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
Reads0
Chats0
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
Citations
More filters
Journal ArticleDOI
Unsupervised K-Means Clustering Algorithm
TL;DR: An unsupervised learning schema is constructed for the k-means algorithm so that it is free of initializations without parameter selection and can also simultaneously find an optimal number of clusters.
Journal ArticleDOI
Identification of overlapping community structure in complex networks using fuzzy c-means clustering
TL;DR: A novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing NG's Q function, an approximation mapping of network nodes into Euclidean space and fuzzy c-means clustering is devised.
Journal ArticleDOI
Fuzzy min-max neural networks - Part 2: Clustering
TL;DR: This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged and a brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented.
A Survey of Current Methods in Medical Image Segmentation
TL;DR: A critical appraisal of the current status of semi-automated and automated methods for the segmentation of anatomical medical images is presented with an emphasis placed on revealing the advantages and disadvantages of these methods for medical imaging applications.
Journal ArticleDOI
Alternative c-means clustering algorithms
Kuo-Lung Wu,Miin-Shen Yang +1 more
TL;DR: This AFCM algorithm has successfully been used in segmenting the magnetic resonance image of Ophthalmology to differentiate the abnormal tissues from the normal tissues and is recommended for use in cluster analysis.
References
More filters
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.