Abstract
Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we recover the partition with respect to which the chain is lumpable. We also discuss the case of well-clustered networks. Finally, we illustrate our strategy on several examples.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 7907-7912 |
| Number of pages | 6 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Volume | 105 |
| Issue number | 23 |
| DOIs | |
| State | Published - Jun 10 2008 |
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Keywords
- k means
- Lumpability
- MNCut
- Partitioning
ASJC Scopus subject areas
- Genetics
- General
Cite this
Optimal partition and effective dynamics of complex networks. / E, Weinan; Li, Tiejun; Vanden Eijnden, Eric.
In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 105, No. 23, 10.06.2008, p. 7907-7912.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimal partition and effective dynamics of complex networks
AU - E, Weinan
AU - Li, Tiejun
AU - Vanden Eijnden, Eric
PY - 2008/6/10
Y1 - 2008/6/10
N2 - Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we recover the partition with respect to which the chain is lumpable. We also discuss the case of well-clustered networks. Finally, we illustrate our strategy on several examples.
AB - Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose a strategy along the lines of optimal prediction for the Markov chains associated with the dynamics on these networks. We develop the necessary ingredients for such an optimal partition strategy, and we compare our strategy with the previous ones. We show that when the Markov chain is lumpable, we recover the partition with respect to which the chain is lumpable. We also discuss the case of well-clustered networks. Finally, we illustrate our strategy on several examples.
KW - k means
KW - Lumpability
KW - MNCut
KW - Partitioning
UR - http://www.scopus.com/inward/record.url?scp=46149083017&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=46149083017&partnerID=8YFLogxK
U2 - 10.1073/pnas.0707563105
DO - 10.1073/pnas.0707563105
M3 - Article
C2 - 18303119
AN - SCOPUS:46149083017
VL - 105
SP - 7907
EP - 7912
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
SN - 0027-8424
IS - 23
ER -