Maya Kallas

The proliferation of kernel methods lies essentially on the kernel trick, which induces an implicit nonlinear transformation with reduced computational cost. Still, the inverse transformation is often necessary. The resolution of this so-called pre-image problem enables new fields of applications of these methods. The pre-image problem with solutions with constraints imposed by physiology are studied. The non-negativity is probably the most commonly stated constraints when dealing with natural signals and images. Non-negativity constraints on the result, as well as on the additivity of the contributions, are studied. Time series analysis according to a predictive approach is defined. Autoregressive models are developed in the transformed space, while the prediction requires solving the pre-image problem. Two kernel-based predictive models are considered: the first one is derived by solving a least-squares problem, and the second one by providing the adequate Yule-Walker equations. The classification task for electrocardiograms, in order to detect anomalies is studied. Detection and multi-class classification are explored in the light of support vector machines and self-organizing maps.

A new technique for fault diagnosis in order to estimate the fault affecting nonlinear systems, within the frame of kernel machines is evaluated. To this end, the kernel methods are combined to the PCA, the so-called kernel PCA (KPCA), to diagnose a nonlinear system. As KPCA is applied in a high dimensional feature space, it is necessary to get back to the input space where the estimation can be interpreted.We derived an iterative pre-image technique that minimizes the square prediction error and the distance between the estimation of a new measure and the one just before it.

• Signal Processing
• Features Extraction
• Pattern Recognition
• Machine Learning
• Kernel Methods
• Pre-image Problem
• Diagnosis of nonlinear systems
• Time series prediction

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