Cluster detection in background noise

If a feature space contains a set of clusters and background noise, it may be difficult to extract the clusters correctly. In particular, when we use a partitioning scheme such as k-means clustering, where k is the correct number of clusters, the background noise points are forced to join the clusters, thus biasing their statistics. This paper describes a preprocessing technique that gives each data point a weight related to the density of data points in its vicinity. Points belonging to clusters thus get relatively high weights, while background noise points get relatively low weights, k-means clustering of the resulting weighted points converges faster and yields more accurate clusters. Cluster detection Dot density measurement Dot patterns k-means clustering Noise clustering l. INTRODUCTION Many methods have been developed for detecting clusters of feature points in a feature space; see Ref. (1) for a recent review of the subject. An important class of methods is based on partitioning the space into regions each of which (ideally) contains one cluster. "Isodata", or k-means clustering, which will be described later, is a classical example of this approach. If the feature space contains background noise in addition to the clusters, partition-based methods may have difficulties in extracting the clusters correctly. This is because the background noise points are forced to join the clusters, thus biasing their statistics. In fact, the background noise points include "outliers" that lie far from the cluster centers, and such outliers have strong influences on the estimates of the cluster means and covariance matrices. This paper describes a preprocessing technique that gives each data point a weight related to the density of data points in its vicinity. Points belonging to clusters thus get relatively high weights, while background noise points get relatively low weights. When this technique is used prior to k-means clustering, the clustering algorithm converges faster and yields more accurate estimates of the cluster statistics. Section 2 of this paper describes the preprocessing technique; Section 3 presents experimental results; and Section 4 suggests circumstances under which the technique should be especially appropriate. The basic idea of our technique is to give lower weights to points that lie far from the clusters, so that these points have less influence on the estimates of the cluster statistics. The weights are computed as follows. (1) For each point P we compute A(P)-V W(Q) "~ d(P, Q)" where d is (Euclidean) distance, and …