Non-linear System Identification with Composite Relevance Vector Machines

Nonlinear system identification based on relevance vector machines (RVMs) has been traditionally addressed by stacking the input and/or output regressors and then performing standard RVM regression. This letter introduces a full family of composite kernels in order to integrate the input and output information in the mapping function efficiently and hence generalize the standard approach. An improved trade-off between accuracy and sparsity is obtained in several benchmark problems. Also, the RVM yields confidence intervals for the predictions, and it is less sensitive to free parameter selectionPublicad

Kernel antenna array processing

We introduce two support vector machine (SVM)-based approaches for solving antenna problems such as beamforming, sidelobe suppression, and maximization of the signal-to-noise ratio. A basic introduction to SVM optimization is provided and a complex nonlinear SVM formulation developed to handle antenna array processing in space and time. The new optimization formulation is compared with both the minimum mean square error and the minimum variance distortionless response methods. Several examples are included to show the performance of the new approachesPublicad

Kernel-Based Framework for Multitemporal and Multisource Remote Sensing Data Classification and Change Detection

The multitemporal classification of remote sensing images is a challenging problem, in which the efficient combination of different sources of information (e.g., temporal, contextual, or multisensor) can improve the results. In this paper, we present a general framework based on kernel methods for the integration of heterogeneous sources of information. Using the theoretical principles in this framework, three main contributions are presented. First, a novel family of kernel-based methods for multitemporal classification of remote sensing images is presented. The second contribution is the development of nonlinear kernel classifiers for the well-known difference and ratioing change detection methods by formulating them in an adequate high-dimensional feature space. Finally, the presented methodology allows the integration of contextual information and multisensor images with different levels of nonlinear sophistication. The binary support vector (SV) classifier and the one-class SV domain description classifier are evaluated by using both linear and nonlinear kernel functions. Good performance on synthetic and real multitemporal classification scenarios illustrates the generalization of the framework and the capabilities of the proposed algorithms.Publicad

Learning non-linear time scales with Kernel γ-Filters

A family of kernel methods, based on the γ-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) γ-filter, but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel γ-filters. The improved performance in several application examples suggests that a more appropriate representation of signal states is achieved.Publicad

Sparse deconvolution using support vector machines

Sparse deconvolution is a classical subject in digital signal processing, having many practical applications. Support vector machine (SVM) algorithms show a series of characteristics, such as sparse solutions and implicit regularization, which make them attractive for solving sparse deconvolution problems. Here, a sparse deconvolution algorithm based on the SVM framework for signal processing is presented and analyzed, including comparative evaluations of its performance from the points of view of estimation and detection capabilities, and of robustness with respect to non-Gaussian additive noise.Publicad

Support vector machines framework for linear signal processing

This paper presents a support vector machines (SVM) framework to deal with linear signal processing (LSP) problems. The approach relies on three basic steps for model building: (1) identifying the suitable base of the Hilbert signal space in the model, (2) using a robust cost function, and (3) minimizing a constrained, regularized functional by means of the method of Lagrange multipliers. Recently, autoregressive moving average (ARMA) system identification and non-parametric spectral analysis have been formulated under this framework. The generalized, yet simple, formulation of SVM LSP problems is particularized here for three different issues: parametric spectral estimation, stability of Infinite Impulse Response filters using the gamma structure, and complex ARMA models for communication applications. The good performance shown on these different domains suggests that other signal processing problems can be stated from this SVM framework.Publicad