observations. Specifically, a novel graph-regularized matrix factorization model, on the one hand, is developed to preserve the local geometric similarities of the learned common representations from different views. On the other hand, the semantic consistency constraint is introduced to stimulate these view-specific representations toward a unified discriminative representation. Moreover, the importance of different views is adaptively determined to reduce the negative influence of the unbalanced incomplete views. Furthermore, an efficient learning algorithm is proposed to solve the resulting optimization problem. Extensive experimental results performed on several incomplete multiview datasets demonstrate that the proposed method can achieve superior clustering performance in comparison with some state-of-the-art multiview learning methods.

Learning Salient and Discriminative Descriptor for Palmprint Feature Extraction and Identification

Palmprint recognition has been widely applied in security and, particularly, authentication. In the past decade, various palmprint recognition methods have been proposed and achieved promising recognition performance. However, most of these methods require rich a priori knowledge and cannot adapt well to different palmprint recognition scenarios, including contact-based, contactless, and multispectral palmprint recognition. This problem limits the application and popularization of palmprint recognition. In this article, motivated by the least square regression, we propose a salient and discriminative descriptor learning method (SDDLM) for general scenario palmprint recognition. Different from the conventional palmprint feature extraction methods, the SDDLM jointly learns noise and salient information from the pixels of palmprint images, simultaneously. The learned noise enforces the projection matrix to learn salient and discriminative features from each palmprint sample. Thus, the SDDLM can be adaptive to multiscenarios. Experiments were conducted on the IITD, CASIA, GPDS, PolyU near infrared (NIR), noisy IITD, and noisy GPDS palmprint databases, and palm vein and dorsal hand vein databases. It can be seen from the experimental results that the proposed SDDLM consistently outperformed the classical palmprint recognition methods and state-of-the-art methods for palmprint recognition.

Low-Rank Preserving t-Linear Projection for Robust Image Feature Extraction

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

Incomplete Multiview Spectral Clustering With Adaptive Graph Learning

In this paper, we propose a general framework for incomplete multiview clustering. The proposed method is the first work that exploits the graph learning and spectral clustering techniques to learn the common representation for incomplete multiview clustering. First, owing to the good performance of low-rank representation in discovering the intrinsic subspace structure of data, we adopt it to adaptively construct the graph of each view. Second, a spectral constraint is used to achieve the low-dimensional representation of each view based on the spectral clustering. Third, we further introduce a co-regularization term to learn the common representation of samples for all views, and then use the k -means to partition the data into their respective groups. An efficient iterative algorithm is provided to optimize the model. Experimental results conducted on seven incomplete multiview datasets show that the proposed method achieves the best performance in comparison with some state-of-the-art methods, which proves the effectiveness of the proposed method in incomplete multiview clustering.