Efficient nonlinear dimension reduction for clustered data using kernel functions

We propose a nonlinear feature extraction method which is based on centroids and kernel functions. The dimension reducing nonlinear transformation is obtained by implicitly mapping the input data into a feature space using a kernel function, and then finding a linear mapping based on an orthonormal basis of centroids in the feature space that maximally separates the between-class relationship. The proposed method utilizes an efficient algorithm to compute an orthonormal basis of centroids in the feature space transformed by a kernel function and achieves dramatic computational savings. The experimental results demonstrate that our method is capable of extracting nonlinear features effectively so that competitive performance of classification can be obtained in the reduced dimensional space.