  Sparse random projection (RP) is a popular tool for dimensionality reduction
that shows promising performance with low computational complexity. However, in
the existing sparse RP matrices, the positions of non-zero entries are usually
randomly selected. Although they adopt uniform sampling with replacement, due
to large sampling variance, the number of non-zeros is uneven among rows of the
projection matrix which is generated in one trial, and more data information
may be lost after dimension reduction. To break this bottleneck, based on
random sampling without replacement in statistics, this paper builds a stable
sparse subspace embedded matrix (S-SSE), in which non-zeros are uniformly
distributed. It is proved that the S-SSE is stabler than the existing matrix,
and it can maintain Euclidean distance between points well after dimension
reduction. Our empirical studies corroborate our theoretical findings and
demonstrate that our approach can indeed achieve satisfactory performance.
