BibTeX
@MISC{Sun_completedictionary,
author = {Ju Sun and Qing Qu and John Wright},
title = {Complete Dictionary Recovery Using Nonconvex Optimization},
year = {}
}
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Abstract
We consider the problem of recovering a complete (i.e., square and invertible) dictionary A0, from Y = A0X0 with Y ∈ Rn×p. This recovery set-ting is central to the theoretical understanding of dictionary learning. We give the first efficient al-gorithm that provably recoversA0 whenX0 has O (n) nonzeros per column, under suitable proba-bility model forX0. Prior results provide recov-ery guarantees whenX0 has only O ( n) nonze-ros per column. Our algorithm is based on non-convex optimization with a spherical constraint, and hence is naturally phrased in the language of manifold optimization. Our proofs give a geomet-ric characterization of the high-dimensional objec-tive landscape, which shows that with high prob-ability there are no spurious local minima. Ex-periments with synthetic data corroborate our the-ory. Full version of this paper is available online:
Keyphrases
prior result high prob-ability full version high-dimensional objec-tive landscape first efficient al-gorithm dictionary a0 geomet-ric characterization theoretical understanding suitable proba-bility model forx0 recovery set-ting manifold optimization spurious local minimum recov-ery guarantee whenx0 available online dictionary learning non-convex optimization spherical constraint synthetic data
