Data Clustering Analysis on Grassmann Manifold Metric

Abstract

In the standard spectrum clustering algorithm, the metric based on Euclidean space can not represent the complicate space distribution feature of some data set, which might lead to the clustering result inaccuracy. While the geometric relationship between data can be describe more precise by manifold space. Considering Grassmann manifold is a entropy of Lie group, which not only has the smooth curved surface but also has the feature more fit for measuring the distance between data. All these can make the clustering result more accurate. The improved spectrum clustering analysis algorithm based on the distance metric under Graasmann manifold is proposed by this paper. The similarity between data is analyzed under manifold space. Experimental results show that the proposed algorithm can cluster data set either belonging the same or different subspace more accurately, further more, it can cluster data set with more complicate geometric structure under manifold space efficiently.