Publisher = {JMLR Workshop and Conference Proceedings},

Title = {Coordinate-descent for learning orthogonal matrices through Givens rotations},

Url = {http://jmlr.org/proceedings/papers/v32/shalit14.pdf},

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.},

Author = {Uri Shalit and Gal Chechik},

Editor = {Tony Jebara and Eric P. Xing},

Year = {2014},

Booktitle = {Proceedings of the 31st International Conference on Machine Learning (ICML-14)},

Pages = {548-556}

}