Introduction to algorithms
An Algorithmic Regularity Lemma for Hypergraphs
SIAM Journal on Computing
The regularity lemma and its applications in graph theory
Theoretical aspects of computer science
An Optimal Algorithm for Checking Regularity
SIAM Journal on Computing
Optimal Cluster Preserving Embedding of Nonmetric Proximity Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral Grouping Using the Nyström Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dominant Sets and Pairwise Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algorithmic aspects of the regularity lemma
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Szemerédi-type clustering of peer-to-peer streaming system
Proceedings of the 2011 International Workshop on Modeling, Analysis, and Control of Complex Networks
Graph matching and clustering using kernel attributes
Neurocomputing
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Szemerédi's regularity lemma is a deep result from extremal graph theory which states that every graph can be well-approximated by the union of a constant number of random-like bipartite graphs, called regular pairs. Although the original proof was non-constructive, efficient (i.e., polynomial-time) algorithms have been developed to determine regular partitions for arbitrary graphs. This paper reports a first attempt at applying Szemerédi's result to computer vision and pattern recognition problems. Motivated by a powerful auxiliary result which, given a partitioned graph, allows one to construct a small reduced graph which inherits many properties of the original one, we develop a two-step pairwise clustering strategy in an attempt to reduce computational costs while preserving satisfactory classification accuracy. Specifically, Szemerédi's partitioning process is used as a preclustering step to substantially reduce the size of the input graph in a way which takes advantage of the strong notion of edge-density regularity. Clustering is then performed on the reduced graph using standard algorithms and the solutions obtained are then mapped back into the original graph to create the final groups. Experimental results conducted on standard benchmark datasets from the UCI machine learning repository as well as on image segmentation tasks confirm the effectiveness of the proposed approach.