CorrIndex: a permutation invariant performance index

Elaheh Sobhani (1, 2) , Pierre Comon (1) , Christian Jutten (3) , Massoud Babaie-Zadeh (2)

1 GIPSA-GAIA - GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes
2 SUT - Sharif University of Technology [Tehran]
3 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing

Permutation and scale ambiguity are relevant issues in tensor decomposition and source separation algorithms. Although these ambiguities are inevitable when working on real data sets, it is preferred to eliminate these uncertainties for evaluating algorithms on synthetic data sets. The existing methods and measures for this purpose are either greedy and unreliable or computationally costly. In this paper, we propose a new performance index, called CorrIndex, whose reliability can be proved theoretically. Moreover, compared to the previous methods and measures, it has the lowest computational cost. By providing two theorems and a table of comparisons, we will show these advantages of CorrIndex compared to other measures.

Mots clés: Assignment; Bipartite graph; Blind Source Separation; ICA; Permutation ambiguity; Tensor decomposition; Hungarian algorithm; Optimal transport; Performance index

Domaines: Traitement du signal et de l'image [eess.SP]

Elaheh Sobhani, Pierre Comon, Christian Jutten, Massoud Babaie-Zadeh. CorrIndex: a permutation invariant performance index. Signal Processing, 2022, 195, pp.108457. ⟨10.1016/j.sigpro.2022.108457⟩. ⟨hal-03230210v2⟩