Abstract: Most machine learning tasks confront the problem of dimensionality reduction for extracting meaningful features 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 both path and distance feature is proposed based on spectral graph theory which aims at preserving local meaningful neighborhood structures in the original data. In the experiments of both face recognition and information retrieval, it achieves positive results.

Key words: information retrieval , face recognition, dimensionality reduction, spectral graph