Self-adapted mixture distance measure for clustering uncertain data

Abstract

Distance measure plays an important role in clustering uncertain data. However, existing distance measures for clustering uncertain data suffer from some issues. Geometric distance measure can not identify the difference between uncertain objects with different distributions heavily overlapping in locations. Probability distribution distance measure can not distinguish the difference between different pairs of completely separated uncertain objects. In this paper, we propose a self-adapted mixture distance measure for clustering uncertain data which considers the geometric distance and the probability distribution distance simultaneously, thus overcoming the issues in previous distance measures. The proposed distance measure consists of three parts: (1) The induced kernel distance: it can be used to measure the geometric distance between uncertain objects. (2) The Jensen–Shannon divergence: it can be used to measure the probability distribution distance between uncertain objects. (3) The self-adapted weight parameter: it can be used to adjust the importance degree of the induced kernel distance and the Jensen–Shannon divergence according to the location overlapping information of the dataset. The proposed distance measure is symmetric, finite and parameter adaptive. Furthermore, we integrate the self-adapted mixture distance measure into the partition-based and density-based algorithms for clustering uncertain data. Extensive experimental results on synthetic datasets, real benchmark datasets and real world uncertain datasets show that our proposed distance measure outperforms the existing distance measures for clustering uncertain data.