Visual hierarchical cluster structure: A refined co-association matrix based visual assessment of cluster tendency

•We employ a refined and transformed co-association matrix as the input of VAT.•An efficient path-based similarity algorithm is presented and its time complexity is O(N2).•A simple approach to analyze D* and obtain the clustering is designed.•A visual hierarchical cluster structure can be presented.

A hierarchical clustering algorithm, such as Single-linkage, can depict the hierarchical relationship of clusters, but its clustering quality mainly depends on the similarity measure used. Visual assessment of cluster tendency (VAT) reorders a similarity matrix to reveal the cluster structure of a data set, and a VAT-based clustering discovers clusters by image segmentation techniques. Although VAT can visually present the cluster structure, its performance also relies on the similarity matrix employed. In this paper, we take a refined co-association matrix, which is originally used in ensemble clustering, as an initial similarity matrix and transform it by path-based measure, and then apply it to VAT. The final clustering is achieved by directly analyzing the transformed and reordered similarity matrix. The proposed method can deal with data sets with some complex cluster structures and reveal the relationship of clusters hierarchically. The experimental results on synthetic and real data sets demonstrate the above mentioned properties.