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Development of assessment criteria for clustering algorithms

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In this paper, new measures—called clustering performance measures (CPMs)—for assessing the reliability of a clustering algorithm are proposed. These CPMs are defined using a validation measure, which determines how well the algorithm works with a given set of parameter values, and a repeatability measure, which is used for studying the stability of the clustering solutions and has the ability to estimate the correct number of clusters in a dataset. These proposed CPMs can be used to evaluate clustering algorithms that have a structure bias to certain types of data distribution as well as those that have no structure biases. Additionally, we propose a novel cluster validity index, V I index, which is able to handle non-spherical clusters. Five clustering algorithms on different types of real-world data and synthetic data are evaluated. The first dataset type refers to a communications signal dataset representing one modulation scheme under a variety of noise conditions, the second represents two breast cancer datasets, while the third type represents different synthetic datasets with arbitrarily shaped clusters. Additionally, comparisons with other methods for estimating the number of clusters indicate the applicability and reliability of the proposed cluster validity V I index and repeatability measure for correct estimation of the number of clusters.

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  1. This paper is an extension of [24] and contains further investigations and experimental results. The current manuscript represents a significant extension.

  2. Software codes for the CPMs may be available on request from


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The authors would like to acknowledge the financial support of the Egyptian Ministry of Higher Eduction, Egypt, for S. A. Salem and many fruitful discussions with Dr. L. B. Jack formerly of the University of Liverpool.

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Correspondence to Sameh A. Salem.

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Salem, S.A., Nandi, A.K. Development of assessment criteria for clustering algorithms. Pattern Anal Applic 12, 79–98 (2009).

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