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Nonnegative matrix factorization (NMF) and spectral clustering are two of the most widely used clustering techniques. However, NMF cannot deal with the nonlinear data, and spectral clustering relies on the postprocessing. In this article, we propose a Robust Matrix factorization with Spectral embedding (RMS) approach for data clustering, which inherits the advantages of NMF and spectral clustering, while avoiding their shortcomings. In addition, to cluster the data represented by multiple views, we present the multiview version of RMS (M-RMS), and the weights of different views are self-tuned. The main contributions of this research are threefold: 1) by integrating spectral clustering and matrix factorization, the proposed methods are able to capture the nonlinear data structure and obtain the cluster indicator directly; 2) instead of using the squared Frobenius-norm, the objectives are developed with the $\ell _{2,1}$ -norm, such that the effects of the outliers are alleviated; and 3) the proposed methods are totally parameter-free, which increases the applicability for various real-world problems. Extensive experiments on several single-view/multiview data sets demonstrate the effectiveness of our methods and verify their superior clustering performance over the state of the arts. [ABSTRACT FROM AUTHOR]

Data clustering is a fundamental problem in the field of machine learning. Among the numerous clustering techniques, matrix factorization-based methods have achieved impressive performances because they are able to provide a compact and interpretable representation of the input data. However, most of the existing works assume that each class has a global centroid, which does not hold for data with complicated structures. Besides, they cannot guarantee that the sample is associated with the nearest centroid. In this work, we present a concept factorization with the local centroids (CFLCs) approach for data clustering. The proposed model has the following advantages: 1) the samples from the same class are allowed to connect with multiple local centroids such that the manifold structure is captured; 2) the pairwise relationship between the samples and centroids is modeled to produce a reasonable label assignment; and 3) the clustering problem is formulated as a bipartite graph partitioning task, and an efficient algorithm is designed for optimization. Experiments on several data sets validate the effectiveness of the CFLC model and demonstrate its superior performance over the state of the arts. [ABSTRACT FROM AUTHOR]

Ridge regression is frequently utilized by both supervised and semisupervised learnings. However, the trivial solution might occur, when ridge regression is directly applied for clustering. To address this issue, an uncorrelated constraint is introduced to the ridge regression with embedding the manifold structure. In particular, we choose uncorrelated constraint over orthogonal constraint, since the closed-form solution can be obtained correspondingly. In addition to the proposed uncorrelated ridge regression, a soft pseudo label is utilized with $\ell _{1}$ ball constraint for clustering. Moreover, a brand new strategy, i.e., a rescaled technique, is proposed such that optimal scaling within the uncorrelated constraint can be achieved automatically to avoid the inconvenience of tuning it manually. Equipped with the rescaled uncorrelated ridge regression with the soft label, a novel clustering method can be developed based on solving the related clustering model. Consequently, extensive experiments are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional subspace clustering method obtains explicit data representation that captures the global structure of data and clusters via the associated subspace. However, due to the limitation of intrinsic linearity and fixed structure, the advantages of prior structure are limited. To address this problem, in this brief, we embed the structured graph learning with adaptive neighbors into the deep autoencoder networks such that an adaptive deep clustering approach, namely, autoencoder constrained clustering with adaptive neighbors (ACC_AN), is developed. The proposed method not only can adaptively investigate the nonlinear structure of data via a parameter-free graph built upon deep features but also can iteratively strengthen the correlations among the deep representations in the learning process. In addition, the local structure of raw data is preserved by minimizing the reconstruction error. Compared to the state-of-the-art works, ACC_AN is the first deep clustering method embedded with the adaptive structured graph learning to update the latent representation of data and structured deep graph simultaneously. [ABSTRACT FROM AUTHOR]

Hashing offers a desirable and effective solution for efficiently retrieving the nearest neighbors from large-scale data because of its low storage and computation costs. One of the most appealing techniques for hashing learning is matrix factorization. However, most hashing methods focus only on building the mapping relationships between the Euclidean and Hamming spaces and, unfortunately, underestimate the naturally sparse structures of the data. In addition, parameter tuning is always a challenging and head-scratching problem for sparse hashing learning. To address these problems, in this article, we propose a novel hashing method termed adaptively sparse matrix factorization hashing (SMFH), which exploits sparse matrix factorization to explore the parsimonious structures of the data. Moreover, SMFH adopts an orthogonal transformation to minimize the quantization loss while deriving the binary codes. The most distinguished property of SMFH is that it is adaptive and parameter-free, that is, SMFH can automatically generate sparse representations and does not require human involvement to tune the regularization parameters for the sparse models. Empirical studies on four publicly available benchmark data sets show that the proposed method can achieve promising performance and is competitive with a variety of state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Video summarization is the technique to condense large-scale videos into summaries composed of key-frames or key-shots so that the viewers can browse the video content efficiently. Recently, supervised approaches have achieved great success by taking advantages of recurrent neural networks (RNNs). Most of them focus on generating summaries by maximizing the overlap between the generated summary and the ground truth. However, they neglect the most critical principle, i.e., whether the viewer can infer the original video content from the summary. As a result, existing approaches cannot preserve the summary quality well and usually demand large amounts of training data to reduce overfitting. In our view, video summarization has two tasks, i.e., generating summaries from videos and inferring the original content from summaries. Motivated by this, we propose a dual learning framework by integrating the summary generation (primal task) and video reconstruction (dual task) together, which targets to reward the summary generator under the assistance of the video reconstructor. Moreover, to provide more guidance to the summary generator, two property models are developed to measure the representativeness and diversity of the generated summary. Practically, experiments on four popular data sets (SumMe, TVsum, OVP, and YouTube) have demonstrated that our approach, with compact RNNs as the summary generator, using less training data, and even in the unsupervised setting, can get comparable performance with those supervised ones adopting more complex summary generators and trained on more annotated data. [ABSTRACT FROM AUTHOR]

