CorrIndex: A permutation invariant performance index.

• Critical survey of existing performance indices. • Introduce an index, called CorrIndex, whose reliability is proved theoretically. • Provides interpretable upper and lower bounds, with a low computational cost. • Possible applications include Blind Source Separation or Tensor Decompositions. Permutation and scaling ambiguities 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. As shown in the paper, the existing performance indices 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 previous performance indices, it has a low computational cost. Theoretical results and computer experiments demonstrate these advantages of CorrIndex compared to other indices. [ABSTRACT FROM AUTHOR]