Multivariate Scale-free dynamics: Testing Fractal Connectivity

Sébastien Combrexelle (1) , Herwig Wendt (1, 2) , Gustavo Didier (3) , Patrice Abry (4)

1 IRIT-SC - Signal et Communications
2 CNRS - Centre National de la Recherche Scientifique
3 Tulane University
4 ENS de Lyon - École normale supérieure de Lyon

Scale-free dynamics commonly appear in individual components of multivariate data. Yet, while the behavior of cross-components is crucial in modeling real-world multivariate data, their examination often suggests departures from exact multivariate self-similarity (also termed fractal connectivity). The present paper introduces a multivariate Gaussian stochastic process with Hadamard (i.e., entry-wise) self-similar scale-free dynamics, controlled by a matrix Hurst parameter H, that allows departures from fractal connectivity. The properties of its wavelet coefficients and wavelet spectrum are studied, enabling the estimation of H and of the fractal connectivity parameter. Furthermore, it permits the computation of closed-form confidence intervals for the estimates based on approximate (wavelet) covariances. Finally, these developments enable us to devise a test for fractal connectivity. Monte Carlo simulations are used to assess the accuracy of the proposed approximate confidence intervals and the performance of the fractal connectivity test.

Mots clés: Hypothesis testing; Multivariate self-similarity; Fractal connectivity; Wavelet spectrum

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Sébastien Combrexelle, Herwig Wendt, Gustavo Didier, Patrice Abry. Multivariate Scale-free dynamics: Testing Fractal Connectivity. 42nd IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), Mar 2017, New Orleans, United States. pp.3984-3988. ⟨hal-01912795⟩