论文标题
使用多尺度非负核图的歧管几何形状的研究
Study of Manifold Geometry using Multiscale Non-Negative Kernel Graphs
论文作者
论文摘要
现代机器学习系统越来越多地接受了大量嵌入在高维空间中的数据。通常，这是在不分析数据集结构的情况下完成的。在这项工作中，我们提出了一个研究数据几何结构的框架。我们利用最近引入的非负内核（NNK）回归图来估计数据歧管（曲率）的点密度，内在维度和线性。我们通过在输入数据中迭代合并邻域将图形构造和几何估计进一步概括为多尺度。我们的实验证明了我们提出的方法比其他基线的有效性在估计合成和真实数据集的数据歧管的局部几何形状方面的有效性。
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the geometric structure of the data. We make use of our recently introduced non-negative kernel (NNK) regression graphs to estimate the point density, intrinsic dimension, and the linearity of the data manifold (curvature). We further generalize the graph construction and geometric estimation to multiple scale by iteratively merging neighborhoods in the input data. Our experiments demonstrate the effectiveness of our proposed approach over other baselines in estimating the local geometry of the data manifolds on synthetic and real datasets.
