Very Fast Graph Clustering for Single and Multiple Views
Keywords: Graph Clustering
Abstract: Clustering is a fundamental step in learning and analyzing graphs.
Commonly accepted criteria for evaluating graph clustering quality
without ground truth are
the "normalized cut" (ncut),
and the "ratio cut" (rcut).
Traditional algorithms that minimize
ncut and rcut
take $O(mnk)$ to cluster
a graph of $n$ nodes and $m$ edges into $k$ clusters.
Faster algorithms sacrifice accuracy for speed
and run in $O(m {+} n k^2)$.
A very recent algorithm runs in $O(m {+} n k \log k )$.
The space complexity of these algorithms ranges from $O(n^2)$
to $O(n \log k)$.
We describe a new algorithm with running time of $O(m \log m)$
that achieves accuracy similar to traditional algorithms.
Our algorithm is simple to implement, and requires only $O(m)$ memory.
It can also be applied in the multi-view setting,
where multiple graphs share the same set of nodes.
Our algorithm can cluster a small number of views
with no increase in its running time.
We describe
a randomized implementation that allows a qualitative comparison
between various internal clustering criteria.
Our experiments suggest a new criterion
that we call "linfcut" as superior to both
the ncut and the Cheeger criteria,
computing clusters that "make more sense" to a human observer.
Our algorithm performs a search for edges between clusters.
Its speed is the result of a strong "ignorance" (pruning) condition
that allows ignoring most of the edges after little computation.
Supplementary Material: zip
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 6749
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