Redefining clustering for high-dimensional applications

Abstract

Clustering problems are well-known in the database literature for their use in numerous applications, such as customer segmentation, classification, and trend analysis. High-dimensional data has always been a challenge for clustering algorithms because of the inherent sparsity of the points. Recent research results indicate that, in high-dimensional data, even the concept of proximity or clustering may not be meaningful. We introduce a very general concept of projected clustering which is able to construct clusters in arbitrarily aligned subspaces of lower dimensionality. The subspaces are specific to the clusters themselves. This definition is substantially more general and realistic than the currently available techniques which limit the method to only projections from the original set of attributes. The generalized projected clustering technique may also be viewed as a way of trying to redefine clustering for high-dimensional applications by searching for hidden subspaces with clusters which are created by interattribute correlations. We provide a new concept of using extended cluster feature vectors in order to make the algorithm scalable for very large databases. The running time and space requirements of the algorithm are adjustable and are likely to trade-off with better accuracy.