Data bubbles for non-vector data: speeding-up hierarchical clustering in arbitrary metric spaces

To speed-up clustering algorithms, data summarization methods have been proposed, which first summarize the data set by computing suitable representative objects. Then, a clustering algorithm is applied to these representatives only, and a clustering structure for the whole data set is derived, based on the result for the representatives. Most previous methods are, however, limited in their application domain. They are in general based on sufficient statistics such as the linear sum of a set of points, which assumes that the data is from a vector space. On the other hand, in many important applications, the data is from a metric non-vector space, and only distances between objects can be exploited to construct effective data summarizations. In this paper, we develop a new data summarization method based only on distance information that can be applied directly to non-vector data. An extensive performance evaluation shows that our method is very effective in finding the hierarchical clustering structure of non-vector data using only a very small number of data summarizations, thus resulting in a large reduction of runtime while trading only very little clustering quality.