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Pattern Recognition with Fuzzy Objective Function Algorithms

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Citations
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Mathematical Classification and Clustering

Boris Mirkin
TL;DR: This paper presents a meta-analyses of Hierarchy as a Clustering Structure, a model for hierarchical clustering based on the model developed in [Bouchut-Boyaval, M3].
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Robust clustering methods: a unified view

TL;DR: This paper analyzes several popular robust clustering methods and concludes that they have much in common, establishing a connection between fuzzy set theory and robust statistics, and pointing out the similarities between robust clusters methods and statistical methods.
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Fuzzy min-max neural networks. I. Classification

TL;DR: The fuzzy min-max classifier neural network implementation is explained, the learning and recall algorithms are outlined, and several examples of operation demonstrate the strong qualities of this new neural network classifier.
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Characterization and detection of noise in clustering

TL;DR: The approach presented is applicable to a variety of fuzzy clustering algorithms as well as regression analysis, and its ability to detect ‘good’ clusters amongst noisy data is demonstrated.
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Why triangular membership functions

TL;DR: It is shown that under some additional mild assumptions these triangular fuzzy sets comply with a request for a uniformly excited codebook in the case of the input interfaces and a satisfaction of a zero-error reconstruction criterion being formulated for the output interface.
References
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Journal ArticleDOI

Nearest neighbor pattern classification

TL;DR: The nearest neighbor decision rule assigns to an unclassified sample point the classification of the nearest of a set of previously classified points, so it may be said that half the classification information in an infinite sample set is contained in the nearest neighbor.
Book

Introduction to Statistical Pattern Recognition

TL;DR: This completely revised second edition presents an introduction to statistical pattern recognition, which is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field.

A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters

J. C. Dunn
TL;DR: 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.