Parametrization of Linear Systems Using Diffusion Kernels

Ronen Talmon, Dan Kushnir, Ronald R. Coifman, Israel Cohen, Sharon Gannot
2012 IEEE Transactions on Signal Processing  
Modeling natural and artificial systems has a key role in various applications, and has long been a task that drew enormous efforts. In this work, instead of exploring predefined models, we aim at implicitly identifying the system degrees of freedom. This approach circumvents the dependency of a specific predefined model for a specific task or system, and enables a generic data-driven method to characterize a system based solely on its output observations. We claim that each system can be
more » ... system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic modeling for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and real examples has shown accurate recovery of parameters. Abstract Modeling natural and artificial systems has a key role in various applications, and has long been a task that drew enormous efforts. In this work, instead of exploring predefined models, we aim at implicitly identifying the system degrees of freedom. This approach circumvents the dependency of a specific predefined model for a specific task or system, and enables a generic data-driven method to characterize a system based solely on its output observations. We claim that each system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic modeling for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and real examples has shown accurate recovery of parameters.
doi:10.1109/tsp.2011.2177973 fatcat:eihx7lgmxrhznkft65icjtwlnq