4 research outputs found
Relations Between Adjacency and Modularity Graph Partitioning
In this paper the exact linear relation between the leading eigenvector of
the unnormalized modularity matrix and the eigenvectors of the adjacency matrix
is developed. Based on this analysis a method to approximate the leading
eigenvector of the modularity matrix is given, and the relative error of the
approximation is derived. A complete proof of the equivalence between
normalized modularity clustering and normalized adjacency clustering is also
given. Some applications and experiments are given to illustrate and
corroborate the points that are made in the theoretical development.Comment: 11 page
Determining the Number of Clusters via Iterative Consensus Clustering β
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition probability matrix are used to determine the number of clusters. For noisy or high-dimensional data, an iterative technique is presented to refine this consensus matrix in way that encourages a block-diagonal form. It is shown that the resulting consensus matrix is generally superior to existing similarity matrices for this type of spectral analysis.