Online CP Decomposition for Sparse Tensors

Abstract

Tensor decomposition techniques such as CANDECOMP/PARAFAC (CP) decomposition have achieved great success across a range of scientific fields. They have been traditionally applied to dense, static data. However, today's datasets are often highly sparse and dynamically changing over time. Traditional decomposition methods such as Alternating Least Squares (ALS) cannot be easily applied to sparse tensors, due to poor efficiency. Furthermore, existing online tensor decomposition methods mostly target dense tensors, and thus also encounter significant scalability issues for sparse data. To address this gap, we propose a new incremental algorithm for tracking the CP decompositions of online sparse tensors on-the-fly. Experiments on nine real-world datasets show that our algorithm is able to produce quality decompositions of comparable quality to the most accurate algorithm, ALS, whilst at the same time achieving speed improvements of up to 250 times and 100 times less memory.