An Extraction and Regularization Approach to Additive Clustering

Additive clustering provides a conceptually simple similarity model which is, nevertheless, capable of accommodating arbitrary similarity structures. The discrete nature of the clusters, coupled with the general flexibility of the model, however, means that the derivation of additive clustering models from given similarity data is difficult. After reviewing a number of previously developed algorithms, a new two stage algorithm for generating additive cluster models is developed. In the first stage, an extraction process generates a manageable number of candidate clusters which, in the second stage, are subject to a regularization process. The number of clusters included in the derived model is controlled by a parameter specifying the target level of variance to be accounted for by the final model. Several applications of the proposed algorithm are presented, including three involving previously examined data sets that facilitate an evaluation of performance relative to several other algorithms. It is argued that the proposed algorithm exhibits comparable performance in relation to these previous algorithms, and has the advantage of being developed within a framework that potentially allows the optimization of the tradeoff between goodness-of-fit and model parsimony. Copyright Springer-Verlag New York Inc. 1999