Dimensionality reduction with dimension selection

We propose a novel method called sparse dimensionality reduction (SDR) in this paper. It performs dimension selection while reducing data dimensionality. Different from traditional dimensionality reduction methods, this method does not require dimensionality estimation. The number of final dimensions is the outcome of the sparse component of this method. In a nutshell, the idea is to transform input data to a suitable space where redundant dimensions are compressible. The structure of this method is very flexible which accommodates a series of variants along this line. In this paper, the data transformation is carried out by Laplacian eigenmaps and the dimension selection is fulfilled by l2/l1 norm. A Nesterov algorithm is proposed to solve the approximated SDR objective function. Experiments have been conducted on images from video sequences and protein structure data. It is evident that the SDR algorithm has subspace learning capability and may be applied to computer vision applications potentially