179
This is the standard form of a trace minimization problem, and it can be solved
by choosing T as the k smallest eigenvectors of the matrix T D
−1/2 (D + − D − −
W )D
−1/2 T as columns [100]. Resubstituting F = D
−1/2 T and using Proposition 3 in
von Luxburg [101], F is the matrix with the k smallest eigenvectors of the Laplacian
matrix L sns as columns. Clustering methods can then be applied to (some of) the
columns to get a discrete partition as before.
This is the standard form of a trace minimization problem, and it can be solved
by choosing T as the k smallest eigenvectors of the matrix T D
−1/2 (D + − D − −
W )D
−1/2 T as columns [100]. Resubstituting F = D
−1/2 T and using Proposition 3 in
von Luxburg [101], F is the matrix with the k smallest eigenvectors of the Laplacian
matrix L sns as columns. Clustering methods can then be applied to (some of) the
columns to get a discrete partition as before.