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Tensor sparse coding for Positive Definite Matrices

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2014年第3期36卷 592-605页

作者： Sivalingam, Ravishankar Boley, Daniel Morellas, Vassilios Papanikolopoulos, Nikolaos Univ Minnesota Dept Comp Sci & Engn Minneapolis MN 55455 USA

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

关键词： sparse coding positive definite matrices region covariance descriptors computer vision optimization

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Modeling receptive fields with non-negative sparse coding

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NEUROCOMPUTING 2003年 52-4卷 547-552页

作者： Hoyer, PO Aalto Univ Neural Networks Res Ctr FIN-02015 Espoo Finland

An important approach in visual neuroscience considers how the processing of the early visual system is dependent on the statistics of the natural environment. A particularly influential model in this respect has been sparse coding. In this paper we argue for a non-negative variant of the model. This is based partly on neurophysiological grounds and partly on the intuitive understanding of parts-based representations. We discuss the logic behind our reasoning and show experiments on natural images demonstrating the usefulness of the new model. (C) 2003 Elsevier Science B.V. All rights reserved.

关键词： natural image statistics sparse coding non-negative representations

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Local and global regularized sparse coding for data representation

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NEUROCOMPUTING 2016年第PartA期175卷 188-197页

作者： Shu, Zhenqiu Zhou, Jun Huang, Pu Yu, Xun Yang, Zhangjing Zhao, Chunxia Jiangsu Univ Technol Sch Comp Engn Changzhou 213001 Peoples R China Griffith Univ Sch Informat & Commun Technol Nathan Qld 4111 Australia Nanjing Univ Posts & Telecommun Sch Comp Sci & Technol Nanjing 210023 Jiangsu Peoples R China Nanjing Audit Univ Sch Technol Nanjing 211815 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Jiangsu Peoples R China

Recently, sparse coding has been widely adopted for data representation in real-world applications. In order to consider the geometric structure of data, we propose a novel method, local and global regularized sparse coding (LGSC), for data representation. LGSC not only models the global geometric structure by a global regression regularizer, but also takes into account the manifold structure using a local regression regularizer. Compared with traditional sparse coding methods, the proposed method can preserve both global and local geometric structures of the original high-dimensional data in a new representation space. Experimental results on benchmark datasets show that the proposed method can improve the performance of clustering. (C) 2015 Elsevier B.V. All rights reserved.

关键词： sparse coding Data representation Regularizer Regression Clustering

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Non-negative and local sparse coding based on l2-norm and Hessian regularization

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INFORMATION SCIENCES 2019年 486卷 88-100页

作者： Zhang, Jinghui Wan, Yuan Chen, Zhiping Meng, Xiaojing Wuhan Univ Technol Sch Sci Wuhan 430070 Hubei Peoples R China

Due to the efficiency of representing visual data and reducing dimension of complex structure, methods of sparse coding have been widely investigated and achieved ideal performance in image classification. These sparse coding methods learn both a dictionary and the sparse codes from the original data together under the constraint to l(1)-norm. However, the introduction of( )l(1)-norm tends to choose small number of atoms from the relevant bases in process of dictionary learning, abandoning other high-related bases, which results in the neglect of group effect and weak generalization of the model. In this paper, we propose a novel sparse coding model which introduces the l(2)-norm constraint and the second-order Hessian energy in the optimization function. This model eliminates the restrictions on the number of selected base vectors in the dictionary learning, and makes better use of the topological structure information as well, thus the intrinsic geometric characteristics of the data is described more accurately. In addition, our model is extended with a non-negative local constraint, which ensures similar features to share their local bases. Extensive experimental results on the real-world datasets show that the proposed model extraordinarily outperforms several state-of-the-art image representative methods. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Hessian regularization Elastic net model sparse coding Image classification

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Notions of associative memory and sparse coding

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NEURAL NETWORKS 1996年第8期9卷 1429-1458页

作者： Okada, M Osaka UniversityJapan

This paper summarizes associative memory models and sparse representation of memory in these models. Important properties of the associative memory models are their storage capacity, basin of attraction, and the existence of spurious memories. sparse coding and nonmonotonic output functions are proposed to improve them. sparsely coded associative memory model has an extremely large storage capacity which diverges as the mean firing rate of memory patterns approaches 0. The storage capacity strongly depends on the shape of the output function as well as the mean firing rate, even in the case of monotonic output functions. Dynamical properties of the model are analyzed by means of a statistical neurodynamical method. We emphasize the necessity of a feedback mechanism to control the mean firing rate in the recall process. Recently, there have been some experimental results suggesting its existence in the brain. On the other hand, it has been shown that the storage capacity can be markedly improved by replacing the usual monotonic output function with a nonmonotonic one. Another remarkable property of the model with the nonmonotonic neurons is that it seems to have no, or almost no, spurious memory. An associative memory model using nonmonotonic modules with a feedforward inhibition is discussed. The modules consist of two types of threshold units, each of which has a different threshold and can be considered as a biologically plausible representation of the nonmonotonic output function. The above model is compared with the monotonic one. The difference in the storage capacity between the two models becomes small when the sparse patterns are stored. Finally, we discuss the biological plausibility of the discussed associative memory models and sparse coding. Copyright (C) 1996 Elsevier Science Ltd.

