Spectral Clustering Revisited: Information Hidden in the Fiedler Vector

03/22/2020
by   Adela DePavia, et al.
0

We are interested in the clustering problem on graphs: it is known that if there are two underlying clusters, then the signs of the eigenvector corresponding to the second largest eigenvalue of the adjacency matrix can reliably reconstruct the two clusters. We argue that the vertices for which the eigenvector has the largest and the smallest entries, respectively, are unusually strongly connected to their own cluster and more reliably classified than the rest. This can be regarded as a discrete version of the Hot Spots conjecture and should be useful in applications. We give a rigorous proof for the stochastic block model and several examples.

READ FULL TEXT
research
08/18/2023

Eigenvalue-based Incremental Spectral Clustering

Our previous experiments demonstrated that subsets collections of (short...
research
09/26/2017

The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters

We prove a conjecture by Van Dam and Sotirov on the smallest eigenvalue ...
research
01/06/2023

Bounds for a alpha-eigenvalues

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D...
research
08/30/2017

A Compressive Sensing Approach to Community Detection with Applications

The community detection problem for graphs asks one to partition the n v...
research
10/21/2008

Foundations of a Multi-way Spectral Clustering Framework for Hybrid Linear Modeling

The problem of Hybrid Linear Modeling (HLM) is to model and segment data...
research
08/21/2017

Preconditioned Spectral Clustering for Stochastic Block Partition Streaming Graph Challenge

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demo...
research
10/12/2019

Spectral clustering in the weighted stochastic block model

This paper is concerned with the statistical analysis of a real-valued s...

Please sign up or login with your details

Forgot password? Click here to reset