Unsupervised feature selection is fundamentally important for processing unlabeled high-dimensional data, and several methods have been proposed on this topic. Most existing embedded unsupervised methods just emphasize the data structure in the input space, which may contain large noise. Therefore, they are limited to perceive the discriminative information implied within the low-dimensional manifold. In addition, these methods always involve several parameters to be tuned, which is time-consuming. In this paper, we present a self-tuned discrimination-aware (STDA) approach for unsupervised feature selection. The main contributions of this paper are threefold: 1) it adopts the advantage of discriminant analysis technique to select the valuable features; 2) it learns the local data structure adaptively in the discriminative subspace to alleviate the effect of data noise; and 3) it performs feature selection and clustering simultaneously with an efficient optimization strategy, and saves the additional efforts to tune parameters. Experimental results on a toy data set and various real-world benchmarks justify the effectiveness of STDA on both feature selection and data clustering, and demonstrate its promising performance against the state of the arts. [ABSTRACT FROM AUTHOR]

Image matting is generally modeled as a space transform from the color space to the alpha space. By estimating the alpha factor of the model, the foreground of an image can be extracted. However, there is some dimensional information redundancy in the alpha space. It usually leads to the misjudgments of some pixels near the boundary between the foreground and the background. In this paper, a manifold matting framework named Patch Alignment Manifold Matting is proposed for image matting. In particular, we first propose a part modeling of color space in the local image patch. We then perform whole alignment optimization for approximating the alpha results using subspace reconstructing error. Furthermore, we utilize Nesterov’s algorithm to solve the optimization problem. Finally, we apply some manifold learning methods in the framework, and obtain several image matting methods, such as named ISOMAP matting and its derived Cascade ISOMAP matting. The experimental results reveal that the manifold matting framework and its two examples are effective when compared with several representative matting methods. [ABSTRACT FROM AUTHOR]

k nearest neighbor (kNN) method is a popular classification method in data mining and statistics because of its simple implementation and significant classification performance. However, it is impractical for traditional kNN methods to assign a fixed k value (even though set by experts) to all test samples. Previous solutions assign different $k$ values to different test samples by the cross validation method but are usually time-consuming. This paper proposes a kTree method to learn different optimal $k$ values for different test/new samples, by involving a training stage in the kNN classification. Specifically, in the training stage, kTree method first learns optimal $k$ values for all training samples by a new sparse reconstruction model, and then constructs a decision tree (namely, kTree) using training samples and the learned optimal $k$ values. In the test stage, the kTree fast outputs the optimal $k$ value for each test sample, and then, the kNN classification can be conducted using the learned optimal $k$ value and all training samples. As a result, the proposed kTree method has a similar running cost but higher classification accuracy, compared with traditional kNN methods, which assign a fixed k value to all test samples. Moreover, the proposed kTree method needs less running cost but achieves similar classification accuracy, compared with the newly kNN methods, which assign different k values to different test samples. This paper further proposes an improvement version of kTree method (namely, k*Tree method) to speed its test stage by extra storing the information of the training samples in the leaf nodes of kTree, such as the training samples located in the leaf nodes, their kNNs, and the nearest neighbor of these kNNs. We call the resulting decision tree as k*Tree, which enables to conduct kNN classification using a subset of the training samples in the leaf nodes rather than all training samples used in the newly kNN methods. This actually reduces running cost of test stage. Finally, the experimental results on 20 real data sets showed that our proposed methods (i.e., kTree and k*Tree) are much more efficient than the compared methods in terms of classification tasks. [ABSTRACT FROM PUBLISHER]

