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A kernel-based approach to supervised nonparametric identification of Wiener systems

A kernel-based approach to supervised nonparametric identification of Wiener systems

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This chapter addresses the problem of nonparametric identification of Wiener systems using a Kernel-based approach. Salient features of the proposed framework are its ability to exploit both positive and negative samples, and the fact that it does not require prior knowledge of the dimension of the output of the linear subsystem. Thus, it can be considered as a generalization to dynamical systems of kernel-based nonlinear manifold embedding methods recently developed in the machine-learning field. The main result of the chapter shows that while in principle, the proposed approach results in a non-convex problem, a tractable convex relaxation can be obtained by using a combination of polynomial optimization and rank-minimization techniques. The main advantage of the proposed algorithm stems from the fact that, since it is based on kernel ideas, it uses scalar inner products of the observed data, rather than the data itself. Hence, it can comfortably handle cases involving systems with high dimensional outputs. A practical scenario where such situation arises is activity classification from video data, since here each data point is a frame in a video sequence, and hence its dimension is typically O(103) even when using low resolution videos.

Chapter Contents:

  • 2.1 Introduction and motivation
  • 2.2 Preliminaries
  • 2.2.1 Notation and definitions
  • 2.2.2 Solving polynomial optimization problems via convex optimization
  • 2.2.3 Exploiting sparsity in polynomial optimization
  • 2.3 Problem statement
  • 2.4 Maximum margin Hankel classifiers
  • 2.4.1 Further computational complexity reduction
  • 2.4.2 Exploiting sparsity
  • 2.5 Examples
  • 2.5.1 Synthetic data
  • 2.5.1.1 Performance of W as a classifier
  • 2.5.1.2 Advantages of using negative sequences during training
  • 2.5.2 Application: activity recognition from video data
  • 2.6 Conclusions
  • Acknowledgments
  • References

Inspec keywords: convex programming; video signal processing; minimisation; image resolution; covariance matrices; image classification; learning (artificial intelligence); concave programming

Other keywords: nonconvex problem; Wiener systems; rank-minimization techniques; machine-learning field; low-resolution videos; kernel ideas; tractable convex relaxation; video sequence; supervised nonparametric identification; polynomial optimization; dynamical systems; kernel-based nonlinear manifold embedding method

Subjects: Image recognition; Video signal processing; Optimisation techniques; Optimisation techniques; Interpolation and function approximation (numerical analysis); Computer vision and image processing techniques; Linear algebra (numerical analysis); Linear algebra (numerical analysis); Knowledge engineering techniques; Interpolation and function approximation (numerical analysis)

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