A shadowed set-based three-way clustering ensemble approach

Abstract

As one of the essential topics in ensemble learning, a clustering ensemble is employed to aggregate multiple base patterns to generate a single clustering output for improving robustness and quality. In this work, we proposed a novel clustering ensemble method, a shadowed set-based multi-granular three-way clustering ensemble (S-M3WCE). In particular, the approach generated a set of clustering members via the possibilistic C-means clustering (PCM) approach. Then all objects initially are partitioned into three regions by shadowed sets: the core region, shadowed region, and exclusion region, according to their possibilistic membership degrees. The procedure will capture the uncertainty and noisy objects in the data set through multiple different clustering results. Second, objects are further assigned to four approximate regions borrowed from the idea of multi-granularity rough sets by analyzing the uncertainty between objects and clusters. Objects in different approximation regions have diverse importance to clusters, and there has a partially ordered relationship between different approximation regions. Finally, we again handle the above four regions using the shadowed set, which eventually produces the output of the three-way clustering. The proposed method is evaluated using four artificial data sets and eight UCI data sets based on three evaluation criteria: clustering accuracy, adjusted rand index, and normalized mutual information. The experimental results show that the proposed algorithm achieves optimal effectiveness and efficiency against the other six representative clustering ensemble algorithms.