Conditions of Optimal Classification for Piecewise Affine Regression

Ferrari-Trecate, Giancarlo; Schinkel, M.

doi:10.1007/3-540-36580-x_16

Cited by 11 publications

(6 citation statements)

References 7 publications

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“…Examples of such works include, in the case of switched linear models, the algebraic-geometric method [32,21,30], the product-of-errors based method [18]. Other methods such as the mixed integer programming approach [27], the bounded-error approach [3], the bayesian learning based procedure [17], the clusteringbased strategies [13,14,22,4] apply to piecewise affine systems, i.e., particular switched linear/affine systems where the switching surfaces are the faces of a set of non-overlapping polyhedra. An excellent survey can be found in [25] where most of the methods developed prior to 2007 have been summarized.…”

Section: Prior Workmentioning

confidence: 99%

Identification of switched linear systems via sparse optimization

2011

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The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we present here a sparse optimization approach inspired by very recent developments from the community of compressed sensing. We formally pose the problem of identifying each submodel as a combinatorial ℓ0 optimization problem. This is indeed an NP-hard problem which can interestingly, as shown by recent literature, be relaxed into a (convex) ℓ1-norm minimization problem. We present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating-submodels. Some simulation results are included to support the potentialities of the proposed method.

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Section: Prior Workmentioning

confidence: 99%

Identification of switched linear systems via sparse optimization

2011

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“…HIT implements the clustering-based algorithms described in (Ferrari-Trecate et al, 2001bFerrari-Trecate and Schinkel, 2003). In addition, HIT provides facilities for plotting and validating the identified models.…”

Section: Implementation As Matlab Toolboxmentioning

confidence: 99%

Automated piecewise power-law modeling of biological systems

Machina

Ponosov²,

Voit

2010

Journal of Biotechnology

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“…The identification of PWA models can be performed in the input/output or the state-space form. Ferrari-Trecate and Schinkel (2003) proposed an identification algorithm by clustering parameter vectors, each of which is locally estimated using the nearest neighobors of each data point. Ragot et al (2003) proposed a method for identifying the parameters of submodels by choosing an adapted weighting function, which allows one to select the data for which each submodel is active.…”

Section: Identification Of Pwa Modelsmentioning

confidence: 99%