As a typical dimensionality reduction technique, random projection has been widely applied in a variety of fields concerning categorization. The construction of random projection has also been deeply studied, based on the principle of preserving the pairwise distances of a set of data projected from a high-dimensional space onto a low-dimensional subspace. Considering random projection is mainly exploited for the task of classification, this paper is novelly developed to study random projection from the viewpoint of feature selection, rather than of the traditional distance preservation. This yields a somewhat surprising result, that is, theoretically the sparsest random matrix with only one nonzero element in each column, can present better feature selection performance than other more dense matrices. Extensive experiments on binary classification also confirm the theoretical conjecture. Apparently, this result will be very attractive for dimensionality reduction due to its breakthrough on both complexity reduction and performance improvement.