Person reidentification usually refers to matching people in different camera views in nonoverlapping multicamera networks. Many existing methods learn a similarity measure by projecting the raw feature to a latent subspace to make the same target’s distance smaller than different targets’ distances. However, the same targets captured in different camera views should hold the same intrinsic attributes while different targets should hold different intrinsic attributes. Projecting all the data to the same subspace would cause loss of such an information and comparably poor discriminability. To address this problem, in this paper, a method based on elastic projections is proposed to learn a pairwise similarity measure for person reidentification. The proposed model learns two projections, positive projection and negative projection, which are both representative and discriminative. The representability refers to: for the same targets captured in two camera views, the positive projection can bridge the corresponding appearance variation and represent the intrinsic attributes of the same targets, while for the different targets captured in two camera views, the negative projection can explore and utilize the different attributes of different targets. The discriminability means that the intraclass distance should become smaller than its original distance after projection, while the interclass distance becomes larger on the contrary, which is the elastic property of the proposed model. In this case, prior information of the original data space is used to give guidance for the learning phase; more importantly, similar targets (but not the same) are effectively reduced by forcing the same targets to become more similar and different targets to become more distinct. The proposed model is evaluated on three benchmark data sets, including VIPeR, GRID, and CUHK, and achieves better performance than other methods. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance. [ABSTRACT FROM PUBLISHER]

The performance of graph-based feature selection methods relies heavily on the quality of the construction of the similarity matrix. However, most of the graphs on these methods are initially fixed, where few of them are constrained. Once the graph is determined, it will remain constant in the whole optimization process. In other words, in case that the graph constructed on the raw data is not appropriate, it will drag down the entire algorithm. Aiming to tackle this defect, a novel unsupervised feature selection via adaptive graph learning and constraint (EGCFS) is proposed to select the uncorrelated yet discriminative features by exploiting the embedded graph learning and constraint. The adaptive graph learning method incorporates the structure of the similarity matrix into the optimization process, which not only learns the graph structure adaptively but also obtains the closed-form solution of the graph coefficient. Special graph constraint is embedded with the feature selection process to connect nearer data points with larger probability. The idea of maximizing between-class scatter matrix and the adaptive graph structure is integrated into a uniform framework to obtain excellent structural performance. Moreover, the proposed embedded graph constraint not only performs with manifold structure but also validates the link between graph-based approach and $k$ -means from a unique perspective. Experiments on several benchmark data sets verify the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Existing image reconstruction methods frequently improve their robustness by using various nonsquared loss functions, which are still potentially sensitive to the outliers. More specifically, when certain samples in data sets encounter severe contamination, these methods cannot identify and filter out the ill ones, and thus lead to the functional degeneration of the associated models. To address this issue, we propose a general framework, named robust and sparse weight learning (RSWL), to compute the adaptive weights based on an objective for robustness and sparsity. More importantly, the degree of the sparsity is steerable, such that only $k$ well-reserved samples are activated during the optimization of our model. As a result, the severely polluted or damaged samples are eliminated, and the robustness is ensured. The framework is further leveraged against a 2-D image reconstruction task. Theoretical analysis and extensive experiments are presented to demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

For large-scale image retrieval task, a hashing technique has attracted extensive attention due to its efficient computing and applying. By using the hashing technique in image retrieval, it is crucial to generate discrete hash codes and preserve the neighborhood ranking information simultaneously. However, both related steps are treated independently in most of the existing deep hashing methods, which lead to the loss of key category-level information in the discretization process and the decrease in discriminative ranking relationship. In order to generate discrete hash codes with notable discriminative information, we integrate the discretization process and the ranking process into one architecture. Motivated by this idea, a novel ranking optimization discrete hashing (RODH) method is proposed, which directly generates discrete hash codes (e.g., +1/−1) from raw images by balancing the effective category-level information of discretization and the discrimination of ranking information. The proposed method integrates convolutional neural network, discrete hash function learning, and ranking function optimizing into a unified framework. Meanwhile, a novel loss function based on label information and mean average precision (MAP) is proposed to preserve the label consistency and optimize the ranking information of hash codes simultaneously. Experimental results on four benchmark data sets demonstrate that RODH can achieve superior performance over the state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

This paper examines a matrix-regularized multiple kernel learning (MKL) technique based on a notion of $(r,~p)$ norms. For the problem of learning a linear combination in the support vector machine-based framework, model complexity is typically controlled using various regularization strategies on the combined kernel weights. Recent research has developed a generalized $\ell _{p}$ -norm MKL framework with tunable variable $p$ ($p\ge 1$) to support controlled intrinsic sparsity. Unfortunately, this “1-D” vector $\ell _{p}$ -norm hardly exploits potentially useful information on how the base kernels “interact.” To allow for higher order kernel-pair relationships, we extend the “1-D” vector $\ell _{p}$ -MKL to the “2-D” matrix $(r,~p)$ norms ($1\le r,~p<\infty $). We develop a new formulation and an efficient optimization strategy for $(r,~p)$ -MKL with guaranteed convergence. A theoretical analysis and experiments on seven UCI data sets shed light on the superiority of $(r,~p)$ -MKL over $\ell _{p}$ -MKL in various scenarios. [ABSTRACT FROM AUTHOR]

