NORMO: A new method for estimating the number of components in CP tensor decomposition

Abstract

Tensor decompositions are multi-way analysis tools which have been successfully applied in a wide range of different fields. However, there are still challenges that remain few explored, namely the following: when applying tensor decomposition techniques, what should we expect from the result? How can we evaluate its quality? It is expected that, when the number of components is suitable, then few redundancy is observed in the decomposition result. Based on this assumption, we propose a new method, NORMO, which aims at estimating the number of components in CANDECOMP/PARAFAC (CP) decomposition so that no redundancy is observed in the result. To the best of our knowledge, this work encompasses the first attempt to tackle such problem. According to our experiments, the number of non-redundant components estimated by NORMO is among the most accurate estimates of the true CP number of components in both synthetic and real-world tensor datasets (thus validating the rationale guiding our method). Moreover, NORMO is more efficient than most of its competitors. Additionally, our method can be used to discover multi-levels of granularity in the patterns discovered.