Scientific Computing with Python 3

Spectral clustering

An interesting application of eigenvectors is for clustering data. Using the eigenvectors of a matrix derived from a distance matrix, unlabelled data can be separated into groups. Spectral clustering methods get their name from the use of the spectrum of this matrix. A distance matrix for n elements (for example, the pairwise distance between data points) is an n × n symmetric matrix. Given such an n × n distance matrix M with distance values m_ij, we can create the Laplacian matrix of the data points as follows:

Here, I is the identity matrix and D is the diagonal matrix containing the row sums of M,

 

The data clusters are obtained ...