Graph-Based Dissimilarity Measurement for Cluster Analysis of Any-Type-Attributed Data

Heterogeneous attribute data composed of attributes with different types of values are quite common in a variety of real-world applications. As data annotation is usually expensive, clustering has provided a promising way for processing unlabeled data, where the adopted similarity measure plays a key role in determining the clustering accuracy. However, it is a very challenging task to appropriately define the similarity between data objects with heterogeneous attributes because the values from heterogeneous attributes are generally with very different characteristics. Specifically, numerical attributes are with quantitative values, while categorical attributes are with qualitative values. Furthermore, categorical attributes can be categorized into nominal and ordinal ones according to the order information of their values. To circumvent the awkward gap among the heterogeneous attributes, this article will propose a new dissimilarity metric for cluster analysis of such data. We first study the connections among the heterogeneous attributes and build graph representations for them. Then, a metric is proposed, which computes the dissimilarities between attribute values under the guidance of the graph structures. Finally, we develop a new
$k$
-means-type clustering algorithm associated with this proposed metric. It turns out that the proposed method is competent to perform cluster analysis of datasets composed of an arbitrary combination of numerical, nominal, and ordinal attributes. Experimental results show its efficacy in comparison with its counterparts.