In this brief, a novel self-weighted orthogonal linear discriminant analysis (SOLDA) problem is proposed, and a self-weighted supervised discriminative feature selection (SSD-FS) method is derived by introducing sparsity-inducing regularization to the proposed SOLDA problem. By using the row-sparse projection, the proposed SSD-FS method is superior to multiple sparse feature selection approaches, which can overly suppress the nonzero rows such that the associated features are insufficient for selection. More specifically, the orthogonal constraint ensures the minimal number of selectable features for the proposed SSD-FS method. In addition, the proposed feature selection method is able to harness the discriminant power such that the discriminative features are selected. Consequently, the effectiveness of the proposed SSD-FS method is validated theoretically and experimentally. [ABSTRACT FROM AUTHOR]

Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on \ell 2 -norm and \ell 2,1 -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time. [ABSTRACT FROM AUTHOR]

In this paper, we mainly focus on how to achieve the translated subspace representation for each class, which could simultaneously indicate the distribution of the associated class and the differences from its complementary classes. By virtue of the reconstruction problem, the class-specific subspace classifier (CSSC) problem could be represented as a series of biobjective optimization problems, which minimize and maximize the reconstruction errors of the related class and its complementary classes, respectively. Besides, the regularization term is specifically introduced to ensure the whole system’s stability. Accordingly, a regularized class-specific subspace classifier (RCSSC) method can be further proposed based on solving a general quadratic ratio problem. The proposed RCSSC method consistently converges to the global optimal subspace and translation under the variations of the regularization parameter. Furthermore, the proposed RCSSC method could be extended to the unregularized case, which is known as unregularized CSSC (UCSSC) method via orthogonal decomposition technique. As a result, the effectiveness and the superiority of both proposed RCSSC and UCSSC methods can be verified analytically and experimentally. [ABSTRACT FROM PUBLISHER]

Finding a consensus embedding from multiple views is the mainstream task in multiview graph-based clustering, in which the key problem is to handle the inconsistence among multiple views. In this article, we consider clustering effectiveness and practical applicability collectively, and propose a parameter-free model to alleviate the inconsistence of multiple views cleverly. To be specific, the proposed model considers the diversities of multiple views as two-layers. The first layer considers the inconsistence among different features of each view and the second layer considers linking the preembeddings of multiple views attentively. By this way, a consensus embedding can be learned via kernel method effectively and the whole learning procedure is parameter-free. To solve the optimization problem involved in the proposed model, we propose an alternative algorithm which is efficient and easy to implement in practice. In the experiments, we evaluate the proposed model on synthetic and real datasets and the experimental results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Traditional machine learning and pattern recognition techniques are intimately linked to the notion of feature spaces. Adopting this view, each object is described in terms of a vector of numerical attributes and is, therefore, mapped to a point in a Euclidean (geometric) vector space, so that the distances between the points reflect the observed (dis)similarities between the respective objects. This kind of representation is attractive because geometric spaces offer powerful analytical as well as computational tools that are simply not available in other representations. Indeed, classical machine learning methods are tightly related to geometrical concepts, and numerous powerful tools have been developed during the last few decades, starting from the maximal likelihood method in the 1920s to perceptrons in the 1960s and, more recently, to kernel machines and deep learning architectures. [ABSTRACT FROM PUBLISHER]

Regular machine learning and data mining techniques study the training data for future inferences under a major assumption that the future data are within the same feature space or have the same distribution as the training data. However, due to the limited availability of human labeled training data, training data that stay in the same feature space or have the same distribution as the future data cannot be guaranteed to be sufficient enough to avoid the over-fitting problem. In real-world applications, apart from data in the target domain, related data in a different domain can also be included to expand the availability of our prior knowledge about the target future data. Transfer learning addresses such cross-domain learning problems by extracting useful information from data in a related domain and transferring them for being used in target tasks. In recent years, with transfer learning being applied to visual categorization, some typical problems, e.g., view divergence in action recognition tasks and concept drifting in image classification tasks, can be efficiently solved. In this paper, we survey state-of-the-art transfer learning algorithms in visual categorization applications, such as object recognition, image classification, and human action recognition. [ABSTRACT FROM PUBLISHER]

