[Reading] Lecture 13 - On Spectral Clustering: Analysis and an algorithm

A big problem of spectral clustering is that it is very slow when we solve the eigenvector problem and the Laplacian matrix is big. Therefore, it is a little wasteful to exploit only one (the second) eigenvector and abandon the others to generate only one normalized cuts at a a time. In this paper the methods how to use the 3rd, 4th, ... eigenvectors are presented. According to their algorithm, after the eigenvector is obtained and represented as column in a matrix M, each row of M is normalized and can be clustered by Kmeans. I've tried to understand the physical meaning of the step of normalization in row but in vain. I think maybe it is just a trick operated in the mathematics and not easy to be interpreted by the physical meaning.

Reference:
Lie Lu, and Alan Hanjalic,"Audio Keywords Discovery for Text-Like Audio Content Analysis and Retrieval," to appear IEEE Trans. on Multimedia, 2007-2008.