k-means Approach to the Karhunen-Loeve Transform

We present a simultaneous generalization of the well-known Karhunen-Loéve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n = 0 we obtain the classical k-means, while for k = 1 we obtain PCA algorithm. Moreover, by our approach we can obtain clusters with different dimensionality which describe the structure of date. We show that for some data exploration problems this method gives better result then either of the classical approaches.