Remote sensing image scene classification has attracted great attention because of its wide applications. Although convolutional neural network (CNN)-based methods for scene classification have achieved excellent results, the large-scale variation of the features and objects in remote sensing images limits the further improvement of the classification performance. To address this issue, we present multiscale representation for scene classification, which is realized by a global–local two-stream architecture. This architecture has two branches of the global stream and local stream, which can individually extract the global features and local features from the whole image and the most important area. In order to locate the most important area in the whole image using only image-level labels, a weakly supervised key area detection strategy of structured key area localization (SKAL) is specially designed to connect the above two streams. To verify the effectiveness of the proposed SKAL-based two-stream architecture, we conduct comparative experiments based on three widely used CNN models, including AlexNet, GoogleNet, and ResNet18, on four public remote sensing image scene classification data sets, and achieve the state-of-the-art results on all the four data sets. Our codes are provided in https://github.com/hw2hwei/SKAL. [ABSTRACT FROM AUTHOR]

Feature extraction is the first and most critical step in image classification. Most existing image classification methods use hand-crafted features, which are not adaptive for different image domains. In this paper, we develop an evolutionary learning methodology to automatically generate domain-adaptive global feature descriptors for image classification using multiobjective genetic programming (MOGP). In our architecture, a set of primitive 2-D operators are randomly combined to construct feature descriptors through the MOGP evolving and then evaluated by two objective fitness criteria, i.e., the classification error and the tree complexity. After the entire evolution procedure finishes, the best-so-far solution selected by the MOGP is regarded as the (near-)optimal feature descriptor obtained. To evaluate its performance, the proposed approach is systematically tested on the Caltech-101, the MIT urban and nature scene, the CMU PIE, and Jochen Triesch Static Hand Posture II data sets, respectively. Experimental results verify that our method significantly outperforms many state-of-the-art hand-designed features and two feature learning techniques in terms of classification accuracy. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) has been widely used as the technique of feature exaction. However, LDA may be invalid to address the data from different domains. The reasons are as follows: 1) the distribution discrepancy of data may disturb the linear transformation matrix so that it cannot extract the most discriminative feature and 2) the original design of LDA does not consider the unlabeled data so that the unlabeled data cannot take part in the training process for further improving the performance of LDA. To address these problems, in this brief, we propose a novel transferable LDA (TLDA) method to extend LDA into the scenario in which the data have different probability distributions. The whole learning process of TLDA is driven by the philosophy that the data from the same subspace have a low-rank structure. The matrix rank in TLDA is the key learning criterion to conduct local and global linear transformations for restoring the low-rank structure of data from different distributions and enlarging the distances among different subspaces. In doing so, the variations of distribution discrepancy within the same subspace can be reduced, i.e., data can be aligned well and the maximally separated structure can be achieved for the data from different subspaces. A simple projected subgradient-based method is proposed to optimize the objective of TLDA, and a strict theory proof is provided to guarantee a quick convergence. The experimental evaluation on public data sets demonstrates that our TLDA can achieve better classification performance and outperform the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Feature representation learning, an emerging topic in recent years, has achieved great progress. Powerful learned features can lead to excellent classification accuracy. In this article, a selective and robust feature representation framework with a supervised constraint (SRSC) is presented. SRSC seeks a selective, robust, and discriminative subspace by transforming the original feature space into the category space. Particularly, we add a selective constraint to the transformation matrix (or classifier parameter) that can select discriminative dimensions of the input samples. Moreover, a supervised regularization is tailored to further enhance the discriminability of the subspace. To relax the hard zero-one label matrix in the category space, an additional error term is also incorporated into the framework, which can lead to a more robust transformation matrix. SRSC is formulated as a constrained least square learning (feature transforming) problem. For the SRSC problem, an inexact augmented Lagrange multiplier method (ALM) is utilized to solve it. Extensive experiments on several benchmark data sets adequately demonstrate the effectiveness and superiority of the proposed method. The proposed SRSC approach has achieved better performances than the compared counterpart methods. [ABSTRACT FROM AUTHOR]

Many modern clustering models can be divided into two separated steps, i.e., constructing a similarity graph (SG) upon samples and partitioning each sample into the corresponding cluster based on SG. Therefore, learning a reasonable SG has become a hot issue in the clustering field. Many previous works that focus on constructing better SG have been proposed. However, most of them follow an ideal assumption that the importance of different features is equal, which is not adapted in practical applications. To alleviate this problem, this article proposes a self-weighted clustering with adaptive neighbors (SWCAN) model that can assign weights for different features, learn an SG, and partition samples into clusters simultaneously. In experiments, we observe that the SWCAN can assign weights for different features reasonably and outperform than comparison clustering models on synthetic and practical data sets. [ABSTRACT FROM AUTHOR]

In this article, the recursive problems of both orthogonal linear discriminant analysis (OLDA) and orthogonal least squares regression (OLSR) are investigated. Different from other works, the associated recursive problems are addressed via a novel recursive regression method, which achieves the dimensionality reduction in the orthogonal complement space heuristically. As for the OLDA, an efficient method is developed to obtain the associated optimal subspace, which is closely related to the orthonormal basis of the optimal solution to the ridge regression. As for the OLSR, the scalable subspace is introduced to build up an original OLSR with optimal scaling (OS). Through further relaxing the proposed problem into a convex parameterized orthogonal quadratic problem, an effective approach is derived, such that not only the optimal subspace can be achieved but also the OS could be obtained automatically. Accordingly, two supervised dimensionality reduction methods are proposed via obtaining the heuristic solutions to the recursive problems of the OLDA and the OLSR. [ABSTRACT FROM AUTHOR]

