关键词: 聚类, 流形, K均值聚类, 谱正则化, 谱聚类

Abstract: In real applications in pattern recognition and computer vison, high dimensional data always lie approximately on a low dimensional manifold. How to improve the performance of clustering algorithm on high dimensional data by using the manifold structure is a research hotspot in machine learning and data mining community. In this paper, a novel clustering algorithm called Nonlinear Discriminant K-means Clustering (NDisKmeans), which has taken the manifold structure of high dimensional into account, is proposed. By introducing the spectracl regularization technology, NDisKmeans first represents the desired low dimensional coordinates as linear combinations of smooth vectors predefined on the data manifold; then maximizes the ratio between inter-clusters scatter and total scatter to cluster the high dimensional data. A convergent iterative procedure is devised to solute the matrix of the combination coefficient and clustering assignment matrix. NDisKmeans overcomes the limilation of linear mapping of DisKmeans algorithm; therefore, it significantly improves the clustering performance. The systematic and extensive experiments on UCI and real world data sets have shown the effectiveness of the proposed NDisKmeans method.

Key words: clustering, manifold, K-means clustering, spectral regularization, spectral clustering