Incremental Nonnegative Tucker Decomposition with Block-Coordinate Descent and Recursive Approaches

Abstract

Nonnegative Tucker decomposition (NTD) is a robust method used for nonnegative multilinear feature extraction from nonnegative multi-way arrays. The standard version of NTD assumes that all of the observed data are accessible for batch processing. However, the data in many real-world applications are not static or are represented by a large number of multi-way samples that cannot be processing in one batch. To tackle this problem, a dynamic approach to NTD can be explored. In this study, we extend the standard model of NTD to an incremental or online version, assuming volatility of observed multi-way data along one mode. We propose two computational approaches for updating the factors in the incremental model: one is based on the recursive update model, and the other uses the concept of the block Kaczmarz method that belongs to coordinate descent methods. The experimental results performed on various datasets and streaming data demonstrate high efficiently of both algorithmic approaches, with respect to the baseline NTD methods.