Open Access
A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters
J. C. Dunn
- Vol. 3, pp 32-57
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TLDR
In this paper, two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space, and the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the LSE criterion function.Abstract:
Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...read more
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Republique algerienne democratique et populaire ministere de l'enseignement superieur et de la recherche scientifique universite aboubekr belkaid tlemcen faculte des sciences de la nature et de la vie et sciences de la terre et de l'univers
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References
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Journal ArticleDOI
Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters
TL;DR: A family of graph-theoretical algorithms based on the minimal spanning tree are capable of detecting several kinds of cluster structure in arbitrary point sets; description of the detected clusters is possible in some cases by extensions of the method.
Journal ArticleDOI
A new approach to clustering
TL;DR: A new method of representation of the reduced data, based on the idea of “fuzzy sets,” is proposed to avoid some of the problems of current clustering procedures and to provide better insight into the structure of the original data.
Journal ArticleDOI
The application of computers to taxonomy.
TL;DR: A method is described for handling large quantities of taxonomic data by an electronic computer so as to yield the outline of a classification based on equally weighted features that enables Similarity to be expressed numerically, and would allow taxonomic rank to be measured in terms of it.
Journal ArticleDOI
State of the art in pattern recognition
TL;DR: This paper reviews statistical, adaptive, and heuristic techniques used in laboratory investigations of pattern recognition problems and includes correlation methods, discriminant analysis, maximum likelihood decisions minimax techniques, perceptron-like algorithms, feature extraction, preprocessing, clustering and nonsupervised learning.
Journal ArticleDOI
An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique
I. Gitman,Martin D. Levine +1 more
TL;DR: It is proven that if certain assumptions are satisfied, then the algorithm will derive the optimal partition in the sense of maximum separation.