An Equivalence Between Sparse Approximation and Support Vector Machines
Citable URI:
http://hdl.handle.net/1721.1/7289
| Title: | An Equivalence Between Sparse Approximation and Support Vector Machines |
| Author: | Girosi, Federico |
| Issue Date: | 1997-05-01 |
| Abstract: | In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem. |
| URI: | http://hdl.handle.net/1721.1/7289 |
| Other Identifiers: | AIM-1606 CBCL-147 |
| Series/Report no.: | AIM-1606, CBCL-147 |
| Keywords: | Support Vector Machines, Sparse Approximation, Sparse Coding, Reproducing Kernel Hilbert Spaces |
Files in this item
| Files | Size | Format |
|---|---|---|
| AIM-1606.pdf | 497.4Kb | application/pdf |
| AIM-1606.ps | 305.2Kb | application/postscript |
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