The Analysis of a Simple k - Means Clustering

K-means clustering is a very popular clustering technique which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's algorithm. In this paper we present a simple and eecient implementation of Lloyd's k-means clustering algorithm, which we call the ltering algorithm. This algorithm is very easy to implement. It diiers from most other approaches in that it precomputes a kd-tree data structure for the data points rather than the center points. We establish the practical eeciency of the ltering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real data from applications in color quantization, compression, and segmentation. Abstract K-means clustering is a very popular clustering technique which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's algorithm. In this paper we present a simple and eecient implementation of Lloyd's k-means clustering algorithm, which we call the ltering algorithm. This algorithm is very easy to implement. It diiers from most other approaches in that it pre-computes a kd-tree data structure for the data points rather than the center points. We establish the practical eeciency of the ltering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real data from applications in color quantization, compression, and segmentation.