Papers › Core consistency diagnosis for Block Term Decomposition in rank (Lᵣ, Lᵣ, 1)
Core consistency diagnosis for Block Term Decomposition in rank (Lᵣ, Lᵣ, 1)
Noramon Dron, Javier Escudero
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 (Lᵣ, Lᵣ, 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 (Lᵣ, Lᵣ, 1). We found that selecting appropriate R and Lᵣ 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 (Lᵣ, Lᵣ, 1), and the resulting metric can assist in the process of determining the number of components in this tensor factorisation.
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