We run experiments showing that algorithm clarans (, 2005) finds better K-medoids solutions than the Voronoi iteration algorithm. This finding, along with the similarity between the Voronoi iteration algorithm and Lloyd's K-means algorithm, suggests that clarans may be an effective K-means initializer. We show that this is the case, with clarans outperforming other seeding algorithms on 23 23 datasets with a mean decrease over K-means++ of 30 for initialization mse and 3 or final mse. We describe how the complexity and runtime of clarans can be improved, making it a viable initialization scheme for large datasets.
The work most similar to in the @math -means setting is that of @cite_3 , where it is indirectly shown that finds a solution within a factor 25 of the optimal @math -medoids clustering. The local search approximation algorithm they propose is a hybrid of and , alternating between the two, with sampling from a kd-tree during the -like step. Their source code includes an implementation of an algorithm they call Swap', which is exactly the algorithm of @cite_1 .
@cite_1 @cite_3
1575476631 2199495299
Spatial data mining is the discovery of interesting relationships and characteristics that may exist implicitly in spatial databases. In this paper, we explore whether clustering methods have a role to play in spatial data mining. To this end, we develop a new clustering method called CLAHANS which is based on randomized search. We also develop two spatial data mining algorithms that use CLAHANS. Our analysis and experiments show that with the assistance of CLAHANS, these two algorithms are very effective and can lead to discoveries that are difficult to find with current spatial data mining algorithms. Furthermore, experiments conducted to compare the performance of CLAHANS with that of existing clustering methods show that CLAHANS is the most efficient. In k-means clustering we are given a set of n data points in d-dimensional space Rd and an integer k, and the problem is to determine a set of k points in &#211C;d, called centers, to minimize the mean squared distance from each data point to its nearest center. No exact polynomial-time algorithms are known for this problem. Although asymptotically efficient approximation algorithms exist, these algorithms are not practical due to the extremely high constant factors involved. There are many heuristics that are used in practice, but we know of no bounds on their performance.We consider the question of whether there exists a simple and practical approximation algorithm for k-means clustering. We present a local improvement heuristic based on swapping centers in and out. We prove that this yields a (9+e)-approximation algorithm. We show that the approximation factor is almost tight, by giving an example for which the algorithm achieves an approximation factor of (9-e). To establish the practical value of the heuristic, we present an empirical study that shows that, when combined with Lloyd's algorithm, this heuristic performs quite well in practice.