A Performance Guarantee for Spectral Clustering

07/10/2020
by   March Boedihardjo, et al.
0

The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this paper we study the central question: when is spectral clustering able to find the global solution to the minimum ratio cut problem? First we provide a condition that naturally depends on the intra- and inter-cluster connectivities of a given partition under which we may certify that this partition is the solution to the minimum ratio cut problem. Then we develop a deterministic two-to-infinity norm perturbation bound for the the invariant subspace of the graph Laplacian that corresponds to the k smallest eigenvalues. Finally by combining these two results we give a condition under which spectral clustering is guaranteed to output the global solution to the minimum ratio cut problem, which serves as a performance guarantee for spectral clustering.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/29/2018

Certifying Global Optimality of Graph Cuts via Semidefinite Relaxation: A Performance Guarantee for Spectral Clustering

Spectral clustering has become one of the most widely used clustering te...
research
02/10/2011

How the result of graph clustering methods depends on the construction of the graph

We study the scenario of graph-based clustering algorithms such as spect...
research
03/11/2013

Spectral Clustering with Epidemic Diffusion

Spectral clustering is widely used to partition graphs into distinct mod...
research
03/29/2017

Improving Spectral Clustering using the Asymptotic Value of the Normalised Cut

Spectral clustering is a popular and versatile clustering method based o...
research
11/23/2019

Weighted Laplacian and Its Theoretical Applications

In this paper, we develop a novel weighted Laplacian method, which is pa...
research
11/18/2021

The self-consistent field iteration for p-spectral clustering

The self-consistent field (SCF) iteration, combined with its variants, i...
research
04/20/2020

Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities

In this paper, we show how sparse or isoperimetric cuts of a probability...

Please sign up or login with your details

Forgot password? Click here to reset