Since multiple criteria can be adopted to estimate the similarity among the given data points, problem regarding diverse representations of pairwise relations is brought about. To address this issue, a novel self-adaptive multimeasure (SAMM) fusion problem is proposed, such that different measure functions can be adaptively merged into a unified similarity measure. Different from other approaches, we optimize similarity as a variable instead of presetting it as a priori, such that similarity can be adaptively evaluated based on integrating various measures. To further obtain the associated subspace representation, a graph-based dimensionality reduction problem is incorporated into the proposed SAMM problem, such that the related subspace can be achieved according to the unified similarity. In addition, sparsity-inducing $\ell _{2,0}$ regularization is introduced, such that a sparse projection is obtained for efficient feature selection (FS). Consequently, the SAMM-FS method can be summarized correspondingly. [ABSTRACT FROM AUTHOR]

Given a training set of face photo-sketch pairs, face sketch synthesis targets at learning a mapping from the photo domain to the sketch domain. Despite the exciting progresses made in the literature, it retains as an open problem to synthesize high-quality sketches against blurs and deformations. Recent advances in generative adversarial training provide a new insight into face sketch synthesis, from which perspective the existing synthesis pipelines can be fundamentally revisited. In this paper, we present a novel face sketch synthesis method by multidomain adversarial learning (termed MDAL), which overcomes the defects of blurs and deformations toward high-quality synthesis. The principle of our scheme relies on the concept of “interpretation through synthesis.” In particular, we first interpret face photographs in the photodomain and face sketches in the sketch domain by reconstructing themselves respectively via adversarial learning. We define the intermediate products in the reconstruction process as latent variables, which form a latent domain. Second, via adversarial learning, we make the distributions of latent variables being indistinguishable between the reconstruction process of the face photograph and that of the face sketch. Finally, given an input face photograph, the latent variable obtained by reconstructing this face photograph is applied for synthesizing the corresponding sketch. Quantitative comparisons to the state-of-the-art methods demonstrate the superiority of the proposed MDAL method. [ABSTRACT FROM AUTHOR]

Random projection is a popular machine learning algorithm, which can be implemented by neural networks and trained in a very efficient manner. However, the number of features should be large enough when applied to a rather large-scale data set, which results in slow speed in testing procedure and more storage space under some circumstances. Furthermore, some of the features are redundant and even noisy since they are randomly generated, so the performance may be affected by these features. To remedy these problems, an effective feature selection method is introduced to select useful features hierarchically. Specifically, a novel criterion is proposed to select useful neurons for neural networks, which establishes a new way for network architecture design. The testing time and accuracy of the proposed method are improved compared with traditional methods and some variations on both classification and regression tasks. Extensive experiments confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified model called flexible affinity matrix learning (FAML) for unsupervised and semisupervised classification by exploiting both the relationship among data and the clustering structure simultaneously. To capture the relationship among data, we exploit the self-expressiveness property of data to learn a structured matrix in which the structures are induced by different norms. A rank constraint is imposed on the Laplacian matrix of the desired affinity matrix, so that the connected components of data are exactly equal to the cluster number. Thus, the clustering structure is explicit in the learned affinity matrix. By making the estimated affinity matrix approximate the structured matrix during the learning procedure, FAML allows the affinity matrix itself to be adaptively adjusted such that the learned affinity matrix can well capture both the relationship among data and the clustering structure. Thus, FAML has the potential to perform better than other related methods. We derive optimization algorithms to solve the corresponding problems. Extensive unsupervised and semisupervised classification experiments on both synthetic data and real-world benchmark data sets show that the proposed FAML consistently outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Spectral clustering has been widely used in various aspects, especially the machine learning fields. Clustering with similarity matrix and low-dimensional representation of data is the main reason of its promising performance shown in spectral clustering. However, such similarity matrix and low-dimensional representation directly derived from input data may not always hold when the data are high dimensional and has complex distribution. First, the similarity matrix simply based on the distance measurement might not be suitable for all kinds of data. Second, the low-dimensional representation might not be able to reflect the manifold structure of the original data. In this brief, we propose a novel linear space embedded clustering method, which uses adaptive neighbors to address the above-mentioned problems. Linearity regularization is used to make the data representation a linear embedded spectral. We also use adaptive neighbors to optimize the similarity matrix and clustering results simultaneously. Extensive experimental results show promising performance compared with the other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Most existing object detection algorithms are trained based upon a set of fully annotated object regions or bounding boxes, which are typically labor-intensive. On the contrary, nowadays there is a significant amount of image-level annotations cheaply available on the Internet. It is hence a natural thought to explore such “weak” supervision to benefit the training of object detectors. In this paper, we propose a novel scheme to perform weakly supervised object localization, termed object-specific pixel gradient (OPG). The OPG is trained by using image-level annotations alone, which performs in an iterative manner to localize potential objects in a given image robustly and efficiently. In particular, we first extract an OPG map to reveal the contributions of individual pixels to a given object category, upon which an iterative mining scheme is further introduced to extract instances or components of this object. Moreover, a novel average and max pooling layer is introduced to improve the localization accuracy. In the task of weakly supervised object localization, the OPG achieves a state-of-the-art 44.5% top-5 error on ILSVRC 2013, which outperforms competing methods, including Oquabet al.and region-based convolutional neural networks on the Pascal VOC 2012, with gains of 2.6% and 2.3%, respectively. In the task of object detection, OPG achieves a comparable performance of 27.0% mean average precision on Pascal VOC 2007. In all experiments, the OPG only adopts the off-the-shelf pretrained CNN model, without using any object proposals. Therefore, it also significantly improves the detection speed, i.e., achieving three times faster compared with the state-of-the-art method. [ABSTRACT FROM AUTHOR]

