k-Means, Ward and Probabilistic Distance-Based Clustering Methods with Contiguity Constraint

We analyze some possibilities of using contiguity (neighbourhood) matrix as a constraint in the clustering made by the k -means and Ward methods as well as by an approach based on distances and probabilistic assignments aimed at obtaining a solution of the multi-facility location problem (MFLP). Tha...

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Bibliographic Details
Published in:Journal of classification Vol. 38; no. 2; pp. 313 - 352
Main Author: Młodak, Andrzej
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2021
Springer Nature B.V
Subjects:
Algorithms
Bioinformatics
Clustering
Constraints
Empirical analysis
Heterogeneity
Homogeneity
Indexes
Marketing
Mathematics and Statistics
Neighborhoods
Operations research
Original Research
Pattern Recognition
Psychometrics
Quality assessment
Signal,Image and Speech Processing
Simulation
Site selection
Statistical Theory and Methods
Statistics
Peirce index
Probabilistic
Contiguity constraint
Sokal and Sneath index
Means method
clustering
Silhouette index
Ward method
Rand index
Correctness of clustering
ISSN:0176-4268, 1432-1343
Online Access:Get full text
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Summary:We analyze some possibilities of using contiguity (neighbourhood) matrix as a constraint in the clustering made by the k -means and Ward methods as well as by an approach based on distances and probabilistic assignments aimed at obtaining a solution of the multi-facility location problem (MFLP). That is, some special two-stage algorithms being the kinds of clustering with relational constraint are proposed. They optimize division of set of objects into clusters respecting the requirement that neighbours have to belong to the same cluster. In the case of the probabilistic d -clustering, relevant modification of its target function is suggested and studied. Versatile simulation study and empirical analysis verify the practical efficiency of these methods. The quality of clustering is assessed on the basis of indices of homogeneity, heterogeneity and correctness of clusters as well as the silhouette index. Using these tools and similarity indices (Rand, Peirce and Sokal and Sneath), it was shown that the probabilistic d -clustering can produce better results than Ward’s algorithm. In comparison with the k -means approach, the probabilistic d -clustering—although gives rather similar results—is more robust to creation of trivial (of which empty) clusters and produces less diversified (in replications, in terms of correctness) results than k -means approach, i.e. is more predictable from the point of view of the clustering quality.
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ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-020-09370-5