Journal ArticleDOI
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
TLDR
This paper develops 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, and demonstrates that the algorithm is applicable to large-scale clustering tasks such as image segmentation, social network analysis, and gene network analysis.Abstract:
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 analysisread more
Citations
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Journal ArticleDOI
Community detection in graphs
TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Journal ArticleDOI
Community detection in graphs
TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
Journal ArticleDOI
A Comprehensive Survey on Graph Neural Networks
TL;DR: This article provides a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields and proposes a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNS, convolutional GNN’s, graph autoencoders, and spatial–temporal Gnns.
Posted Content
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
TL;DR: In this article, a spectral graph theory formulation of convolutional neural networks (CNNs) was proposed to learn local, stationary, and compositional features on graphs, and the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs while being universal to any graph structure.
Proceedings Article
Spectral Networks and Locally Connected Networks on Graphs
TL;DR: This paper considers possible generalizations of CNNs to signals defined on more general domains without the action of a translation group, and proposes two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian.
References
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Some methods for classification and analysis of multivariate observations
TL;DR: The k-means algorithm as mentioned in this paper partitions an N-dimensional population into k sets on the basis of a sample, which is a generalization of the ordinary sample mean, and it is shown to give partitions which are reasonably efficient in the sense of within-class variance.
Journal ArticleDOI
Normalized cuts and image segmentation
Jianbo Shi,Jitendra Malik +1 more
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
Book
An Introduction to Support Vector Machines and Other Kernel-based Learning Methods
TL;DR: This is the first comprehensive introduction to Support Vector Machines (SVMs), a new generation learning system based on recent advances in statistical learning theory, and will guide practitioners to updated literature, new applications, and on-line software.
Proceedings ArticleDOI
Normalized cuts and image segmentation
Jianbo Shi,Jitendra Malik +1 more
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.