We consider the problem of identifying a switched nonlinear system from a finite collection of input-output data. The constituent subsystems of such a switched system are all nonlinear systems. We model each individual subsystem as a sparse expansion over a dictionary of elementary nonlinear smooth functions shaped by the whole available dataset. Estimating the switched model from data is a doubly challenging problem. First one needs, without any knowledge of the parameters, to decide which subsystem is active at which time instant. Second, the representation of each nonlinear subsystem over the considered basis shall be performed in a high dimensional space. We tackle both tasks simultaneously by sparse optimization. More specifically, we view the switched nonlinear system identification problem as the problem of minimizing the 0 norm of an error vector. We subsequently relax it into an 1 convex minimization problem for which powerful numerical tools exist.
The goal of the paper is to present a new on-line human recognition system, which is able to classify persons with adaptive abilities using an incremental classifier. The proposed incremental SVM is fast, as its training periodrely on only few images and it uses the mathematical properties of SVM to update only the needed parts. In our system, first of all, feature extraction and selection are implemented, based on color and texture features (appearance of the person). Then the incremental SVM classifier has been introduced to recognize a person from a set of 20 persons in CASIA Gait Database. The proposed incremental classifier is updated step by step when a new frame including a person is presented. With this technique, we achieved a correct classification rate of 98.46%, knowing only 5% of the dataset at the beginning of the experiment. A comparison with a non-incremental technique reaches recognition rate of 99% on the same database. Extended analyses have been carried out and showed that the proposed method can be adapted to on-line setting.
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