Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolution-limit-free and local Non-negative Matrix Factorization
  quality functions for graph clustering   Many graph clustering quality functions suffer from a resolution limit, the
inability to find small clusters in large graphs. So called
resolution-limit-free quality functions do not have this limit. This property
was previously introduced for hard clustering, that is, graph partitioning.
  We investigate the resolution-limit-free property in the context of
Non-negative Matrix Factorization (NMF) for hard and soft graph clustering. To
use NMF in the hard clustering setting, a common approach is to assign each
node to its highest membership cluster. We show that in this case symmetric NMF
is not resolution-limit-free, but that it becomes so when hardness constraints
are used as part of the optimization. The resulting function is strongly linked
to the Constant Potts Model. In soft clustering, nodes can belong to more than
one cluster, with varying degrees of membership. In this setting
resolution-limit-free turns out to be too strong a property. Therefore we
introduce locality, which roughly states that changing one part of the graph
does not affect the clustering of other parts of the graph. We argue that this
is a desirable property, provide conditions under which NMF quality functions
are local, and propose a novel class of local probabilistic NMF quality
functions for soft graph clustering.

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The categories of this paper are: math
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg