Computational geometry: an introduction
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Algorithms for clustering data
Algorithms for clustering data
Cluster analysis and related issues
Handbook of pattern recognition & computer vision
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Swarm intelligence
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Data Mining Techniques: For Marketing, Sales, and Customer Support
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CLARANS: A Method for Clustering Objects for Spatial Data Mining
IEEE Transactions on Knowledge and Data Engineering
The new k-windows algorithm for improving the k-means clustering algorithm
Journal of Complexity
Improving the Orthogonal Range Search k -Windows Algorithm
ICTAI '02 Proceedings of the 14th IEEE International Conference on Tools with Artificial Intelligence
Data Mining: Concepts and Techniques
Data Mining: Concepts and Techniques
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Swarm Intelligence in Data Mining (Studies in Computational Intelligence)
Swarm Intelligence in Data Mining (Studies in Computational Intelligence)
Computational Intelligence: An Introduction
Computational Intelligence: An Introduction
Differential evolution and particle swarm optimisation in partitional clustering
Computational Statistics & Data Analysis
K-means clustering versus validation measures: a data-distribution perspective
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Particle Swarm Optimization and Intelligence: Advances and Applications
Particle Swarm Optimization and Intelligence: Advances and Applications
Automatic Clustering Using an Improved Differential Evolution Algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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In spite of the increasing interest into clustering research within the last decades, a unified clustering theory that is independent of a particular algorithm, or underlying the data structure and even the objective function has not be formulated so far. In the paper at hand, we take the first steps towards a theoretical foundation of clustering, by proposing a new notion of "clusterability" of data sets based on the density of the data within a specific region. Specifically, we give a formal definition of what we call "α-clusterable" set and we utilize this notion to prove that the principles proposed in Kleinberg's impossibility theorem for clustering [25], are consistent. We further propose an unsupervised clustering algorithm which is based on the notion of α-clusterable set. The proposed algorithm exploits the ability of the well known and widely used particle swarm optimization [31] to maximize the recently proposed window density function [38]. The obtained clustering quality is compared favorably to the corresponding clustering quality of various other well-known clustering algorithms.