Fuzzy Order Statistics and Their Application to Fuzzy Clustering

Abstract

The median and the median absolute deviation (MAD) are robust statistics based on order statistics. Order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy MAD. The fuzzy c- Means (FCM) clustering algorithm is defined for any p-norm (pFCM), including the norm (1 FCM). The 1 FOM clustering algorithm is implemented via the alternating optimization (AO) method and the clustering centers are shown to be the fuzzy median. The resulting AO-1 FCM clustering algorithm is called the fuzzy c-Medians (FCMED) clustering algorithm. An example illustrates the robustness of the FCMED.

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Document Details

Document Type
Technical Report
Publication Date
Aug 26, 1999
Accession Number
ADA368624

Entities

People

  • Paul R. Kersten

Organizations

  • Naval Air Warfare Center

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Aerial Warfare
  • Algorithms
  • Clustering
  • Computer Science
  • Data Science
  • Data Sets
  • Estimators
  • Fuzzy Sets
  • Heuristic Methods
  • Image Processing
  • Information Processing
  • Information Science
  • Optimization
  • Order Statistics
  • Real Numbers
  • Statistical Distributions
  • Statistics

Readers

  • Neural Network Machine Learning.
  • Operations Research
  • Regression Analysis.