Core consistency diagnosis for Block Term Decomposition in rank (L_r, L_r, 1)

Code

• github.com/noramondron/btdcorcondia
  OfficialIn papernone★ 0

Abstract

Determining the underlying number of components R in tensor decompositions is challenging. Diverse techniques exist for various decompositions, notably the core consistency diagnostic (CORCONDIA) for Canonical Polyadic Decomposition (CPD). Here, we propose a model that intuitively adapts CORCONDIA for rank estimation in Block Term Decomposition (BTD) of rank (L_r, L_r, 1): BTDCORCONDIA. Our metric was tested on simulated and real-world tensor data, including assessments of its sensitivity to noise and the indeterminacy of BTD (L_r, L_r, 1). We found that selecting appropriate R and L_r led to core consistency reaching or close to 100%, and BTDCORCONDIA is efficient when the tensor has significantly more elements than the core. Our results confirm that CORCONDIA can be extended to BTD (L_r, L_r, 1), and the resulting metric can assist in the process of determining the number of components in this tensor factorisation.

Tasks

Reproductions