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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Local quality functions for graph clustering with non-negative matrix factorization.

Twan van Laarhoven1, Elena Marchiori1

  • 1Institute for Computing and Information Sciences, Radboud University Nijmegen, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
PubMed
Summary
This summary is machine-generated.

Non-negative matrix factorization (NMF) for graph clustering can overcome resolution limits. Introducing hardness constraints makes NMF resolution-limit free for hard clustering, while locality is proposed for soft clustering.

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Area of Science:

  • Graph theory
  • Machine learning
  • Data mining

Background:

  • Graph clustering quality functions often face resolution limits, hindering the detection of small clusters in large graphs.
  • Resolution-limit-free functions are desirable for comprehensive graph analysis.
  • Non-negative matrix factorization (NMF) is a technique applicable to graph clustering.

Purpose of the Study:

  • Investigate the resolution-limit-free property of NMF in both hard and soft graph clustering settings.
  • Adapt NMF to overcome resolution limits in graph partitioning.
  • Introduce and analyze a new locality property for soft graph clustering using NMF.

Main Methods:

  • Applied NMF to hard graph clustering, analyzing its resolution-limit properties.
  • Introduced and optimized hardness constraints within NMF for resolution-limit-free hard clustering.
  • Developed and analyzed a novel class of local probabilistic NMF quality functions for soft graph clustering.

Main Results:

  • Symmetric NMF without modifications is not resolution-limit free for hard clustering.
  • Incorporating hardness constraints makes NMF resolution-limit free for hard clustering, linking it to the constant Potts model.
  • The resolution-limit-free property is too stringent for soft clustering; locality is proposed as a suitable alternative.

Conclusions:

  • NMF can be adapted for resolution-limit-free hard graph clustering through hardness constraints.
  • Locality is a desirable and achievable property for NMF-based soft graph clustering.
  • The proposed local probabilistic NMF functions offer a promising approach for soft graph clustering without resolution limits.