Distributed geometric nonnegativematrix factorization and hierarchical alternating least squares–based nonnegative tensor factorization with theMapReduce paradigm

摘要

Nonnegativematrix factorization and its multilinear extension known as nonnegative tensor factorization are commonly used methods in machine learning and data analysis for feature extraction and dimensionality reduction for nonnegative high-dimensional data. Dimensionality reduction for massive amountsofdatausually involves distributed computation acrossmulti-node computer architectures. In this study, we propose various computational strategies for parallel and distributed computation of the latent factors in both factorizationmodels, all of which are based on partitioning the computational tasks according to the MapReduce paradigm. We extend the previously reported distributed hierarchical alternating least squares algorithm to the multi-way array factorizationmodel,where we assume that the observedmulti-way data can be partitioned into chunks along one mode. Moreover, we propose a new geometry-based distributed computational strategy for solving nonnegative matrix factorization problems. Numerical experiments performed using various large-scale data sets demonstrated that these algorithms are efficient and robust to noisy data.