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

TL;DR

This paper introduces an interpretable joint nonnegative matrix factorization method to measure similarities and distances between point clouds, revealing structural differences in data for applications like classification and data denoising.

Contribution

The paper presents a novel joint NMF-based approach for point cloud comparison and a new distance measure that captures shared features and structural differences.

Findings

Effective in revealing structural differences in image and text data

Applicable to classification, plagiarism detection, and denoising

Provides an interpretable basis for data comparison

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.