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Linear program differentiation for single-channel speech separation

Pearlmutter, Barak A. and Olsson, Rasmus K. (2006) Linear program differentiation for single-channel speech separation. In: Proceedings of the 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, 6th - 8th September, 2006, Arlington, VA .

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Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver. For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single-channel speech separation task, leading to 5 dB and 8 dB target-to-interference ratio improvements for same-gender and opposite-gender mixtures, respectively. Furthermore, the dictionaries are successfully applied to a speaker identification task.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Copyright Notice "©2006 IEEE. Reprinted from Proceedings of the 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."
Keywords: Differentiation; Gradient methods; Linear programming; Matrix algebra; Signal representation; Speaker recognition; Constraint matrix; Gradient optimisation; Linear program differentiation; Linear programming; Signal processing; Single-channel speech separation; Sparse representation; Speaker identification task.
Academic Unit: Faculty of Science and Engineering > Computer Science
Item ID: 1376
Depositing User: Barak Pearlmutter
Date Deposited: 18 May 2009 14:41
Refereed: Yes

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