Convex Coding

David Bradley and J. Andrew (Drew) Bagnell
Uncertainty in Artificial Intelligence (UAI), June, 2009.

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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.

Sparse Coding, Fenchel Duality, Boosting, Unsupervised Learning, Convex Optimization

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," Uncertainty in Artificial Intelligence (UAI), June, 2009.

BibTeX Reference
   author = "David Bradley and J. Andrew (Drew) Bagnell",
   editor = "Eric Xing",
   title = "Convex Coding",
   booktitle = "Uncertainty in Artificial Intelligence (UAI)",
   month = "June",
   year = "2009",