关键词： associative memory sparse coding nonmonotonic output function storage capacity basin of attraction

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Discriminative multi-scale sparse coding for single-sample face recognition with occlusion

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PATTERN RECOGNITION 2017年 66卷 302-312页

作者： Yu, Yu-Feng Dai, Dao-Qing Ren, Chuan-Xian Huan, Ke-Kun Sun Yat Sen Univ Intelligent Data Ctr Guangzhou 510275 Guangdong Peoples R China Sun Yat Sen Univ Dept Math Guangzhou 510275 Guangdong Peoples R China JiaYing Univ Sch Math Meizhou 514015 Guangdong Peoples R China

The single sample per person (SSPP) face recognition is a major problem and it is also an important challenge for practical face recognition systems due to the lack of sample data information. To solve SSPP problem, some existing methods have been proposed to overcome the effect of variances to test samples in illumination, expression and pose. However, they are not robust when the test samples are with different kinds of occlusions. In this paper, we propose a discriminative multi-scale sparse coding (DMSC) model to address this problem. We model the possible occlusion variations via the learned dictionary from the subjects not of interest. Together with the single training sample per person, most of types of occlusion variations can be effectively tackled. In order to detect and disregard outlier pixels due to occlusion, we develop a multi-scale error measurements strategy, which produces sparse, robust and highly discriminative coding. Extensive experiments on the benchmark databases show that our DMSC is more robust and has higher breakdown point in dealing with the SSPP problem for face recognition with occlusion as compared to the related state-of-the-art methods.

关键词： Face recognition Multi-scale Intra-class variant sparse coding Outlier pixels

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Graph regularized sparse coding for 3D shape clustering

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KNOWLEDGE-BASED SYSTEMS 2016年第Jan.15期92卷 92-103页

作者： Ben Hamza, A. Concordia Univ Concordia Inst Informat Syst Engn Montreal PQ Canada

Feature descriptors have become an increasingly important tool in shape analysis. Features can be extracted and subsequently used to design robust signatures for shape retrieval, correspondence, classification and clustering. In this paper, we present a graph-theoretic framework for 3D shape clustering using the biharmonic distance map and graph regularized sparse coding. While this work focuses primarily on clustering, our approach is fairly general and can be used to tackle other 3D shape analysis problems. In order to seamlessly capture the similarity between feature descriptors, we perform shape clustering on mid-level features that are generated via graph regularized sparse coding. Extensive experiments are carried out on three standard 3D shape benchmarks to demonstrate the much better performance of the proposed clustering approach in comparison with recent state-of-the-art methods. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Clustering Laplace-Beltrami Biharmonic distance sparse coding

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Reducing covariate factors of gait recognition using feature selection and dictionary-based sparse coding

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SIGNAL IMAGE AND VIDEO PROCESSING 2017年第6期11卷 1131-1138页

作者： Alotaibi, Munif Mahmood, Ausif Univ Bridgeport Bridgeport CT 06604 USA

Human gait recognition is a behavioral biometrics method that aims to determine the identity of individuals through the manner and style of their distinctive walk. It is still a very challenging problem because natural human gait is affected by many covariate factors such as changes in the clothing, variations in viewing angle, and changes in carrying condition. This paper evaluates the most important features of gait under the carrying and clothing conditions. We find that the intra-class variations of the features that remain static during the gait cycle affect the recognition accuracy adversely. Thus, we introduce an effective and robust feature selection method based on the gait energy image. The new gait representation is less sensitive to these covariate factors. We also propose an augmentation technique to overcome some of the problems associated with the intra-class gait fluctuations, as well as if the amount of the training data is relatively small. Finally, we use dictionary learning with sparse coding and linear discriminant analysis to seek the best discriminative data representation before feeding it to the Nearest Centroid classifier. When our method is applied on the large CASIA-B gait data set, we are able to outperform existing gait methods by achieving the highest average result.

关键词： Gait recognition sparse coding Augmentation Dictionary learning Feature selection

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Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency

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NEURAL NETWORKS 2017年 89卷 84-96页

作者： Zhang, Ying-Ying Yang, Cai Zhang, Ping Nanyang Normal Univ Phys & Elect Engn Coll Nanyang 473061 Peoples R China Nanyang Normal Univ Comp & Informat Technol Coll Nanyang 473061 Peoples R China

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods - highlight-inhibition function, contextbased saliency weighting, and the graph cut - are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Log-Euclidean kernel sparse coding Region covariance Saliency

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Multi -view image clustering based on sparse coding and manifold consensus

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NEUROCOMPUTING 2020年 403卷 53-62页

作者： Zhu, Xiaofei Guo, Jiafeng Nejdl, Wolfgang Liao, Xiangwen Dietze, Stefan Chongqing Univ Technol Coll Comp Sci & Engn Chongqing 400054 Peoples R China Chinese Acad Sci Inst Comp Technol Beijing 100190 Peoples R China Leibniz Univ Hannover L3S Res Ctr D-30167 Hannover Germany Fuzhou Univ Coll Math & Comp Sci Fuzhou 350108 Peoples R China Leibniz Inst Social Sci Knowledge Technol Social Sci D-50667 Cologne Germany

Multi-view clustering has received an increasing attention in many applications, where different views of objects can provide complementary information to each other. Existing approaches on multi-view clustering mainly focus on extending Non-negative Matrix Factorization (NMF) by enforcing the constraint over the coefficient matrices from different views in order to preserve their consensus. In this paper, we argue that it is more reasonable to utilize the high-level manifold consensus rather than the low-level coefficient matrix consensus (as conducted in state-of-the-art approaches) to better capture the underlying clustering structure of the data. For this purpose, we propose MMRSC (Multiple Manifold Regularized sparse coding), which aims to preserve the consensus over multiple manifold structures from different views. Experimental results on two publicly available real-world image datasets demonstrate that our proposed approach can significantly outperform the state-of-the-art approaches for the multi-view image clustering task. Moreover, we also conduct computational complexity analysis and the result shows that MMRSC can effective handle the multi-view clustering problem without increasing the computational cost as compared to GraphSC.

关键词： Multi-view clustering sparse coding Manifold consensus

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