K-multiple-means: A multiple-means clustering method with specified K clusters

In this paper, we make an extension of K-means for the clustering of multiple means. The popular K-means clustering uses only one center to model each class of data. However, the assumption on the shape of the clusters prohibits it to capture the non-convex patterns. Moreover, many categories consist of multiple subclasses which obviously cannot be represented by a single prototype. We propose a K-Multiple-Means (KMM) method to group the data points with multiple sub-cluster means into specified k clusters. Unlike the methods which use the agglomerative strategies, the proposed method formalizes the multiple-means clustering problem as an optimization problem and updates the partitions of m subcluster means and k clusters by an alternating optimization strategy. Notably, the partition of the original data with multiple-means representation is modeled as a bipartite graph partitioning problem with the constrained Laplacian rank. We also show the theoretical analysis of the connection between our method and the K-means clustering. Meanwhile, KMM is linear scaled with respect to n. Experimental results on several synthetic and well-known real-world data sets are conducted to show the effectiveness of the proposed algorithm.