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Multivariate Scale-free dynamics: Testing Fractal Connectivity

Combrexelle, Sébastien and Wendt, Herwig and Didier, Gustavo and Abry, Patrice Multivariate Scale-free dynamics: Testing Fractal Connectivity. (2017) In: 42nd IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), 5 March 2017 - 9 March 2017 (New Orleans, United States).

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Official URL: http://doi.org/10.1109/ICASSP.2017.7952904

Abstract

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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:https://ieeexplore.ieee.org/document/7952904
HAL Id:hal-01912795
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Tulane University (USA)
Other partners > Université de Lyon - UDL (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:09 Oct 2018 09:48

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