Homophilic Clustering by Locally Asymmetric Geometry
  Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper proposes a novel algorithm to address this issue. The locally asymmetric geometries of neighborhoods between data points result in a directed similarity graph to model the structural connectivity of data points. Performing similarity propagation on this directed graph simply by its adjacency matrix powers leads to an interesting discovery, in the sense that if the in-degrees are ordered by the corresponding sorted out-degrees, they will be self-organized to be homophilic layers according to the different distributions of cluster densities, which is dubbed the Homophilic In-degree figure (the HI figure). With the HI figure, we can easily single out all cores of clusters, identify the boundary between cluster and noise, and visualize the intrinsic structures of clusters. Based on the in-degree homophily, we also develop a simple efficient algorithm of linear space complexity to cluster noisy data. Extensive experiments on toy and real-world scientific data validate the effectiveness of our algorithms. 
Deli Zhao and Xiaoou Tang
cs.CV