Weighted Graph Cuts without Eigenvectors A Multilevel Approach

A variety of clustering algorithms have recently been proposed to handle data that is not linearly separable; spectral clustering and kernel k-means are two of the main methods. In this paper, we discuss an equivalence between the objective functions used in these seemingly different methods - in pa...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 29; no. 11; pp. 1944 - 1957
Main Authors: Dhillon, I.S., Yuqiang Guan, Kulis, B.
Format: Journal Article
Language:English
Published: Los Alamitos, CA IEEE 01.11.2007
IEEE Computer Society
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Artificial Intelligence
Cluster Analysis
Clustering
Clustering algorithms
Computer science; control theory; systems
Data mining
Data processing. List processing. Character string processing
Eigenvectors
Exact sciences and technology
Graph Partitioning
Graphs
Image analysis
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image segmentation
k-means
Kernel
Kernels
Large-scale systems
Mathematical analysis
Memory organisation. Data processing
Multilevel
Network analysis
Optimization methods
Partitioning algorithms
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Reproducibility of Results
Segmentation
Sensitivity and Specificity
Social network services
Software
Spectral Clustering
Studies
Cluster analysis
Image processing
K means algorithm
Information extraction
Data mining
Graph decomposition
Network analysis
Classification
Genetics
segmentation
Fast algorithm
graph partitioning
Pattern analysis
Bioinformatics
Multilevel system
spectral clustering
Data analysis
Social network
Graph theory
Clustering
Weighted graph
Image segmentation
Image analysis
Graph cut
Social analysis
Objective function
Graph method
Artificial intelligence
kernel k-means
ISSN:0162-8828, 1939-3539
Online Access:Get full text
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Summary:A variety of clustering algorithms have recently been proposed to handle data that is not linearly separable; spectral clustering and kernel k-means are two of the main methods. In this paper, we discuss an equivalence between the objective functions used in these seemingly different methods - in particular, a general weighted kernel k-means objective is mathematically equivalent to a weighted graph clustering objective. We exploit this equivalence to develop a fast high-quality multilevel algorithm that directly optimizes various weighted graph clustering objectives, such as the popular ratio cut, normalized cut, and ratio association criteria. This eliminates the need for any eigenvector computation for graph clustering problems, which can be prohibitive for very large graphs. Previous multilevel graph partitioning methods such as Metis have suffered from the restriction of equal-sized clusters; our multilevel algorithm removes this restriction by using kernel k-means to optimize weighted graph cuts. Experimental results show that our multilevel algorithm outperforms a state-of-the-art spectral clustering algorithm in terms of speed, memory usage, and quality. We demonstrate that our algorithm is applicable to large-scale clustering tasks such as image segmentation, social network analysis, and gene network analysis.
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ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2007.1115