An Interpretable Joint Nonnegative Matrix Factorization-Based Point Cloud Distance Measure

Abstract

In this paper, we propose a new method for determining shared features of and measuring the distance between data sets or point clouds. Our approach uses the joint factorization of two data matrices X_1,X_2 into non-negative matrices X_1 = AS_1, X_2 = AS_2 to derive a similarity measure that determines how well the shared basis A approximates X_1, X_2. We also propose a point cloud distance measure built upon this method and the learned factorization. Our method reveals structural differences in both image and text data. Potential applications include classification, detecting plagiarism or other manipulation, data denoising, and transfer learning.

Tasks

Reproductions