A bilinear formulation for vector sparsity optimization

  • Authors:

  • Dori Peleg;Ron Meir

  • Affiliations:

  • Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion, Haifa 32000, Israel;Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion, Haifa 32000, Israel

  • Venue:
  • Signal Processing
  • Year:
  • 2008

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Abstract

Sparsity plays an important role in many fields of engineering. The cardinality penalty function, often used as a measure of sparsity, is neither continuous nor differentiable and therefore smooth optimization algorithms cannot be applied directly. In this paper we present a continuous yet non-differentiable sparsity function which constitutes a tight lower bound on the cardinality function. The novelty of this approach is that we cast the problem of minimizing the new sparsity function as a problem with a bilinear objective function. We present a numerical comparison to other sparsity encouraging penalty functions for several applications. Additionally, we apply the techniques developed to minimize an objective function with a truncated hinge loss function. We present highly competitive results for all of the applications.