Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates

Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic nonnegative matrix factorization (NMF) to extract short-lived temporal motifs from a long time series. Prior work has typically fit this model by multiplicative parameter updatesan approach widely considered to be suboptimal for NMF, especially in large-scale data applications. Here, we describe how to extend two popular and computationally scalable NMF algorithmsHierarchical Alternating Least Squares (HALS) and Alternatining Nonnegative Least Squares (ANLS)for the CNMF model. Both methods demonstrate performance advantages over multiplicative updates on large-scale synthetic and real world data.