Feature extraction plays a significant role in pattern recognition. Recently, many representation-based feature extraction methods have been proposed and achieved successes in many applications. As an excellent unsupervised feature extraction method, latent low-rank representation (LatLRR) has shown its power in extracting salient features. However, LatLRR has the following three disadvantages: 1) the dimension of features obtained using LatLRR cannot be reduced, which is not preferred in feature extraction; 2) two low-rank matrices are separately learned so that the overall optimality may not be guaranteed; and 3) LatLRR is an unsupervised method, which by far has not been extended to the supervised scenario. To this end, in this paper, we first propose to use two different matrices to approximate the low-rank projection in LatLRR so that the dimension of obtained features can be reduced, which is more flexible than original LatLRR. Then, we treat the two low-rank matrices in LatLRR as a whole in the process of learning. In this way, they can be boosted mutually so that the obtained projection can extract more discriminative features. Finally, we extend LatLRR to the supervised scenario by integrating feature extraction with the ridge regression. Thus, the process of feature extraction is closely related to the classification so that the extracted features are discriminative. Extensive experiments are conducted on different databases for unsupervised and supervised feature extraction, and very encouraging results are achieved in comparison with many state-of-the-arts methods. [ABSTRACT FROM AUTHOR]

Network in network (NiN) is an effective instance and an important extension of deep convolutional neural network consisting of alternating convolutional layers and pooling layers. Instead of using a linear filter for convolution, NiN utilizes shallow multilayer perceptron (MLP), a nonlinear function, to replace the linear filter. Because of the powerfulness of MLP and $ 1\times 1 $ convolutions in spatial domain, NiN has stronger ability of feature representation and hence results in better recognition performance. However, MLP itself consists of fully connected layers that give rise to a large number of parameters. In this paper, we propose to replace dense shallow MLP with sparse shallow MLP. One or more layers of the sparse shallow MLP are sparely connected in the channel dimension or channel–spatial domain. The proposed method is implemented by applying unshared convolution across the channel dimension and applying shared convolution across the spatial dimension in some computational layers. The proposed method is called convolution in convolution (CiC). The experimental results on the CIFAR10 data set, augmented CIFAR10 data set, and CIFAR100 data set demonstrate the effectiveness of the proposed CiC method. [ABSTRACT FROM PUBLISHER]

Understanding the progression of chronic diseases can empower the sufferers in taking proactive care. To predict the disease status in the future time points, various machine learning approaches have been proposed. However, a few of them jointly consider the dual heterogeneities of chronic disease progression. In particular, the predicting task at each time point has features from multiple sources, and multiple tasks are related to each other in chronological order. To tackle this problem, we propose a novel and unified scheme to coregularize the prior knowledge of source consistency and temporal smoothness. We theoretically prove that our proposed model is a linear model. Before training our model, we adopt the matrix factorization approach to address the data missing problem. Extensive evaluations on real-world Alzheimer’s disease data set have demonstrated the effectiveness and efficiency of our model. It is worth mentioning that our model is generally applicable to a rich range of chronic diseases. [ABSTRACT FROM AUTHOR]

