论文标题
基于可解释的关节非负矩阵分解的点云距离测量
An Interpretable Joint Nonnegative Matrix Factorization-Based Point Cloud Distance Measure
论文作者
论文摘要
在本文中，我们提出了一种新方法，用于确定数据集或点云之间的距离的共享特征。我们的方法使用两个数据矩阵的联合分解$ x_1，x_2 $中的非负矩阵$ x_1 = as_1，x_2 = as_2 $，以得出一个相似的度量，以确定共享基础$ a $ a $ a $近似$ x_1，x_1，x_2 $。我们还提出了基于此方法和学习分解的点云距离度量。我们的方法揭示了图像和文本数据的结构差异。潜在的应用包括分类，检测窃或其他操纵，数据降解和转移学习。
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.
