Search Machine Learning Repository: Coordinate-descent for learning orthogonal matrices through Givens rotations
Authors: Uri Shalit and Gal Chechik
Conference: Proceedings of the 31st International Conference on Machine Learning (ICML-14)
Year: 2014
Pages: 548-556
Abstract: Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinate-descent in Euclidean spaces. It is based on {\em Givens-rotations}, a fast-to-compute operation that affects a small number of entries in the learned matrix, and preserves orthogonality. We show two applications of this approach: an algorithm for tensor decompositions used in learning mixture models, and an algorithm for sparse-PCA. We study the parameter regime where a Givens rotation approach converges faster and achieves a superior model on a genome-wide brain-wide mRNA expression dataset.
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