The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Combinatorics, Probability and Computing
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Combinatorics, Probability and Computing
A tutorial on spectral clustering
Statistics and Computing
Bipartite isoperimetric graph partitioning for data co-clustering
Data Mining and Knowledge Discovery
Empirical Evaluation of Graph Partitioning Using Spectral Embeddings and Flow
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Eigenvalue bounds, spectral partitioning, and metrical deformations via flows
Journal of the ACM (JACM)
A Note on Edge-based Graph Partitioning and its Linear Algebraic Structure
Journal of Mathematical Modelling and Algorithms
Local clustering of large graphs by approximate fiedler vectors
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Approximate computation and implicit regularization for very large-scale data analysis
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Computer Science Review
A spanning tree-based encoding of the MAX CUT problem for evolutionary search
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
Local information-based fast approximate spectral clustering
Pattern Recognition Letters
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Computing graph separators is an important step in many graph algorithms. A popular technique for finding separators involves spectral methods. However, there has not been much prior analysis of the quality of the separators produced by this technique; instead it is usually claimed that spectral methods "work well in practice." We present an initial attempt at such an analysis. In particular, we consider two popular spectral separator algorithms and provide counterexamples showing that these algorithms perform poorly on certain graphs. We also consider a generalized definition of spectral methods that allows the use of some specified number of the eigenvectors corresponding to the smallest eigenvalues of the Laplacian matrix of a graph, and we show that if such algorithms use a constant number of eigenvectors, then there are graphs for which they do no better than using only the second smallest eigenvector. Furthermore, using the second smallest eigenvector of these graphs produces partitions that are poor with respect to bounds on the gap between the isoperimetric number and the cut quotient of the spectral separator. Even if a generalized spectral algorithm uses $n^\epsilon$ for \mbox{$0