  As a typical dimensionality reduction technique, random projection can be
simply implemented with linear projection, while maintaining the pairwise
distances of high-dimensional data with high probability. Considering this
technique is mainly exploited for the task of classification, this paper is
developed to study the construction of random matrix from the viewpoint of
feature selection, rather than of traditional distance preservation. This
yields a somewhat surprising theoretical result, that is, the sparse random
matrix with exactly one nonzero element per column, can present better feature
selection performance than other more dense matrices, if the projection
dimension is sufficiently large (namely, not much smaller than the number of
feature elements); otherwise, it will perform comparably to others. For random
projection, this theoretical result implies considerable improvement on both
complexity and performance, which is widely confirmed with the classification
experiments on both synthetic data and real data.
