An Interpretable Joint Nonnegative Matrix Factorization-Based Point Cloud Distance Measure
This provides a new interpretable distance measure for comparing datasets, which could benefit researchers and practitioners in fields like computer vision and natural language processing, though it appears incremental as it builds on existing factorization techniques.
The paper tackles the problem of measuring similarity and distance between datasets or point clouds by proposing a joint nonnegative matrix factorization method that identifies shared features through a common basis matrix. The method demonstrates structural differences in both image and text data, with potential applications in classification, plagiarism detection, denoising, and transfer learning.
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.