DAO-CP: Data-Adaptive Online CP decomposition for tensor stream.

Abstract

How can we accurately and efficiently decompose a tensor stream? Tensor decomposition is a crucial task in a wide range of applications and plays a significant role in latent feature extraction and estimation of unobserved entries of data. The problem of efficiently decomposing tensor streams has been of great interest because many real-world data dynamically change over time. However, existing methods for dynamic tensor decomposition sacrifice the accuracy too much, which limits their usages in practice. Moreover, the accuracy loss becomes even more serious when the tensor stream has an inconsistent temporal pattern since the current methods cannot adapt quickly to a sudden change in data. In this paper, we propose DAO-CP, an accurate and efficient online CP decomposition method which adapts to data changes. DAO-CP tracks local error norms of the tensor streams, detecting a change point of the error norms. It then chooses the best strategy depending on the degree of changes to balance the trade-off between speed and accuracy. Specifically, DAO-CP decides whether to (1) reuse the previous factor matrices for the fast running time or (2) discard them and restart the decomposition to increase the accuracy. Experimental results show that DAO-CP achieves the state-of-the-art accuracy without noticeable loss of speed compared to existing methods.