Dimensionality Reduction with Point-distributions Similarity Invariant

Existing dimensionality reduction methods all perform dimensionality reduction by preserving some invariant in the space before and after dimensionality reduction. This paper proposes a new dimensionality reduction invariant: preserving the invariant of the point-distribution similarity. We also design a linear-time and effective method to achieve dimensionality reduction while preserving this invariant. We theoretically prove the feasibility of our method for dimensionality reduction. Furthermore, our results on benchmark datasets and single-cell expression data demonstrate the effectiveness and efficiency of the proposed method.