Subspace Classifier in the Hilbert Space

To improve the performance of the subspace classifier, it is effective to reduce the dimensionality of the intersections between subspaces. For this purpose, the feature space is mapped implicitly to the infinite dimensional Hilbert space and the subspace classifier is applied in the Hilbert space. Keywords. Pattern Recognition, Subspace Classifier, Hilbert Space, Kernel Functions, Support Vector Machine 1 Introduction The subspace classifier is the pattern recognition method that uses a linear subspace for describing a class (Oja, 1983). In training, a subspace is fit to training samples so that the sum of the squared distances between the samples and the subspace is minimized. In classifying an unlabeled sample, the sample is classified to the class whose subspace is the nearest. The subspace classifier was developed in the early days of pattern recognition study, but nowadays it is still in focus (Deshuang, 1996; Prakesh and Murty, 1996, 1997). It is known that the performance ..