Journal ArticleDOI
Robust principal component analysis
Reads0
Chats0
TLDR
In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.Abstract:
This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individuallyq We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.read more
Citations
More filters
Journal ArticleDOI
Principal component analysis: a review and recent developments
TL;DR: The basic ideas of PCA are introduced, discussing what it can and cannot do, and some variants of the technique have been developed that are tailored to various different data types and structures.
Book
Proximal Algorithms
Neal Parikh,Stephen Boyd +1 more
TL;DR: The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided.
Journal ArticleDOI
Robust Recovery of Subspace Structures by Low-Rank Representation
TL;DR: It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, it is proved that under certain conditions LRR can exactly recover the row space of the original data.
Journal ArticleDOI
A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography
Oleg Kuybeda,Gabriel A. Frank,Alberto Bartesaghi,Mario J. Borgnia,Sriram Subramaniam,Guillermo Sapiro +5 more
TL;DR: The genetic identity of each virus particle present in the mixture can be assigned based solely on the structural information derived from single envelope glycoproteins displayed on the virus surface by the nuclear norm-based, collaborative alignment method presented here.
Journal ArticleDOI
Exact matrix completion via convex optimization
TL;DR: In this paper, a convex programming problem is used to find the matrix with the minimum nuclear norm that is consistent with the observed entries in a low-rank matrix, which is then used to recover all the missing entries from most sufficiently large subsets.
References
More filters
Journal ArticleDOI
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.
Book
Principal Component Analysis
TL;DR: In this article, the authors present a graphical representation of data using Principal Component Analysis (PCA) for time series and other non-independent data, as well as a generalization and adaptation of principal component analysis.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Journal ArticleDOI
A global geometric framework for nonlinear dimensionality reduction.
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Journal ArticleDOI
Indexing by Latent Semantic Analysis
TL;DR: A new method for automatic indexing and retrieval to take advantage of implicit higher-order structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries.