| Title: | Spectral Modularity Clustering |
|---|---|
| Description: | Implements the network clustering algorithm described in Newman (2006) <doi:10.1103/PhysRevE.74.036104>. The complete iterative algorithm comprises of two steps. In the first step, the network is expressed in terms of its leading eigenvalue and eigenvector and recursively partition into two communities. Partitioning occurs if the maximum positive eigenvalue is greater than the tolerance (10e-5) for the current partition, and if it results in a positive contribution to the Modularity. Given an initial separation using the leading eigen step, 'rSpectral' then continues to maximise for the change in Modularity using a fine-tuning step - or variate thereof. The first stage here is to find the node which, when moved from one community to another, gives the maximum change in Modularity. This node’s community is then fixed and we repeat the process until all nodes have been moved. The whole process is repeated from this new state until the change in the Modularity, between the new and old state, is less than the predefined tolerance. A slight variant of the fine-tuning step, which can improve speed of the calculation, is also provided. Instead of moving each node into each community in turn, we only consider moves of neighbouring nodes, found in different communities, to the community of the current node of interest. The two steps process is repeatedly applied to each new community found, subdivided each community into two new communities, until we are unable to find any division that results in a positive change in Modularity. |
| Authors: | Colin Mclean [aut] (algorithm implementation in Rcpp functions), Anatoly Sorokin [aut, cre] (R functions, cranification, documentation, testing, maintenance) |
| Maintainer: | Anatoly Sorokin <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.0.11 |
| Built: | 2024-08-12 04:35:14 UTC |
| Source: | https://github.com/cmclean5/rspectral |
This package implements the Spectral Modularity clustering algorithm for
igraph and graphNEL graphs. The algorithm
was proposed in (Newman 2006) and an example
of its application to the real biological network could be found in
(Roy et al. 2018).
Colin Mclean <[email protected]>
Newman MEJ (2006).
“Finding community structure in networks using the eigenvectors of matrices.”
Phys. Rev. E, 74(3), 036104.
doi:10.1103/PhysRevE.74.036104, https://link.aps.org/doi/10.1103/PhysRevE.74.036104.
Roy M, Sorokina O, McLean C, Tapia-González S, DeFelipe J, Armstrong JD, Grant SGN (2018).
“Regional Diversity in the Postsynaptic Proteome of the Mouse Brain.”
Proteomes, 6(3), 31.
ISSN 2227-7382, doi:10.3390/proteomes6030031, https://www.mdpi.com/2227-7382/6/3/31.
Useful links:
graphNEL objectsSpectral clustering for graphNEL objects
spectral_graphNEL(g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L)spectral_graphNEL(g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L)
g |
|
Cn_min |
minimum cluster size |
tol |
tolerance |
names |
are we dealing with alphaNumeric (1) or numeric (!1) ids |
fix_neig |
whether to fix neighbouring nodes found in same community |
data.frame with node names and membership information
library(graph) V = letters[1:12] g2 = randomEGraph(V, edges=20) mem.df = spectral_graphNEL(g2) head(mem.df)library(graph) V = letters[1:12] g2 = randomEGraph(V, edges=20) mem.df = spectral_graphNEL(g2) head(mem.df)
igraph objectsThis function invoke spectral_igraph_membership to calculate
clustering and convert it into communities object for
seamless work with native igraph clustering functions.
spectral_igraph_communities( g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L )spectral_igraph_communities( g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L )
g |
|
Cn_min |
minimum cluster size |
tol |
tolerance |
names |
are we dealing with alphaNumeric (1) or numeric (!1) ids |
fix_neig |
whether to fix neighbouring nodes found in same community |
communities object
data(karate,package='igraphdata') c<-spectral_igraph_communities(karate)data(karate,package='igraphdata') c<-spectral_igraph_communities(karate)
igraph objectsThis function implements the network clustering algorithm described in (M. E. J. Newman, 2006).
spectral_igraph_membership( g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L )spectral_igraph_membership( g, Cn_min = 1L, tol = 1e-05, names = 1L, fix_neig = 0L )
g |
|
Cn_min |
minimum cluster size |
tol |
tolerance |
names |
are we dealing with alphaNumeric (1) or numeric (!1) ids |
fix_neig |
whether to fix neighbouring nodes found in same community |
The complete iterative algorithm comprises of two steps. In the
first step, the network is expressed in terms of its leading eigenvalue and eigenvector
and recursively partition into two communities. Partitioning occurs if the maximum
positive eigenvalue is greater than the tolerance (tol=10-5) for the current
partition, and if it results in a positive contribution to the Modularity.
Given an initial separation using the leading eigen step, the function then continues to
maximise for the change in Modularity using a fine-tuning step - or variate thereof. The
first stage here is to find the node which, when moved from one community to another,
gives the maximum change in Modularity. This node’s community is then fixed and we repeat
the process until all nodes have been moved. The whole process is repeated from this new
state until the change in the Modularity, between the new and old state, is less than the
predefined tolerance (tol).
A slight variant of the fine-tuning step, which can reduce execution time by factor 2 to
5, is also provided. Instead of moving each node into each community in turn, we only
consider moves of neighbouring nodes, found in different communities, to the community of
the current node of interest. This variant of the node-moving algorithm effectively 'fixes'
neigbouring nodes fix_neig in the community being considered.
The two steps process is repeatedly applied to each new community found, subdivided each community
into two new communities, until we are unable to find any division that results in a positive change
in Modularity. An additional stopping criteria, based on the minimum cluster size Cn_min, is
also provided.
data.frame with node names and membership information
data(karate,package='igraphdata') df.mem<-spectral_igraph_membership(karate)data(karate,package='igraphdata') df.mem<-spectral_igraph_membership(karate)