Parametrization of linear systems using diffusion kernels

Ronen Talmon, Dan Kushnir, Ronald R. Coifman, Israel Cohen, Sharon Gannot

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Modeling natural and artificial systems has played a key role in various applications and has long been a task that has drawn enormous efforts. In this work, instead of exploring predefined models, we aim to identify implicitly 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 model 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 practical examples has shown accurate recovery of parameters.

Original languageEnglish
Article number6094236
Pages (from-to)1159-1173
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2012

Bibliographical note

Funding Information:
Manuscript received May 20, 2011; revised September 21, 2011; accepted November 10, 2011. Date of publication December 02, 2011; date of current version February 10, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Z. Jane Wang. This research was supported by the Israel Science Foundation (Grant 1130/11).


  • Kernel
  • linear systems
  • modeling
  • multidimensional signal processing
  • non-parametric estimation
  • nonlinear dynamical systems
  • system identification


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