Clustering signed networks with the geometric mean of Laplacians

Pedro Mercado, Francesco Tudisco, Matthias Hein

Research output: Contribution to conferencePaper

8 Citations (Scopus)

Abstract

Signed networks allow to model positive and negative relationships. We analyze
existing extensions of spectral clustering to signed networks. It turns out that
existing approaches do not recover the ground truth clustering in several situations
where either the positive or the negative network structures contain no noise. Our
analysis shows that these problems arise as existing approaches take some form of
arithmetic mean of the Laplacians of the positive and negative part. As a solution
we propose to use the geometric mean of the Laplacians of positive and negative
part and show that it outperforms the existing approaches. While the geometric
mean of matrices is computationally expensive, we show that eigenvectors of the
geometric mean can be computed efficiently, leading to a numerical scheme for
sparse matrices which is of independent interest.

Conference

ConferenceNIPS 2016 - Neural Information Processing Systems
Abbreviated titleNIPS
CountrySpain
CityBarcelona
Period5/12/1610/12/16

Fingerprint

Geometric mean
Signed
Clustering
Spectral Clustering
Network Structure
Numerical Scheme
Eigenvector
Model

Keywords

  • signed networks
  • spectral clustering
  • Laplacians
  • geometric mean
  • neural networks

Cite this

Mercado, P., Tudisco, F., & Hein, M. (2016). Clustering signed networks with the geometric mean of Laplacians. Paper presented at NIPS 2016 - Neural Information Processing Systems, Barcelona, Spain.
Mercado, Pedro ; Tudisco, Francesco ; Hein, Matthias. / Clustering signed networks with the geometric mean of Laplacians. Paper presented at NIPS 2016 - Neural Information Processing Systems, Barcelona, Spain.
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abstract = "Signed networks allow to model positive and negative relationships. We analyzeexisting extensions of spectral clustering to signed networks. It turns out thatexisting approaches do not recover the ground truth clustering in several situationswhere either the positive or the negative network structures contain no noise. Ouranalysis shows that these problems arise as existing approaches take some form ofarithmetic mean of the Laplacians of the positive and negative part. As a solutionwe propose to use the geometric mean of the Laplacians of positive and negativepart and show that it outperforms the existing approaches. While the geometricmean of matrices is computationally expensive, we show that eigenvectors of thegeometric mean can be computed efficiently, leading to a numerical scheme forsparse matrices which is of independent interest.",
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author = "Pedro Mercado and Francesco Tudisco and Matthias Hein",
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Mercado, P, Tudisco, F & Hein, M 2016, 'Clustering signed networks with the geometric mean of Laplacians' Paper presented at NIPS 2016 - Neural Information Processing Systems, Barcelona, Spain, 5/12/16 - 10/12/16, .

Clustering signed networks with the geometric mean of Laplacians. / Mercado, Pedro; Tudisco, Francesco; Hein, Matthias.

2016. Paper presented at NIPS 2016 - Neural Information Processing Systems, Barcelona, Spain.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Clustering signed networks with the geometric mean of Laplacians

AU - Mercado, Pedro

AU - Tudisco, Francesco

AU - Hein, Matthias

PY - 2016/12/5

Y1 - 2016/12/5

N2 - Signed networks allow to model positive and negative relationships. We analyzeexisting extensions of spectral clustering to signed networks. It turns out thatexisting approaches do not recover the ground truth clustering in several situationswhere either the positive or the negative network structures contain no noise. Ouranalysis shows that these problems arise as existing approaches take some form ofarithmetic mean of the Laplacians of the positive and negative part. As a solutionwe propose to use the geometric mean of the Laplacians of positive and negativepart and show that it outperforms the existing approaches. While the geometricmean of matrices is computationally expensive, we show that eigenvectors of thegeometric mean can be computed efficiently, leading to a numerical scheme forsparse matrices which is of independent interest.

AB - Signed networks allow to model positive and negative relationships. We analyzeexisting extensions of spectral clustering to signed networks. It turns out thatexisting approaches do not recover the ground truth clustering in several situationswhere either the positive or the negative network structures contain no noise. Ouranalysis shows that these problems arise as existing approaches take some form ofarithmetic mean of the Laplacians of the positive and negative part. As a solutionwe propose to use the geometric mean of the Laplacians of positive and negativepart and show that it outperforms the existing approaches. While the geometricmean of matrices is computationally expensive, we show that eigenvectors of thegeometric mean can be computed efficiently, leading to a numerical scheme forsparse matrices which is of independent interest.

KW - signed networks

KW - spectral clustering

KW - Laplacians

KW - geometric mean

KW - neural networks

UR - https://papers.nips.cc/paper/6164-clustering-signed-networks-with-the-geometric-mean-of-laplacians

M3 - Paper

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Mercado P, Tudisco F, Hein M. Clustering signed networks with the geometric mean of Laplacians. 2016. Paper presented at NIPS 2016 - Neural Information Processing Systems, Barcelona, Spain.