BICP: Block-Incremental CP Decomposition with Update Sensitive Refinement

Shengyu Huang, K. Selçuk Candan, Maria Luisa Sapino

Abstract: With many applications relying on multi-dimensional datasets for decision making, tensors (or multi-dimensional arrays) are emerging as a popular data representation to support diverse types of data, such as sensor streams and social networks. Consequently, tensor decomposition forms the basis for many data analysis and knowledge discovery tasks, from clustering, trend detection, anomaly detection, to correlation analysis. In applications where data evolves over time and the tensor-based analysis results need to be continuously maintained, re-computation of the whole tensor decomposition with each update will cause high computational costs and incur large memory overheads. In this paper, we propose a two-phase block-incremental CP-based tensor decomposition technique, BICP, that efficiently and effectively maintains tensor decomposition results in the presence of dynamically evolving tensor data. In its first phase, instead of repeatedly conducting ALS on each sub-tensor, BICP only revises the decompositions of the tensors that contain updated data. Moreover, when updates are relatively small with respect to the block size, BICP relies on a incremental factor tracking to avoid re-decomposition the updated sub-tensor. In its second phase, BICP limits the block-centric refinement process to only those blocks that are critical given the update. Experiment results show that the proposed method significantly reduces the execution time while assuring high accuracy.