Clustering using PK-D: A connectivity and density dissimilarity

Abstract

We present a new dissimilarity, which combines connectivity and density information. Usually, connectivity and density are conceived as mutually exclusive concepts; however, we discuss a novel procedure to merge both information sources. Once we have calculated the new dissimilarity, we apply MDS in order to find a low dimensional vector space representation. The new data representation can be used for clustering and data visualization, which is not pursued in this paper. Instead we use clustering to estimate the gain from our approach consisting of dissimilarity + MDS. Hence, we analyze the partitions’ quality obtained by clustering high dimensional data with various well known clustering algorithms based on density, connectivity and message passing, as well as simple algorithms like k-means and Hierarchical Clustering (HC). The quality gap between the partitions found by k-means and HC alone compared to k-means and HC using our new low dimensional vector space representation is remarkable. Moreover, our tests using high dimensional gene expression and image data confirm these results and show a steady performance, which surpasses spectral clustering and other algorithms relevant to our work.