Tight Continuous Relaxation of the Balanced k-Cut Problem

05/24/2015
by   Syama Sundar Rangapuram, et al.
0

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced k-cut of the graph, are either based on greedy techniques or heuristics which have weak connection to the original motivation of minimizing the normalized cut. In this paper we propose a new tight continuous relaxation for any balanced k-cut problem and show that a related recently proposed relaxation is in most cases loose leading to poor performance in practice. For the optimization of our tight continuous relaxation we propose a new algorithm for the difficult sum-of-ratios minimization problem which achieves monotonic descent. Extensive comparisons show that our method outperforms all existing approaches for ratio cut and other balanced k-cut criteria.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/24/2015

Constrained 1-Spectral Clustering

An important form of prior information in clustering comes in form of ca...
research
06/24/2015

Kernel Cuts: MRF meets Kernel & Spectral Clustering

We propose a new segmentation model combining common regularization ener...
research
11/17/2019

Approximation of Steiner Forest via the Bidirected Cut Relaxation

The classical algorithm of Agrawal, Klein and Ravi [SIAM J. Comput., 24 ...
research
03/19/2021

Continuous iterative algorithms for anti-Cheeger cut

As a judicious correspondence to the classical maxcut, the anti-Cheeger ...
research
03/27/2018

Compassionately Conservative Balanced Cuts for Image Segmentation

The Normalized Cut (NCut) objective function, widely used in data cluste...
research
05/05/2011

GANC: Greedy Agglomerative Normalized Cut

This paper describes a graph clustering algorithm that aims to minimize ...
research
10/25/2021

Shift of Pairwise Similarities for Data Clustering

Several clustering methods (e.g., Normalized Cut and Ratio Cut) divide t...

Please sign up or login with your details

Forgot password? Click here to reset