There are many clustering methods that are referred to as k-means-like. We give the minimal necessary and sufficient components for the mechanism of the k-means (iterative and partitional) clustering method of a finite set of objects, X. Thus k-means is generalized and the methods that mimic k-means are unified. We name these k-center clustering methods. The fundamental mechanism of k-center methods exposes the usual misconceptions of k-means such as (a) ``distance" satisfies some of properties of a mathematical metric, (b) there is a need to measure ``distance" between objects in X, and (c) the centers of clusters have the same nature as the objects of X. Moreover, k-center methods have a common formula to choose or calculate centers of clusters. We characterize the convergent common objective function by expressing it in terms of (a) a distance measure for closeness between center objects and the objects in X and (b) the coherence of clusters. We give a three object example to demonstrate the components of the formal mechanism of a k-center method. We then give examples of various known methods that belong to the class of k-center methods. We exhibit an extensive and thorough comparison of the qualitative k-modes and the numerical spherical k-means. Included are paradigm applications, a matrix environment, an understanding of the duality of a dissimilarity and similarity measure, and an understanding of normalized X and the normalized centers of subsets of X.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-11052004-022839 |
| Date | 01 December 2004 |
| Creators | Cañas, Daniel Alberto |
| Contributors | Dr. Robert Funderlic, Dr, Jon Doyle, Dr. Steffen Heber |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-11052004-022839/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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