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Robust Recovery of Subspace Structures by Low-Rank Representation
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 theirExpand
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A geometric analysis of phase retrieval
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A Geometric Analysis of Phase Retrieval
  • Ju Sun, Qing Qu, J. Wright
  • Mathematics, Computer Science
  • IEEE International Symposium on Information…
  • 22 February 2016
TLDR
We prove that when the measurement vectors $$\varvec{a}_k$$ak’s are generic (i.e., length-n complex vector) and numerous enough, a natural least-squares formulation for GPR has the following benign geometric structure. Expand
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Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture
TLDR
We give the first efficient algorithm that provably recovers a complete (i.e., square and invertible) matrix from a nonconvex optimization problem with a spherical constraint that is highly structured with high probability. Expand
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Hierarchical spatio-temporal context modeling for action recognition
TLDR
The problem of recognizing actions in realistic videos is challenging yet absorbing owing to its great potentials in many practical applications. Expand
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Finding a Sparse Vector in a Subspace: Linear Sparsity Using Alternating Directions
TLDR
In this paper, we focus on a planted sparse model for the subspace: the target sparse vector is embedded in an otherwise random subspace. Expand
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When Are Nonconvex Problems Not Scary?
TLDR
We focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) the objective has a negative directional curvature. Expand
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Complete Dictionary Recovery Over the Sphere II: Recovery by Riemannian Trust-Region Method
TLDR
We consider the problem of recovering a complete (i.e., square and invertible) matrix <inline-formula> <tex-math notation="LaTeX">$ A_{0}$ from arbitrary initializations using a Riemannian trust region algorithm. Expand
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Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees
TLDR
Low-Rank Representation with Positive Semi Definite constraint, or LRR-PSD, can be solved in an exquisite scheme efficiently instead of general-purpose SDP solvers that usually scale up poorly. Expand
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Complete dictionary recovery over the sphere
  • Ju Sun, Qing Qu, J. Wright
  • Mathematics, Computer Science
  • International Conference on Sampling Theory and…
  • 25 April 2015
TLDR
We consider the problem of recovering a complete (i.e., square and invertible) dictionary A0, from Y = A0X0 with Y ϵ Rn×p. Expand
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