A Genetic XK-Means Algorithm with Empty Cluster Reassignment

Abstract

K-Means is a well known and widely used classical clustering algorithm. It is easy to fall into local optimum and it is sensitive to the initial choice of cluster centers. XK-Means (eXploratory K-Means) has been introduced in the literature by adding an exploratory disturbance onto the vector of cluster centers, so as to jump out of the local optimum and reduce the sensitivity to the initial centers. However, empty clusters may appear during the iteration of XK-Means, causing damage to the efficiency of the algorithm. The aim of this paper is to introduce an empty-cluster-reassignment technique and use it to modify XK-Means, resulting in an EXK-Means clustering algorithm. Furthermore, we combine the EXK-Means with genetic mechanism to form a genetic XK-Means algorithm with empty-cluster-reassignment, referred to as GEXK-Means clustering algorithm. The convergence of GEXK-Means to the global optimum is theoretically proved. Numerical experiments on a few real world clustering problems are carried out, showing the advantage of EXK-Means over XK-Means, and the advantage of GEXK-Means over EXK-Means, XK-Means, K-Means and GXK-Means (genetic XK-Means).

K-ARMA Models for Clustering Time Series Data

“…We call this phenomenon model vanishing. This has been observed for k-means algorithms, and mitigation techniques have been developed including empty cluster reassignment [34,18].…”

Occam’s Razor for Big Data? On Detecting Quality in Large Unstructured Datasets

“…This is due to the combinatorial space between "training data" versus "user hypothesis" versus "real-life data". For k-means, GA, and fuzzy clustering to provide accurate predictions, they may be adjusted to topological traits [68][69][70][71][72][73][74][75][76][77]. A genetic algorithm (GA) is understood as a "generic term subsuming all machine learning and optimization methods inspired by neo-Darwinian evolution theory" [74,75], and is often used in a combination with other methods for accurate inference of knowledge, like fuzzy clustering, which is a permutation of k-means [76].…”

“…For k-means, GA, and fuzzy clustering to provide accurate predictions, they may be adjusted to topological traits [68][69][70][71][72][73][74][75][76][77]. A genetic algorithm (GA) is understood as a "generic term subsuming all machine learning and optimization methods inspired by neo-Darwinian evolution theory" [74,75], and is often used in a combination with other methods for accurate inference of knowledge, like fuzzy clustering, which is a permutation of k-means [76]. There is no clear separation between GA versus k-means, and GAs may be merged directly with k-means [70][71][72][73][74][75][76][77], or k-means may be optimized through a GA seed selection [78][79][80][81][82][83].…”

“…A genetic algorithm (GA) is understood as a "generic term subsuming all machine learning and optimization methods inspired by neo-Darwinian evolution theory" [74,75], and is often used in a combination with other methods for accurate inference of knowledge, like fuzzy clustering, which is a permutation of k-means [76]. There is no clear separation between GA versus k-means, and GAs may be merged directly with k-means [70][71][72][73][74][75][76][77], or k-means may be optimized through a GA seed selection [78][79][80][81][82][83]. In the context of big data, the use of classical clustering algorithms combined with accurate training is inseparable from the practical application of GA, or evolutionary algorithms in general.…”

Genetic Algorithm based optimization of Clustering Algorithms for the Healthy Aging Dataset

“…Variants such as KMeans++ have also been active areas of research [17]. Clustering for mixed types of data [18], techniques for clustering algorithm selction [19], feature selection techniques [20,21], application of KMeans algorithm for customer segmentation [22], and improvisations using genetic algorithms or other techniques [23][24][25][26][27][28][29][30] are some other examples of continued interest of the research community towards this topic.…”