Clustering by weighted cuts in directed graphs
نویسندگان
چکیده
In this paper we formulate spectral clustering in directed graphs as an optimization problem, the objective being a weighted cut in the directed graph. This objective extends several popular criteria like the normalized cut and the averaged cut to asymmetric affinity data. We show that this problem can be relaxed to a Rayleigh quotient problem for a symmetric matrix obtained from the original affinities and therefore a large body of the results and algorithms developed for spectral clustering of symmetric data immediately extends to asymmetric cuts.
منابع مشابه
On the Relation Between Low Density Separation, Spectral Clustering and Graph Cuts
One of the intuitions underlying many graph-based methods for clustering and semi-supervised learning, is that class or cluster boundaries pass through areas of low probability density. In this paper we provide some formal analysis of that notion for a probability distribution. We introduce a notion of weighted boundary volume, which measures the length of the class/cluster boundary weighted by...
متن کاملSpectral Theory of Unsigned and Signed Graphs. Applications to Graph Clustering: a Survey
This is a survey of the method of graph cuts and its applications to graph clustering of weighted unsigned and signed graphs. I provide a fairly thorough treatment of the method of normalized graph cuts, a deeply original method due to Shi and Malik, including complete proofs. I also cover briefly the method of ratio cuts, and show how it can be viewed as a special case of normalized cuts. I in...
متن کاملClustering in complex directed networks.
Many empirical networks display an inherent tendency to cluster, i.e., to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs, has been recently generalized to weighted, undirected networks. Here we extend the CC to the case of (binary and weighted) directed networks and we compute it...
متن کاملBipartition of graphs based on the normalized cut and spectral methods
In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices and present an alternative proof for finding eigenvalues of the adjacency matrix of paths and cycles using Chebyshev polynomials. Even though each results i...
متن کامل