Dictionary Learning for Massive Matrix Factorization

Abstract

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factoriza-tion method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.

Cited by in corpus (8)

• Tensor Methods in Computer Vision and Deep Learning
• Online Nonnegative Matrix Factorization with Outliers
• Scalable Online Convolutional Sparse Coding
• Stochastic Subsampling for Factorizing Huge Matrices
• Recursive nearest agglomeration (ReNA): fast clustering for approximation of structured signals
• Fast shared response model for fMRI data
• Distributed rank-1 dictionary learning: Towards fast and scalable solutions for fMRI big data analytics
• Probabilistic sequential matrix factorization