Nonlinear Common Vectors for pattern classification

The Common Vector (CV) method is a linear method, which allows to discriminate between classes of data sets, such as those arising in image and word recognition. In this paper a variation of this method is introduced for finding the projection vectors of each class as elements of the intersection of the null space of that class´ covariance matrix and the range space of the covariance matrix of the pooled data. Then, a novel approach is proposed to apply the method in a nonlinearly mapped higher-dimensional feature space. In this approach, all samples are mapped to a higher-dimensional feature space using a kernel mapping, and then the modified CV method is applied in the transformed space. As a result, each class gives rise to a unique common vector. This approach guarantees a 100% recognition rate for the samples of the training set. Moreover, experiments with several test cases also show that the generalization ability of the proposed method is superior to the kernel-based nonlinear subspace method.