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See All by Looking at A Few: Sparse Modeling for Finding Representative Objects
"... We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently describes the entire dataset. We assume that each data point can be expressed as a linear combination of the representatives and formulate the problem of finding the representatives ..."
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We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently describes the entire dataset. We assume that each data point can be expressed as a linear combination of the representatives and formulate the problem of finding the representatives as a sparse multiple measurement vector problem. In our formulation, both the dictionary and the measurements are given by the data matrix, and the unknown sparse codes select the representatives via convex optimization. In general, we do not assume that the data are lowrank or distributed around cluster centers. When the data do come from a collection of lowrank models, we show that our method automatically selects a few representatives from each lowrank model. We also analyze the geometry of the representatives and discuss their relationship to the vertices of the convex hull of the data. We show that our framework can be extended to detect and reject outliers in datasets, and to efficiently deal with new observations and large datasets. The proposed framework and theoretical foundations are illustrated with examples in video summarization and image classification using representatives. 1.
SingleSample Face Recognition with Image Corruption and Misalignment via Sparse Illumination Transfer ∗
"... Singlesample face recognition is one of the most challenging problems in face recognition. We propose a novel face recognition algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corru ..."
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Singlesample face recognition is one of the most challenging problems in face recognition. We propose a novel face recognition algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required training images to one sample per class. To compensate the missing illumination information typically provided by multiple training images, a sparse illumination transfer (SIT) technique is introduced. The SIT algorithms seek additional illumination examples of face images from one or more additional subject classes, and form an illumination dictionary. By enforcing a sparse representation of the query image, the method can recover and transfer the pose and illumination information from the alignment stage to the recognition stage. Our extensive experiments have demonstrated that the new algorithms significantly outperform the existing algorithms in the singlesample regime and with less restrictions. In particular, the face alignment accuracy is comparable to that of the wellknown Deformable SRC algorithm using multiple training images; and the face recognition accuracy exceeds those of the SRC and Extended SRC algorithms using hand labeled alignment initialization. 1.
Group Model Selection Using Marginal Correlations: The Good, the Bad and the Ugly
"... Abstract — Group model selection is the problem of determining a small subset of groups of predictors (e.g., the expression data of genes) that are responsible for majority of the variation in a response variable (e.g., the malignancy of a tumor). This paper focuses on group model selection in high ..."
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Abstract — Group model selection is the problem of determining a small subset of groups of predictors (e.g., the expression data of genes) that are responsible for majority of the variation in a response variable (e.g., the malignancy of a tumor). This paper focuses on group model selection in highdimensional linear models, in which the number of predictors far exceeds the number of samples of the response variable. Existing works on highdimensional group model selection either require the number of samples of the response variable to be significantly larger than the total number of predictors contributing to the response or impose restrictive statistical priors on the predictors and/or nonzero regression coefficients. This paper provides comprehensive understanding of a lowcomplexity approach to group model selection that avoids some of these limitations. The proposed approach, termed Group Thresholding (GroTh), is based on thresholding of marginal correlations of groups of predictors with the response variable and is reminiscent of existing thresholdingbased approaches in the literature. The most important contribution of the paper in this regard is relating the performance of GroTh to a polynomialtime verifiable property of the predictors for the general case of arbitrary (random or deterministic) predictors and arbitrary nonzero regression coefficients.
SIGNAL CLASSIFICATION BASED ON BLOCKSPARSE TENSOR REPRESENTATION
"... Block sparsity was employed recently in vector/matrix based sparse representations to improve their performance in signal classification. It is known that tensor based representation has potential advantages over vector/matrix based representation in retaining the spatial distributions within the da ..."
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Block sparsity was employed recently in vector/matrix based sparse representations to improve their performance in signal classification. It is known that tensor based representation has potential advantages over vector/matrix based representation in retaining the spatial distributions within the data. In this paper, we extend the concept of block sparsity for tensor representation, and develop a new algorithm for obtaining sparse tensor representations with block structure. We show how the proposed algorithm can be used for signal classification. Experiments on face recognition are provided to demonstrate the performance of the proposed algorithm, as compared with several sparse representation based classification algorithms.
