Title :
Convergence of Gradient Descent for Low-Rank Matrix Approximation
Author :
Pitaval, Renaud-Alexandre ; Wei Dai ; Tirkkonen, Olav
Author_Institution :
Dept. of Commun. & Networking, Aalto Univ., Aalto, Finland
Abstract :
This paper provides a proof of global convergence of gradient search for low-rank matrix approximation. Such approximations have recently been of interest for large-scale problems, as well as for dictionary learning for sparse signal representations and matrix completion. The proof is based on the interpretation of the problem as an optimization on the Grassmann manifold and Fubiny-Study distance on this space.
Keywords :
approximation theory; convergence of numerical methods; gradient methods; learning (artificial intelligence); matrix algebra; search problems; signal representation; Fubiny-Study distance; Grassmann manifold; dictionary learning; global gradient descent convergence; large-scale problems; low-rank matrix approximation; matrix completion; sparse signal representations; Approximation algorithms; Approximation methods; Convergence; Hafnium; Manifolds; Optimized production technology; Sparse matrices; Dimensionality reduction; Grassmann manifold; gradient descent; low-rank matrix; optimization;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2015.2448695
