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Clustering on Graphs:
The Markov Cluster Algorithm
(MCL)
CS 595D Presentation
By Kathy Macropol
MCL Algorithm
Based on the PhD thesis by Stijn van Dongen
Van Dongen, S. (2000) Graph Clustering by Flow
Simulation. PhD Thesis, University of Utrecht, The
Netherlands.
MCL is a graph clustering algorithm.
MCL is freely available for download at
http://www.micans.org/mcl/
Outline
Background
– Clustering
– Random Walks
– Markov Chains
MCL
– Basis
– Inflation Operator
– Algorithm
– Convergence
MCL Analysis
– Comparison to Other Graph Clustering Algorithms
• RNSC, SPC, MCODE
• RRW
Conclusions
Graph Clustering
Clustering – finding natural groupings of items.
Vector Clustering Graph Clustering
Each point has
a vector, i.e.
• x coordinate
• y coordinate
• color
1
3
4
4
4
3
4
34
2
3
Each vertex is
connected to
others by
(weighted or
unweighted)
edges.
Random Walks
Considering a graph, there will be many links within a
cluster, and fewer links between clusters.
This means if you were to start at a node, and then
randomly travel to a connected node, you’re more
likely to stay within a cluster than travel between.
This is what MCL (and several other clustering
algorithms) is based on.
– Other ways to consider graph clustering may include, for
example, looking for cliques. This tends to be sensitive to
changes in node degree, however.
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