The weighted sum of split and diameter clustering

Wang, Y.; Yan, Hong; Sriskandarajah, Chelliah

doi:10.1007/bf01246100

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…When k = 2, an exact polynomial algorithm is proposed in [12,13]. However, to the best of our knowledge, there is no algorithm dealing with this bi-criterion, while supporting various kinds of user constraints.…”

Section: Bi-criterion Constrained Clusteringmentioning

confidence: 99%

“…In the case of bi-partition (k = 2), an exact polynomial algorithm to find Pareto optimal solutions is proposed in [12,13]. For k > 2, [13] also offers a 2-approximation algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…For k > 2, [13] also offers a 2-approximation algorithm. These two algorithms [12,13] are both based on the principle of [5]: a spanning tree is built to find the possible values for split and graph coloring tests are used to verify if a dissimilarity can be the maximal diameter. However none of these bi-criterion cluster analysis approaches does support any kind of user constraints.…”

Section: Related Workmentioning

confidence: 99%

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Constrained clustering by constraint programming

Dao

Duong

Vrain

2017

Artificial Intelligence

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Constrained Clustering allows to make the clustering task more accurate by integrating user constraints, which can be instance-level or cluster-level constraints. Few works consider the integration of different kinds of constraints, they are usually based on declarative frameworks and they are often exact methods, which either enumerate all the solutions satisfying the user constraints, or find a global optimum when an optimization criterion is specified. In a previous work, we have proposed a model for Constrained Clustering based on a Constraint Programming framework. It is declarative, allowing a user to integrate user constraints and to choose an optimization criterion among several ones. In this article we present a new and substantially improved model for Constrained Clustering, still based on a Constraint Programming framework. It differs from our earlier model in the way partitions are represented by means of variables and constraints. It is also more flexible since the number of clusters does not need to be set beforehand; only a lower and an upper bound on the number of clusters have to be provided. In order to make the model-based approach more efficient, we propose new global optimization constraints with dedicated filtering algorithms. We show that such a framework can easily be embedded in a more general process and we illustrate this on the problem of finding the optimal Pareto front of a bi-criterion constrained clustering task. We compare our approach with existing exact approaches, based either on a branch-and-bound approach or on graph coloring on twelve datasets. Experiments show that the model outperforms exact approaches in most cases.

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Section: Bi-criterion Constrained Clusteringmentioning

confidence: 99%

“…In the case of bi-partition (k = 2), an exact polynomial algorithm to find Pareto optimal solutions is proposed in [12,13]. For k > 2, [13] also offers a 2-approximation algorithm.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Constrained clustering by constraint programming

Dao

Duong

Vrain

2017

Artificial Intelligence

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A Monte Carlo evaluation of the moving method, k-means and two self-organising neural networks

Tyree

Long

1998

Pattern Analysis & Applic

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DIVCLUS-T: A monothetic divisive hierarchical clustering method

Chavent

Lechevallier

Briant

2007

Computational Statistics & Data Analysis

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DIVCLUS-T is a divisive hierarchical clustering algorithm based on a monothetic bipartitional approach allowing the dendrogram of the hierarchy to be read as a decision tree. It is designed for either numerical or categorical data. Like the Ward agglomerative hierarchical clustering algorithm and the k-means partitioning algorithm, it is based on the minimization of the inertia criterion. However, unlike Ward and k-means, it provides a simple and natural interpretation of the clusters. The price paid by construction in terms of inertia by DIVCLUS-T for this additional interpretation is studied by applying the three algorithms on six databases from the UCI Machine Learning repository.

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The weighted sum of split and diameter clustering

Abstract: Diameter, Split, Bicriteria clustering, Complexity, Polynomial algorithm, Divisive hierarchical clustering,

Cited by 8 publications

References 14 publications

Constrained clustering by constraint programming

Constrained clustering by constraint programming

A Monte Carlo evaluation of the moving method, k-means and two self-organising neural networks

DIVCLUS-T: A monothetic divisive hierarchical clustering method

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