This paper develops a coarse-to-fine framework for single-image super-resolution (SR) reconstruction. The coarse-to-fine approach achieves high-quality SR recovery based on the complementary properties of both example learning-and reconstruction-based algorithms: example learning-based SR approaches are useful for generating plausible details from external exemplars but poor at suppressing aliasing artifacts, while reconstruction-based SR methods are propitious for preserving sharp edges yet fail to generate fine details. In the coarse stage of the method, we use a set of simple yet effective mapping functions, learned via correlative neighbor regression of grouped low-resolution (LR) to high-resolution (HR) dictionary atoms, to synthesize an initial SR estimate with particularly low computational cost. In the fine stage, we devise an effective regularization term that seamlessly integrates the properties of local structural regularity, nonlocal self-similarity, and collaborative representation over relevant atoms in a learned HR dictionary, to further improve the visual quality of the initial SR estimation obtained in the coarse stage. The experimental results indicate that our method outperforms other state-of-the-art methods for producing high-quality images despite that both the initial SR estimation and the followed enhancement are cheap to implement. [ABSTRACT FROM AUTHOR]

Visual feature learning, which aims to construct an effective feature representation for visual data, has a wide range of applications in computer vision. It is often posed as a problem of nonnegative matrix factorization (NMF), which constructs a linear representation for the data. Although NMF is typically parallelized for efficiency, traditional parallelization methods suffer from either an expensive computation or a high runtime memory usage. To alleviate this problem, we propose a parallel NMF method called alternating least square block decomposition (ALSD), which efficiently solves a set of conditionally independent optimization subproblems based on a highly parallelized fine-grained grid-based blockwise matrix decomposition. By assigning each block optimization subproblem to an individual computing node, ALSD can be effectively implemented in a MapReduce-based Hadoop framework. In order to cope with dynamically varying visual data, we further present an incremental version of ALSD, which is able to incrementally update the NMF solution with a low computational cost. Experimental results demonstrate the efficiency and scalability of the proposed methods as well as their applications to image clustering and image retrieval. [ABSTRACT FROM PUBLISHER]

For regression-based single-image super-resolution (SR) problem, the key is to establish a mapping relation between high-resolution (HR) and low-resolution (LR) image patches for obtaining a visually pleasing quality image. Most existing approaches typically solve it by dividing the model into several single-output regression problems, which obviously ignores the circumstance that a pixel within an HR patch affects other spatially adjacent pixels during the training process, and thus tends to generate serious ringing artifacts in resultant HR image as well as increase computational burden. To alleviate these problems, we propose to use structured output regression machine (SORM) to simultaneously model the inherent spatial relations between the HR and LR patches, which is propitious to preserve sharp edges. In addition, to further improve the quality of reconstructed HR images, a nonlocal (NL) self-similarity prior in natural images is introduced to formulate as a regularization term to further enhance the SORM-based SR results. To offer a computation-effective SORM method, we use a relative small nonsupport vector samples to establish the accurate regression model and an accelerating algorithm for NL self-similarity calculation. Extensive SR experiments on various images indicate that the proposed method can achieve more promising performance than the other state-of-the-art SR methods in terms of both visual quality and computational cost. [ABSTRACT FROM PUBLISHER]

Spatial pyramid matching is a standard architecture for categorical image retrieval. However, its performance is largely limited by the prespecified rectangular spatial regions when pooling local descriptors. In this paper, we propose to learn object-shaped and directional receptive fields for image categorization. In particular, different objects in an image are seamlessly constructed by superpixels, while the direction captures human gaze shifting path. By generating a number of superpixels in each image, we construct graphlets to describe different objects. They function as the object-shaped receptive fields for image comparison. Due to the huge number of graphlets in an image, a saliency-guided graphlet selection algorithm is proposed. A manifold embedding algorithm encodes graphlets with the semantics of training image tags. Then, we derive a manifold propagation to calculate the postembedding graphlets by leveraging visual saliency maps. The sequentially propagated graphlets constitute a path that mimics human gaze shifting. Finally, we use the learned graphlet path as receptive fields for local image descriptor pooling. The local descriptors from similar receptive fields of pairwise images more significantly contribute to the final image kernel. Thorough experiments demonstrate the advantage of our approach. [ABSTRACT FROM PUBLISHER]

It has been widely acknowledged that learning- and reconstruction-based super-resolution (SR) methods are effective to generate a high-resolution (HR) image from a single low-resolution (LR) input. However, learning-based methods are prone to introduce unexpected details into resultant HR images. Although reconstruction-based methods do not generate obvious artifacts, they tend to blur fine details and end up with unnatural results. In this paper, we propose a new SR framework that seamlessly integrates learning- and reconstruction-based methods for single image SR to: 1) avoid unexpected artifacts introduced by learning-based SR and 2) restore the missing high-frequency details smoothed by reconstruction-based SR. This integrated framework learns a single dictionary from the LR input instead of from external images to hallucinate details, embeds nonlocal means filter in the reconstruction-based SR to enhance edges and suppress artifacts, and gradually magnifies the LR input to the desired high-quality SR result. We demonstrate both visually and quantitatively that the proposed framework produces better results than previous methods from the literature. [ABSTRACT FROM AUTHOR]