Abstract
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.
| Language | English |
|---|---|
| Publication status | Published - 5 Dec 2016 |
| Event | NIPS 2016 - Neural Information Processing Systems - Centre Convencions Internacional Barcelona, Barcelona, Spain Duration: 5 Dec 2016 → 10 Dec 2016 |
Conference
| Conference | NIPS 2016 - Neural Information Processing Systems |
|---|---|
| Abbreviated title | NIPS |
| Country | Spain |
| City | Barcelona |
| Period | 5/12/16 → 10/12/16 |
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Keywords
- signed networks
- spectral clustering
- Laplacians
- geometric mean
- neural networks
Cite this
}
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 conference › Paper
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
ER -