基于谱图的维度约简及其应用

为了提取主要特征和方便处理，大多数机器学习任务都要求把高维数据投影到低维空间.在这些拓扑空间中，数据对象的相似性一般由欧式距离来度量.讨论了对某些应用而言，相似性也可以以路径为指标来衡量，并且讨论了特征选取中局部和全局的关系.基于图谱理论，提出了一种结合路径特征和距离特征的维数约简方法，旨在发掘和保持原有数据中有意义的局部近邻关系.在信息检索和人脸识别的试验中，它取得了较好的效果.

Dimensionality reduction based on spectral graph and its application

Most machine learning tasks confront the problem of dimensionality reduction for extracting meaningful festures and processing, convenience. In these topological spaces, it usually adopts Euclidean distance to measure similarity between objects. It is argued that in many learning tasks the path from one object to another will also be a proper alternative. Also the relationship between local and global information is discussed when selecting features. A dimensionality reduction method incorporating beth path and distance feature is proposed based on spectral graph theory which aims at preserving loal meaningful neighborhood structurcs in the original data. In the experiments of beth face recognition and information retrieval, it achieves positive resalts.