國立雲林科技大學
National Yunlin University of Science and Technology
N.Y.U.S.T.
I. M.
Validity index for clusters of different sizes
and densities
Presenter: Jun-Yi Wu
Authors: Krista Rizman Zalik, Borut Zalik
2011 PRL
Intelligent Database Systems Lab
Outline
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Motivation
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Objective
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Methodology
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Experiments
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Conclusion
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Comments
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Motivation
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Most of the previous validity indices have been considerably
dependent on the number of data objects in clusters, on
cluster centroids and on average values.

Most popular validity measures have the tendency to ignore
clusters with low density and are not efficient in validation of
partitions having different sizes and densities.
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Objective
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Two cluster validity indices are proposed for efficient
validation of partitions containing clusters that widely
differ in sizes and densities.

To design a cluster validity index that is suitable for the
validation of partitions having different sizes and densities.
A good partitions:
 Overlap
 Compactness
 Separation distance
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Methodology
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Review several popular validity indices
Dunn index; D Indx
XiE index
Davies-Bouldin’s index; DB index
C index
G index
G+ index
Partition coefficient; PC index
Classification entropy; CE index
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Methodology
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N.Y.U.S.T.
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Review several popular validity indices.
D Index
G+ Index
PC
CE
DB Index
C Index
G Index
XiE
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Methodology
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new clustering validity indices.
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SV-index
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Validation of index SV
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Fuzzification of the SV index
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The proposed index OS exploiting overlap and separation measures
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Overlap measure
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Separation measure and validity index SV
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Validation of index OS
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Methodology
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SV-index
a measure for partition validity that consists of clusters that widely differ in
density or size
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Methodology
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Validation of index SV
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Methodology
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Fuzzification of the SV index
A fuzzy version of the index SV is obtained by integrating the membership
values in the variation measure.
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Methodology
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The proposed index OS exploiting overlap and separation
measure
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Experiment results suggested that inter-cluster separation plays a more
important role in cluster validation.

Indices are limited in their ability to compute the compactness and the
separation in partitions having overlapping clusters and clusters of
different sizes, which leads to an incorrect validation results.

Considering these results a cluster validity index is suggested based on
an overlap and separation measures.
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Methodology
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Overlap measure
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Methodology
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Separation measure and validity index SV
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Methodology
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Validation of index OS
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Experiments
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To demonstrate the effectiveness of the proposed SV and
OS indices for determining the optional number of
clusters.
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Artificial data set A1
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Artificial data set A2
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Artificial data set A3
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Iris data set
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Wine data set
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Glass data set
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Experiments-Artificial data set A1
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Experiments-Artificial data set A2
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Experiments-Artificial data set A3
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Experiments-Artificial data set A3
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Experiments -Iris data set.
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Experiments-Wine data set
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Experiments-Wine data set
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Conclusion
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The experimental results proved that the new indices outperform
the other considered indices, especially when cluster widely differ
in sizes or densities.
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A good partition is expected to have low degree of overlap and a
larger separation distance and compactness.

The maximum value of the ratio of the SV index and the minimum
value of the OS index indicate the optimal partition.
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Comments
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Advantage
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Drawback
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Application
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Clustering
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Validity index
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