k-means Approach to the Karhunen-Loeve Transform
  We present a simultaneous generalization of the well-known Karhunen-Loeve (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. We show that for some data exploration problems this method gives better result then either of the classical approaches. 
Krzysztof Misztal, Przemyslaw Spurek and Jacek Tabor
cs.IT math.IT math.ST stat.TH