Feature weighting on k-means clustering

Data sets with multiple, heterogeneous feature spaces occur frequently. We present an abstract framework for integrating multiple feature spaces in the k-means clustering algorithm. Our main ideas are (i) to represent each data object as a tuple of multiple feature vectors, (ii) to assign a suitable (and possibly different) distortion measure to each feature space, (iii) to combine distortions on different feature spaces, in a convex fashion, by assigning (possibly) different relative weights to each, (iv) for a fixed weighting, to cluster using the proposed convex k-means algorithm, and (v) to determine the optimal feature weighting to be the one that yields the clustering that simultaneously minimizes the average within-cluster dispersion and maximizes the average between-cluster dispersion along all the feature spaces. Using precision/recall evaluations and known ground truth classifications, we empirically demonstrate the effectiveness of feature weighting in clustering on several different application domains.