Groupinvariant Subspace Clustering
"... Abstract—In this paper we consider the problem of groupinvariant subspace clustering where the data is assumed to come from a union of groupinvariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such groupinvariant subspac ..."
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Abstract—In this paper we consider the problem of groupinvariant subspace clustering where the data is assumed to come from a union of groupinvariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such groupinvariant subspaces are also referred to as submodules. Similar to the well known Sparse Subspace Clustering approach where the data is assumed to come from a union of subspaces, we analyze an algorithm which, following a recent work [1], we refer to as Sparse Submodule Clustering (SSmC). The method is based on finding groupsparse selfrepresentation of data points. In this paper we primarily derive general conditions under which such a groupinvariant subspace identification is possible. In particular we extend the geometric analysis in [2] and in the process we identify a related problem in geometric functional analysis. I.
Sparse Illumination Learning and Transfer for SingleSample Face Recognition with Image Corruption and Misalignment
"... Abstract Singlesample face recognition is one of themost challengingproblems in face recognition.Wepropose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and i ..."
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Abstract Singlesample face recognition is one of themost challengingproblems in face recognition.Wepropose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required gallery images to one sample per class. To compensate for the missing illumination information traditionally provided by multiple gallery images, a sparse illumination learning and transfer (SILT) technique is introduced. The illumination in SILT is learned by fitting illumination examples of auxiliary face images from one or more additional subjects with a sparselyused illumination dictionary. By enforcing a sparse representation of the query image in the illumination dictionary, the SILT can effectively Communicated by Julien Mairal, Francis Bach, and Michael Elad. A preliminary version of the results was published in Zhuang et al. (2013).
Int J Comput Vis DOI 10.1007/s112630140749x Sparse Illumination Learning and Transfer for SingleSample Face Recognition with Image Corruption and Misalignment
, 2014
"... Abstract Singlesample face recognition is one of the most challenging problems in face recognition. We propose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, a ..."
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Abstract Singlesample face recognition is one of the most challenging problems in face recognition. We propose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required gallery images to one sample per class. To compensate for the missing illumination information traditionally provided by multiple gallery images, a sparse illumination learning and transfer (SILT) technique is introduced. The illumination in SILT is learned by fitting illumination examples of auxiliary face images from one or more additional subjects with a sparselyused illumination dictionary. By enforcing a sparse representation of the query image in the illumination dictionary, the SILT can effectively
BlockSparsityInduced Adaptive Filter for MultiClustering System Identification
, 2015
"... In order to improve the performance of least mean square (LMS)based adaptive filtering for identifying blocksparse systems, a new adaptive algorithm called blocksparse LMS (BSLMS) is proposed in this paper. The basis of the proposed algorithm is to insert a penalty of blocksparsity, which is a ..."
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In order to improve the performance of least mean square (LMS)based adaptive filtering for identifying blocksparse systems, a new adaptive algorithm called blocksparse LMS (BSLMS) is proposed in this paper. The basis of the proposed algorithm is to insert a penalty of blocksparsity, which is a mixed l2;0 norm of adaptive tapweights with equal group partition sizes, into the cost function of traditional LMS algorithm. To describe a blocksparse system response, we rst propose a MarkovGaussian model, which can generate a kind of system responses of arbitrary average sparsity and arbitrary average block length using given parameters. Then we present theoretical expressions of the steadystate misadjustment and transient convergence behavior of BSLMS with an appropriate group partition size for white Gaussian input data. Based on the above results, we theoretically demonstrate that BSLMS has much better convergence behavior than l0LMS with the same small level of misadjustment. Finally, numerical experiments verify that all of the theoretical analysis agrees well with simulation results in a large range of parameters.