Fast, robust and non-convex subspace recovery
نویسندگان
چکیده
منابع مشابه
Fast, Robust and Non-convex Subspace Recovery
This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer to as Fast Median Subspace (FMS), is designed to robustly determine the underl...
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We present a mathematical analysis of a non-convex energy landscape for Robust Subspace Recovery. We prove that an underlying subspace is the only stationary point and local minimizer in a large neighborhood if a generic condition holds for a dataset. We further show that if the generic condition is satisfied, a geodesic gradient descent method over the Grassmannian manifold can exactly recover...
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A remarkably simple, yet powerful, algorithm termed Coherence Pursuit for robust Principal Component Analysis (PCA) is presented. In the proposed approach, an outlier is set apart from an inlier by comparing their coherence with the rest of the data points. As inliers lie in a low dimensional subspace, they are likely to have strong mutual coherence provided there are enough inliers. By contras...
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We study Robust Subspace Recovery (RSR) in distributed settings. We consider a huge data set in an ad hoc network without a central processor, where each node has access only to one chunk of the data set. We assume that part of the whole data set lies around a low-dimensional subspace and the other part is composed of outliers that lie away from that subspace. The goal is to recover the underly...
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We consider a fundamental problem in unsupervised learning called subspace recovery: given a collection of m points in Rn, if many but not necessarily all of these points are contained in a d-dimensional subspace T can we find it? The points contained in T are called inliers and the remaining points are outliers. This problem has received considerable attention in computer science and in statis...
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ژورنال
عنوان ژورنال: Information and Inference: A Journal of the IMA
سال: 2017
ISSN: 2049-8764,2049-8772
DOI: 10.1093/imaiai/iax012