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Summary and semi-average similarity criteria for individual clusters
There exists much prejudice against the within-cluster summary similarity criterion which supposedly leads to collecting all the entities in one cluster. This is not so if the similarity matrix is pre-processed by subtraction of ``noise'', of which two ways, the uniform and modularity, are mentioned in the paper. Another criterion under consideration is the semi-average within-cluster similarity, which manifests more versatile properties. In fact, both types of criteria emerge in relation to the least-squares data approximation approach to clustering, as shown in the paper. A very simple local optimization algorithm, Add-and-Remove($S$), leads to a suboptimal cluster satisfying some tightness conditions. Three versions of an iterative extraction approach are considered, leading to a portrayal of the cluster structure of the data. Of these, probably most promising is what is referred to as the incjunctive clustering approach. Applications are considered to the analysis of semantics, to integrating different knowledge aspects and consensus clustering.