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Fixed Points Approach to Clustering
| Content Provider | Semantic Scholar |
|---|---|
| Author | Genkin, Alexander |
| Copyright Year | 2003 |
| Abstract | Assume that a dissimilarity measure between elements and subsets of the set being clustered is given. We define the transformation of the set of subsets under which each subset is transformed into the set of all elements whose dissimilarity to its is not greater than a given threshold. Then the cluster is defined as fixed point of this transformation. Three well-known clustering strategies are considered from this point of view: hierarchical clustering, graph-theoretic methods, and conceptual clustering. For hierarchical clustering generalizations are obtained that allow for overlapping clusters and/or clusters not forming a cover. Three properties of dissimilarity are introduced which guarantee the existence of fixed points for each threshold. We develop the relation to the theory of quasi-concave set functions, to help give an additional interpretation of clusters. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.datalaundering.com/download/fixed.pdf |
| Alternate Webpage(s) | http://datalaundering.private.dk/download/fixed.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Cluster analysis Computer cluster Concave function Conceptual clustering Convex set Fixed point (mathematics) Fixed-Point Number Generalization (Psychology) Graph - visual representation Graph theory Hierarchical clustering Subgroup statistical cluster |
| Content Type | Text |
| Resource Type | Article |
