Some new indexes of cluster validity

@article{Bezdek1998SomeNI,
  title={Some new indexes of cluster validity},
  author={James C. Bezdek and Nikhil Ranjan Pal},
  journal={IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society},
  year={1998},
  volume={28 3},
  pages={
          301-15
        }
}
  • J. Bezdek, N. Pal
  • Published 1 June 1998
  • Mathematics, Medicine, Computer Science
  • IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society
We review two clustering algorithms (hard c-means and single linkage) and three indexes of crisp cluster validity (Hubert's statistics, the Davies-Bouldin index, and Dunn's index). We illustrate two deficiencies of Dunn's index which make it overly sensitive to noisy clusters and propose several generalizations of it that are not as brittle to outliers in the clusters. Our numerical examples show that the standard measure of interset distance (the minimum distance between points in a pair of… 
Some new indexes of cluster validity
  • J. Bezdek, N. Pal
  • Mathematics, Medicine
    IEEE Trans. Syst. Man Cybern. Part B
  • 1998
TLDR
This work reviews two clustering algorithms and three indexes of crisp cluster validity and shows that while Dunn's original index has operational flaws, the concept it embodies provides a rich paradigm for validation of partitions that have cloud-like clusters.
Validity index for crisp and fuzzy clusters
TLDR
A cluster validity index and its fuzzification is described, which can provide a measure of goodness of clustering on different partitions of a data set, and results demonstrating the superiority of the PBM-index in appropriately determining the number of clusters are provided.
A new validity index for crisp clusters
TLDR
A new cluster validity index, called the STR index, is defined as the product of two components which determine changes of compactness and separability of clusters during a clustering process, and the maximum value identifies the best clustering scheme.
A comprehensive validity index for clustering
TLDR
A new bounded index for cluster validity called the score function (SF), a double exponential expression that is based on a ratio of standard cluster parameters that is shown to work well on multidimensional and noisy data sets.
A new cluster validity index for prototype based clustering algorithms based on inter- and intra-cluster density
One of the fundamental challenges of clustering is how to evaluate, without auxiliary information, to what extent the obtained clusters fit the natural partitions of the data s et. A common approach
Clustering performance analysis using new correlation based cluster validity indices
TLDR
Two new cluster validity indices are developed based on a correlation between an actual distance between a pair of data points and a centroid distance of clusters that the two points locate in which overcome the weakness previously stated.
Some connectivity based cluster validity indices
TLDR
It is empirically established that incorporation of the property of connectivity significantly improves the capabilities of these indices in identifying the appropriate number of clusters and also shows that connectivity based Dunn-index performs the best as compared to all the other six indices.
Performance Evaluation of Some Symmetry-Based Cluster Validity Indexes
  • S. Saha, S. Bandyopadhyay
  • Mathematics, Computer Science
    IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)
  • 2009
TLDR
It is empirically established that incorporation of the property of symmetry significantly improves the capabilities of these indexes in identifying the appropriate number of clusters.
Mutual equidistant-scattering criterion: A new index for crisp clustering
TLDR
This work proposes a new non-parametric internal validity index based on within-cluster mutual equidistant-scattering for crisp clustering and shows the effectiveness and reliability of this approach to evaluate the hyperparameter K.
A Bounded Index for Cluster Validity
TLDR
A new bounded index for cluster validity, called the score function (SF), is introduced, based on standard cluster properties, and is shown to work well on multi-dimensional data sets and is able to accommodate unique and sub-cluster cases.
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References

SHOWING 1-10 OF 19 REFERENCES
Some new indexes of cluster validity
  • J. Bezdek, N. Pal
  • Mathematics, Medicine
    IEEE Trans. Syst. Man Cybern. Part B
  • 1998
TLDR
This work reviews two clustering algorithms and three indexes of crisp cluster validity and shows that while Dunn's original index has operational flaws, the concept it embodies provides a rich paradigm for validation of partitions that have cloud-like clusters.
A geometric approach to cluster validity for normal mixtures
TLDR
Viewing mixture decomposition as probabilistic clustering as opposed to parametric estimation enables both fuzzy and crisp measures of cluster validity for this problem, and uses the expectation-maximization algorithm to find clusters in the data.
Cluster validation using graph theoretic concepts
TLDR
The generalized Dunn's index and the Davies-Bouldin index for cluster validation using graph structures, such as GG, RNG and MST are generalized and superiority over some existing cluster validity indices is established.
A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters
  • J. Dunn
  • Mathematics, Computer Science
  • 1973
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
A Cluster Separation Measure
A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The
A possibilistic approach to clustering
TLDR
An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function.
Pattern Recognition with Fuzzy Objective Function Algorithms
  • J. Bezdek
  • Computer Science
    Advanced Applications in Pattern Recognition
  • 1981
TLDR
Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with, becomes what you need to get.
Computational geometry: an introduction
TLDR
This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Pattern classification and scene analysis
  • R. Duda, P. Hart
  • Computer Science, Mathematics
    A Wiley-Interscience publication
  • 1973
TLDR
The topics treated include Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, clustering, preprosessing of pictorial data, spatial filtering, shape description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis.
Pattern Recognition Principles
The present work gives an account of basic principles and available techniques for the analysis and design of pattern processing and recognition systems. Areas covered include decision functions,
...
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2
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