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160
Sparse Representation or Collaborative Representation: Which Helps Face Recognition?
"... As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to th ..."
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Cited by 107 (16 self)
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As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l1-norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.
Stable principal component pursuit
- In Proc. of International Symposium on Information Theory
, 2010
"... We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such as videos and hyperspectral images, as well as in the analys ..."
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Cited by 94 (3 self)
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We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises in compressed sensing of structured high-dimensional signals such as videos and hyperspectral images, as well as in the analysis of transformation invariant low-rank structure recovery. We analyze the performance of the natural convex heuristic for solving this problem, under the assumption that measurements are chosen uniformly at random. We prove that this heuristic exactly recovers low-rank and sparse terms, provided the number of observations exceeds the number of intrinsic degrees of freedom of the component signals by a polylogarithmic factor. Our analysis introduces several ideas that may be of independent interest for the more general problem of compressed sensing and decomposing superpositions of multiple structured signals. 1
Robust visual tracking via multi-task sparse learning
- In IEEE conference on computer vision and pattern recognition
, 2012
"... In this paper, we formulate object tracking in a particle filter framework as a multi-task sparse learning problem, which we denote as Multi-Task Tracking (MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each ..."
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Cited by 53 (6 self)
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In this paper, we formulate object tracking in a particle filter framework as a multi-task sparse learning problem, which we denote as Multi-Task Tracking (MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each particle is considered a single task in MTT. By employing popular sparsity-inducing ℓp,q mixed norms (p ∈ {2, ∞} and q = 1), we regularize the representation problem to enforce joint sparsity and learn the particle representations together. As compared to previous methods that handle particles independently, our results demonstrate that mining the interdependencies between particles improves tracking performance and overall computational complexity. Interestingly, we show that the popular L1 tracker [15] is a special case of our MTT formulation (denoted as the L11 tracker) when p = q = 1. The learning problem can be efficiently solved using an Accelerated Proximal Gradient (APG) method that yields a sequence of closed form updates. As such, MTT is computationally attractive. We test our proposed approach on challenging sequences involving heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that MTT methods consistently outperform state-of-the-art trackers. 1.
Linearized Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming
, 2011
"... Abstract. Recently, we have proposed to combine the alternating direction method (ADM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions w ..."
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Cited by 38 (4 self)
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Abstract. Recently, we have proposed to combine the alternating direction method (ADM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show that the decomposed subproblems in the ADM procedure can be substantially alleviated by linearizing the involved quadratic terms arising from the augmented Lagrangian penalty on the model’s linear constraints. When the resolvent operators of the separable functions in the objective have closedform representations, embedding the linearization into the ADM subproblems becomes necessary to yield easy subproblems with closed-form solutions. We thus show theoretically that the blend of ADM, Gaussian back substitution and linearization works effectively for the separable convex minimization model under consideration.
Sparse Bayesian methods for low-rank matrix estimation. arXiv:1102.5288v1 [stat.ML
, 2011
"... Abstract—Recovery of low-rank matrices has recently seen significant ..."
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Cited by 28 (11 self)
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Abstract—Recovery of low-rank matrices has recently seen significant
The Direct Extension of ADMM for Multi-block Convex Minimization Problems is Not Necessarily Convergent
, 2013
"... Abstract. The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend ADMM directly to the case of a multi-block convex min ..."
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Cited by 26 (2 self)
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Abstract. The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of more than two separable convex functions. However, the convergence of this extension has been missing for a long time — neither affirmatively proved convergence nor counter example showing its failure of convergence is known in the literature. In this paper we answer this long-standing open question: the direct extension of ADMM is not necessarily convergent. We present an example showing its failure of convergence, and a sufficient condition ensuring its convergence.
Matrix completion for multi-label image classification
- In NIPS
"... Abstract Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this set ..."
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Cited by 22 (3 self)
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Abstract Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this setting, classification of testing data is posed as a problem of completing unknown label entries on a data matrix that concatenates training and testing features with training labels. We propose two convex algorithms for matrix completion based on a Rank Minimization criterion specifically tailored to visual data, and prove its convergence properties. A major advantage of our approach w.r.t. standard discriminative classification methods for image categorization is its robustness to outliers, background noise and partial occlusions both in the feature and label space. Experimental validation on several datasets shows how our method outperforms state-of-the-art algorithms, while effectively capturing semantic concepts of classes.
Low-rank sparse learning for robust visual tracking
- In ECCV
, 2012
"... Abstract. In this paper, we propose a new particle-filter based tracking algorithm that exploits the relationship between particles (candidate targets). By representing particles as sparse linear combinations of dictionary templates, this algorithm capitalizes on the inherent low-rank structure of p ..."
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Cited by 18 (4 self)
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Abstract. In this paper, we propose a new particle-filter based tracking algorithm that exploits the relationship between particles (candidate targets). By representing particles as sparse linear combinations of dictionary templates, this algorithm capitalizes on the inherent low-rank structure of particle representations that are learned jointly. As such, it casts the tracking problem as a low-rank matrix learning problem. This low-rank sparse tracker (LRST) has a number of attractive properties. (1) Since LRST adaptively updates dictionary templates, it can handle significant changes in appearance due to variations in illumination, pose, scale, etc. (2) The linear representation in LRST explicitly incorporates background templates in the dictionary and a sparse error term, which enables LRST to address the tracking drift problem and to be robust against occlusion respectively. (3) LRST is computationally attractive, since the low-rank learning problem can be efficiently solved as a sequence of closed form update operations, which yield a time complexity that is linear in the number of particles and the template size. We evaluate the performance of LRST by applying it to a set of challenging video sequences and comparing it to 6 popular tracking methods. Our experiments show that by representing particles jointly, LRST not only outperforms the state-of-the-art in tracking accuracy but also significantly improves the time complexity of methods that use a similar sparse linear representation model for particles [1]. 1
Robust Visual Tracking via Structured Multi-Task Sparse Learning
"... Abstract In this paper, we formulate object tracking in a particle filter framework as a structured multi-task sparse learning problem, which we denote as Structured Multi-Task Tracking (S-MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, lea ..."
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Cited by 17 (5 self)
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Abstract In this paper, we formulate object tracking in a particle filter framework as a structured multi-task sparse learning problem, which we denote as Structured Multi-Task Tracking (S-MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each particle is considered a single task in Multi-Task Tracking (MTT). By employing popular sparsity-inducing ℓp,q mixed norms (specificallyp ∈ {2, ∞} and q = 1), we regularize the representation problem to enforce joint sparsity and learn the particle representations together. As compared to previous methods that handle particles independently, our results demonstrate that mining the interdependencies between particles improves tracking Electronic supplementary material The online version of this article (doi:10.1007/s11263-012-0582-z) contains supplementary material, which is available to authorized users.
Competition on Counter Measures to 2D Facial Spoofing Attacks
- In IJCB
, 2011
"... Spoofing identities using photographs is one of the most common techniques to attack 2-D face recognition systems. There seems to exist no comparative studies of different techniques using the same protocols and data. The motivation behind this competition is to compare the performance of different ..."
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Cited by 13 (7 self)
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Spoofing identities using photographs is one of the most common techniques to attack 2-D face recognition systems. There seems to exist no comparative studies of different techniques using the same protocols and data. The motivation behind this competition is to compare the performance of different state-of-the-art algorithms on the same database using a unique evaluation method. Six different teams from universities around the world have participated in the contest. Use of one or multiple techniques from motion, texture analysis and liveness detection appears to be the common trend in this competition. Most of the algorithms are able to clearly separate spoof attempts from real accesses. The results suggest the investigation of more complex attacks. 1.
