  Feature selection is an important tool to deal with high dimensional data. In
unsupervised case, many popular algorithms aim at maintaining the structure of
the original data. In this paper, we propose a simple and effective feature
selection algorithm to enhance sample similarity preservation through a new
perspective, topology preservation, which is represented by persistent diagrams
from the context of computational topology. This method is designed upon a
unified feature selection framework called IVFS, which is inspired by random
subset method. The scheme is flexible and can handle cases where the problem is
analytically intractable. The proposed algorithm is able to well preserve the
pairwise distances, as well as topological patterns, of the full data. We
demonstrate that our algorithm can provide satisfactory performance under a
sharp sub-sampling rate, which supports efficient implementation of our
proposed method to large scale datasets. Extensive experiments validate the
effectiveness of the proposed feature selection scheme.
