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In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel objective function named Low-Rank Representation (LRR), which seeks(More)
The problem of recognizing actions in realistic videos is challenging yet absorbing owing to its great potentials in many practical applications. Most previous research is limited due to the use of simplified action databases under controlled environments or focus on excessively localized features without sufficiently encapsulating the spatio-temporal(More)
Given nonlinear measurements y<sub>k</sub> = |&#x2329;a<sub>k</sub>, x&#x232A;| for k = 1,...,m, is it possible to recover x &#x2208; &#x2102;<sup>n</sup>? This generalized phase retrieval (GPR) problem is a fundamental task in various disciplines. Natural nonconvex methods often work remarkably well for GPR in practice, but lack clear theoretical(More)
Current research on visual action/activity analysis has mostly exploited appearance-based static feature descriptions, plus statistics of short-range motion fields. The deliberate ignorance of dense, long-duration motion trajectories as features is largely due to the lack of mature mechanism for efficient extraction and quantitative representation of visual(More)
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group)\footnote{Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional structural data such as those (approximately) lying on subspaces\footnote{We follow~\cite{liu2010robust} and use the(More)
Is it possible to find the sparsest vector (direction) in a generic subspace S &#x2286; &#x211D;<sup>p</sup> with dim(S) = n &lt;; p? This problem can be considered a homogeneous variant of the sparse recovery problem and finds connections to sparse dictionary learning, sparse PCA, and many other problems in signal processing and machine learning. In this(More)
We consider the problem of recovering a complete (i.e., square and invertible) matrix <inline-formula> <tex-math notation="LaTeX">$ A_{0}$ </tex-math></inline-formula>, from <inline-formula> <tex-math notation="LaTeX">$ Y \in \mathbb R ^{n \times p}$ </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">$ Y = A_{0} X_{0}$(More)
We consider the problem of recovering a complete (i.e., square and invertible) matrix <inline-formula> <tex-math notation="LaTeX">$ A_{0}$ </tex-math></inline-formula>, from <inline-formula> <tex-math notation="LaTeX">$ Y \in \mathbb R ^{n \times p}$ </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">$Y = \boldsymbol A_{0} X_{0}$(More)
Visual vocabulary construction is an integral part of the popular Bag-of-Features (BOF) model. When visual data scale up (in terms of the dimensionality of features or/and the number of samples), most existing algorithms (e.g. k-means) become unfavorable due to the prohibitive time and space requirements. In this paper we propose the random locality(More)
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete applications such as dictionary learning, generalized phase retrieval, and orthogonal tensor decomposition are known to induce(More)