The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

Inspired by recent work on convex formulations of clustering we investigate a new formulation of the Sparse Coding Problem. In sparse coding we attempt to simultaneously represent a sequence of data-vectors sparsely (i.e. sparse approximation) in terms of a ``code'' defined by a set of basis elements, while also finding a code that enables such an approximation. As existing alternating optimization procedures for sparse coding are theoretically prone to severe local minima problems, we propose a convex relaxation of the sparse coding problem and derive a boosting-style algorithm, that serves as a convex ``master problem'' which calls a (potentially non-convex) sub-problem to identify the next code element to add. Finally, we demonstrate the properties of our boosted coding algorithm on an image denoising task.

Keywords

Sparse Coding, Fenchel Duality, Convex Optimization, Unsupervised Learning, Image Denoising

Notes

Associated Center(s) / Consortia: Vision and Autonomous Systems Center and Field Robotics Center

Associated Project(s): CTA Robotics

Text Reference

David Bradley and J. Andrew (Drew) Bagnell, "Convex Coding," tech. report CMU-RI-TR-09-22, Robotics Institute, Carnegie Mellon University, May, 2009

BibTeX Reference

@techreport{Bradley_2009_6395,
   author = "David Bradley and J. Andrew (Drew) Bagnell",
   title = "Convex Coding",
   booktitle = "",
   institution = "Robotics Institute",
   month = "May",
   year = "2009",
   number= "CMU-RI-TR-09-22",
   address= "Pittsburgh, PA",
}

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