The core consistency of a compressed tensor
This work addresses a fundamental requirement for efficient big data tensor decomposition, but it is incremental as it builds on existing heuristics like core consistency.
The paper tackles the problem of ensuring low-rank tensor structure is preserved after compression in tensor decomposition methods, providing theoretical conditions and experimental validation for preserving core consistency.
Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize computations. A fundamental requirement for such methods to work properly is that the low-rank tensor structure is retained upon compression. In lieu of efficient and realistic means of computing and studying the effects of compression on the low rank of a tensor, we study the effects of compression on the core consistency; a widely used heuristic that has been used as a proxy for estimating that low rank. We provide theoretical analysis, where we identify sufficient conditions for the compression such that the core consistency is preserved, and we conduct extensive experiments that validate our analysis. Further, we explore popular compression schemes and how they affect the core consistency.