A genetic algorithm using hyper-quadtrees for low-dimensional k-means clustering

Abstract

The k-means algorithm is widely used for clustering because of its computational efficiency. Given n points in d-dimensional space and the number of desired clusters k, k-means seeks a set of k cluster centers so as to minimize the sum of the squared Euclidean distance between each point and its nearest cluster center. However, the algorithm is very sensitive to the initial selection of centers and is likely to converge to partitions that are significantly inferior to the global optimum. We present a genetic algorithm (GA) for evolving centers in the k-means algorithm that simultaneously identifies good partitions for a range of values around a specified k. The set of centers is represented using a hyper-quadtree constructed on the data. This representation is exploited in our GA to generate an initial population of good centers and to support a novel crossover operation that selectively passes good subsets of neighboring centers from parents to offspring by swapping subtrees. Experimental results indicate that our GA finds the global optimum for data sets with known optima and finds good solutions for large simulated data sets.

An improved column generation algorithm for minimum sum-of-squares clustering

“…The algorithms appear to be scalable for larger values of k due to increasing sparsity of discs in the auxiliary problems. It is worthwhile to mention that some of the state-of-art heuristics proposed in [11,24,36,37,47,59] did not report the optimal solutions found here for the Reinelt's drilling data set with n = 1060 entities and k = 120, 150. To the best of our knowledge, this is the first time that such solutions are reported in the literature.…”

Data Mining Techniques in Software Defect Prediction

“…It analyses the relationship between the ependent or response variable and independent or predictor variables. The relationship is expressed in the form of an equation that predicts the response variable as a linear function of predictor variable [7][8][9][10]. Linear Regression: Y=a+bX+u.…”

A Game Theoretic Approach for Simultaneous Compaction and Equipartitioning of Spatial Data Sets

“…This includes simulated annealing [21], evolutionary algorithms [22], [24], [18], tabu search [11], and ant colony optimization [6]. Also, hybrid approaches that combine multiple algorithms have been proposed in literature [24], [22].…”

“…The data are taken from German Town Data, which is a twodimensional data set with 59 observations, obtained from [35]. The SSE value for KMeans clustering for five clusters is the reported minimum value in literature [24].…”