黎曼流形上的Parzen窗逼近
Parzen Window Approximation on Riemannian Manifold
摘要：
在图动机学习中，标签传播在很大程度上取决于表示为连接数据点之间的边的数据亲和力。亲和性分配隐含地假设流形上的数据均匀分布。该假设可能不成立，并且可能由于向高密度区域漂移而导致不准确的度量分配。漂移影响基于热核的亲和力与全局固定的Parzen窗口要么放弃真正的邻居或迫使遥远的数据点成为邻居的成员。这产生了有偏的亲和矩阵。在本文中，由于不均匀的数据采样的黎曼流形上的偏差是迎合由一个可变的Parzen窗口确定为一个函数的邻域大小，环境尺寸，平坦度范围等，此外，亲和调整使用抵消的影响不均匀的采样负责的偏差。提出了一种亲和度度量，它考虑了不规则采样效应，以产生准确的标签传播。在合成数据集和真实数据集上的大量实验证实，该方法显着提高了分类精度，并优于图拉普拉斯流形正则化方法中现有的Parzen窗口估计。
英文摘要：
In graph motivated learning, label propagation largely depends on data affinity represented as edges between connected data points. The affinity assignment implicitly assumes even distribution of data on the manifold. This assumption may not hold and may lead to inaccurate metric assignment due to drift towards high-density regions. The drift affected heat kernel based affinity with a globally fixed Parzen window either discards genuine neighbors or forces distant data points to become a member of the neighborhood. This yields a biased affinity matrix. In this paper, the bias due to uneven data sampling on the Riemannian manifold is catered to by a variable Parzen window determined as a function of neighborhood size, ambient dimension, flatness range, etc. Additionally, affinity adjustment is used which offsets the effect of uneven sampling responsible for the bias. An affinity metric which takes into consideration the irregular sampling effect to yield accurate label propagation is proposed. Extensive experiments on synthetic and real-world data sets confirm that the proposed method increases the classification accuracy significantly and outperforms existing Parzen window estimators in graph Laplacian manifold regularization methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
