Conference paper
Linear program differentiation for single-channel speech separation
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.
Language: | English |
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Publisher: | IEEE |
Year: | 2006 |
Pages: | 421-426 |
Proceedings: | 2006 16th IEEE Workshop on Machine Learning for Signal Processing |
ISBN: | 1424406560 , 9781424406562 , 1424406579 and 9781424406579 |
ISSN: | 21610363 and 15512541 |
Types: | Conference paper |
DOI: | 10.1109/MLSP.2006.275587 |
Dictionaries Equations Gradient methods Informatics Linear programming Mathematical model Signal processing algorithms Sparse matrices Speech enhancement Vectors constraint matrix differentiation gradient methods gradient optimisation linear program differentiation linear programming matrix algebra signal processing signal representation single-channel speech separation sparse representation speaker identification task speaker recognition