# Joint Cluster Analysis of Attribute and Relationship Data Without Priori Specification of the Number of Clusters

In many applications, attribute and relationship data are available, carrying complementary information about real world entities. In such cases, a joint analysis of both types of data can yield more accurate results than classical clustering algorithms that either use only attribute data or only relationship (graph) data. The Connected k-Center (CkC) has been proposed as the first joint cluster analysis model to discover k clusters which are cohesive on both attribute and relationship data. However, it is well-known that prior knowledge on the number of clusters is often unavailable in applications such as community identification and hotspot analysis. In this paper, we introduce and formalize the problem of discovering an a-priori unspecified number of clusters in the context of joint cluster analysis of attribute and relationship data, called Connected X Clusters (CXC) problem. True clusters are assumed to be compact and distinctive from their neighboring clusters in terms of attribute data and internally connected in terms of relationship data. Different from classical attribute-based clustering methods, the neighborhood of clusters is not defined in terms of attribute data but in terms of relationship data. To efficiently solve the CXC problem, we present JointClust, an algorithm which adopts a dynamic two-phase approach. In the first phase, we find so called cluster atoms. We provide a probability analysis for this phase, which gives us a probabilistic guarantee, that each true cluster is represented by at least one of the initial cluster atoms. In the second phase, these cluster atoms are merged in a bottom-up manner resulting in a dendrogram. The final clustering is determined by our objective function. Our experimental evaluation on several real datasets demonstrates that JointClust indeed discovers meaningful and accurate clusterings without requiring the user to specify the number of clusters.

*Author: Flavia Moser, Simon Fraser University*