An Efficient Algorithm for Non-Negative Matrix Factorization with Random Projections

Abstract: Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction, word embedding, recommender systems etc. In practice, however, its application is challenging for large datasets. The efficiency of NMF is constrained by long data loading times, by large memory requirements and by limited parallelization capabilities. Here we present a novel and efficient compressed NMF algorithm. Our algorithm applies a random compression scheme to drastically reduce the dimensionality of the problem, preserving well the pairwise distances between data points and inherently limiting the memory and communication load. Our algorithm supersedes existing methods in speed. Nonetheless, it matches the best non-compressed algorithms in reconstruction precision.