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

arXiv: https://arxiv.org/abs/2207.05112 · HTML: https://mlsanity.com/paper/2207.05112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Deep Hough Voting for 3D Object Detection in Point Clouds](https://mlsanity.com/paper/1904.09664/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [JSIS3D: Joint Semantic-Instance Segmentation of 3D Point Clouds with Multi-Task Pointwise Networks and Multi-Value Conditional Random Fields](https://mlsanity.com/paper/1904.00699/) (2019)
- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [DPDist : Comparing Point Clouds Using Deep Point Cloud Distance](https://mlsanity.com/paper/2004.11784/) (2020)
- [A generalized Hausdorff distance based quality metric for point cloud geometry](https://mlsanity.com/paper/2003.13669/) (2020)
- [Quantification of BERT Diagnosis Generalizability Across Medical Specialties Using Semantic Dataset Distance](https://mlsanity.com/paper/2008.06606/) (2020)

## Abstract (arXiv)

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 X1,X2 into non-negative matrices X1 = AS1, X2 = AS2 to derive a similarity measure that determines how well the shared basis A approximates X1, X2. 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.