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29
Robust motion segmentation with unknown correspondences
 In ECCV. 2014
"... Abstract. Motion segmentation can be addressed as a subspace clustering problem, assuming that the trajectories of interest points are known. However, establishing point correspondences is in itself a challenging task. Most existing approaches tackle the correspondence estimation and motion segment ..."
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Abstract. Motion segmentation can be addressed as a subspace clustering problem, assuming that the trajectories of interest points are known. However, establishing point correspondences is in itself a challenging task. Most existing approaches tackle the correspondence estimation and motion segmentation problems separately. In this paper, we introduce an approach to performing motion segmentation without any prior knowledge of point correspondences. We formulate this problem in terms of Partial Permutation Matrices (PPMs) and aim to match feature descriptors while simultaneously encouraging point trajectories to satisfy subspace constraints. This lets us handle outliers in both point locations and feature appearance. The resulting optimization problem can be solved via the Alternating Direction Method of Multipliers (ADMM), where each subproblem has an efficient solution. Our experimental evaluation on synthetic and real sequences clearly evidences the benefits of our formulation over the traditional sequential approach that first estimates correspondences and then performs motion segmentation.
Robust orthonormal subspace learning: Efficient recovery of corrupted lowrank matrices
 In CVPR
, 2014
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OF THE UNIVERSITY OF MINNESOTA BY
, 2012
"... Foremost, I would like to express my sincere gratitude to my advisor Prof. Gilad Lerman for the continuous support of my Ph.D study and research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. I could no ..."
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Foremost, I would like to express my sincere gratitude to my advisor Prof. Gilad Lerman for the continuous support of my Ph.D study and research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. I could not have imagined having a better advisor and mentor for my Ph.D study. I also thank my collaborator, Dr. Arthur Szlam, for his inspiring ideas and guidance. Besides my advisor, I would like to thank the rest of my thesis committee: Prof. Fadil Santosa, Prof. Andrew Odlyzko, and Prof. Snigdhansu Chatterjee, for their encouragement, insightful comments and hard questions. My sincere thanks also go to Dr. Fatih Porikli and Dr. Hao Vu, for offering me the summer internship opportunities in their groups and leading me working on diverse exciting projects. I thank my classmates in the same research group: Guangliang Chen, Teng Zhang and Bryan Poling for the stimulating and enlightening discussions. Also I thank my great friends from the Club of Amazing Mathematics & Engineering Ladies (CAMEL)
LETTER Communicated by John Wright Active Subspace: Toward Scalable LowRank Learning
"... We address the scalability issues in lowrank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in largescale settings. Based ..."
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We address the scalability issues in lowrank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in largescale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of lowrank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming largescale NNROPs into smallscale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality. 1
Low Rank Representation on Grassmann Manifolds
"... Abstract. Lowrank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring lowdimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belo ..."
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Abstract. Lowrank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring lowdimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space into the LRR model on Grassmann manifold. The new method has many applications in computer vision tasks. The paper conducts the experiments over two real world examples, clustering handwritten digits and clustering dynamic textures. The experiments show the proposed method outperforms a number of existing methods.
Research Statement
"... My research is in the area of differential geometry, centering around various applications of integrable systems to submanifold geometries. I will first explain the overall goal of this very interdisciplinary and active field, then summarize my contributions and some ongoing and future projects. 1 ..."
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My research is in the area of differential geometry, centering around various applications of integrable systems to submanifold geometries. I will first explain the overall goal of this very interdisciplinary and active field, then summarize my contributions and some ongoing and future projects. 1
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. INVITED PAPER Cyber–Physical Security of a Smart Grid Infrastructure
"... ABSTRACT  It is often appealing to assume that existing solutions can be directly applied to emerging engineering domains. Unfortunately, careful investigation of the unique challenges presented by new domains exposes its idiosyncrasies, thus often requiring new approaches and solutions. In this pa ..."
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ABSTRACT  It is often appealing to assume that existing solutions can be directly applied to emerging engineering domains. Unfortunately, careful investigation of the unique challenges presented by new domains exposes its idiosyncrasies, thus often requiring new approaches and solutions. In this paper, we argue that the Bsmart [ grid, replacing its incredibly successful and reliable predecessor, poses a series of new security challenges, among others, that require novel approaches to the field of cyber security. We will call this new field cyber– physical security. The tight coupling between information and communication technologies and physical systems introduces new security concerns, requiring a rethinking of the commonly used objectives and methods. Existing security approaches are either inapplicable, not viable, insufficiently scalable, incompatible, or simply inadequate to address the challenges posed by highly complex environments such as the smart grid. A concerted effort by the entire industry, the research community, and the policy makers is required to achieve the vision of a secure smart grid infrastructure. KEYWORDS  Cyber–physical systems; security; smart grids I.
Group Testing
"... A strategy for active target detection suitable for the use of mobile agents in a field is presented. In particular, there is an interest in autonomous underwater vehicles. By exploiting notions from group testing, the proposed algorithm decides when to collect new samples depending on whether the m ..."
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A strategy for active target detection suitable for the use of mobile agents in a field is presented. In particular, there is an interest in autonomous underwater vehicles. By exploiting notions from group testing, the proposed algorithm decides when to collect new samples depending on whether the mobile agent perceives the sensor measurements correspond to noise or a target pattern. Under suitable assumptions about the field emanated by the target, i.e. the target signature is locally low rank in the field, one can efficiently sample the field to locate the target using O(m logm logn) samples on an n × n grid where m n is a parameter specifying the group size.
1 Reduced Lighting Matrix Construction 1.1 Search Nearby Light Nodes in Light Cut
"... While we estimate the maximum contribution of one light node, we improve the reliability of estimation by borrowing material and geometry terms from nearby cut nodes. We use bidirectional list to store the nodes on the cut. When a cut node is split, we remove it from the list and insert its two chil ..."
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While we estimate the maximum contribution of one light node, we improve the reliability of estimation by borrowing material and geometry terms from nearby cut nodes. We use bidirectional list to store the nodes on the cut. When a cut node is split, we remove it from the list and insert its two children at the same position in the cut node list. Therefore, the range search to find nearby nodes is simply to traverse in the list. The nearby indices of light node j is computed as: N (j) = k j−1∑ u=k