Distributed geometric nonnegative matrix factorization and hierarchical alternating least squares-based nonnegative tensor factorization with the MapReduce paradigm

Nonnegative matrix 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 amounts of data usually involves distributed computation across multi-node computer architectures. In this study, we propose various computational strategies for parallel and distributed computation of the latent factors in both factorization models, 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 factorization model, where we assume that the observed multi-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.