In this paper we will address a spectral clustering method for undirected graphs pro-posed in Laenen and Sun (2020). This method maximizes the “flow ratio” between clusters and relies on using a Hermitian adjacency matrix as a directed graph …

We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed. Keywords: spectral clustering; graph Laplacian. 1 Introduction.

In this work we study clustering algorithms for digraphs whose cluster structure is defined with respect to the imbalance of edge densities as well as the edge directions between the clusters. Formally, for any set of vertices S0; : : : ; Sk 1 that forms a partition of the vertex set V (G)

Dec 20, 2020 · We test the directed spectral clustering algorithm on networks simulated from a directed stochastic block model (SBM). Good performance on SBMs is considered a necessary condition for useful community detection algorithms.

In this paper, we present a unifying spectral clustering frame-work on directed and undirected graphs based on the spectral relaxation of a novel energy functional, which in turn al-lows us to generalize graph Laplacians. This functional is termed generalized Dirichlet energy (GDE) as it extends the well-known notion of Dirichlet energy.

To overcome these downsides, we pro-pose a spectral clustering algorithm based on a complex-valued matrix representation of digraphs. We analyse its theoretical perfor-mance on a Stochastic Block Model for di-graphs in which the cluster-structure is given not only by variations in edge densities, but also by the direction of the edges.

Nov 10, 2020 · Based on the Hermitian matrix representation of digraphs, we present a nearly-linear time algorithm for digraph clustering, and further show that our proposed algorithm can be implemented in sublinear time under reasonable assumptions.

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 a nity data.

A popular approach to partition undirected graphs is spectral clustering, von Luxburg [Lux], which uses the eigenvectors of a matrix representation of the graph to embed the nodes into a low dimensional Eu-clidean space.

May 22, 2024 · Spectral Clustering is a variant of the clustering algorithm that uses the connectivity between the data points to form the clustering. It uses eigenvalues and eigenvectors of the data matrix to forecast the data into lower dimensions space to cluster the data points.