This function performs propensity clustering that assigns objects (or nodes) in a network to clusters such
that the resulting Cluster and Propensity-based Approximation (CPBA) of the input adjacency matrix optimizes
a specific criterion. Large data sets on which standard propensity clustering may take too long are first
optionally split into smaller blocks. Propensity clustering is then applied to each block,
and the clustering is used for the final CPBA decomposition.
Adjacency matrix of the network: a square, symmetric, non-negative matrix giving the
connection strengths between pairs of nodes. Missing data are not allowed.
decompositionType
Decomposition type. Either the full CPBA (Cluster and Propensity-Based
Approximation) or pure propensity, which is a special case of CPBA when all nodes are in a single cluster.
objectiveFunction
Objective function. Available choices are "Poisson" and "L2norm".
fastUpdates
Logical: should a fast, "approximate", propensity clustering method be used? This
option is recommended unless the number of nodes to be clustered is small (less than 500). The fast
updates may lead to slightly inferior results but are orders of magnitude faster for larger data sets (above
say 500 nodes).
blocks
Optional specification of blocks. If given, must be a vector with length equal the number of columns in
adjacency, each entry giving the block label for the corresponding node.
If not given, blocks will be determined automatically.
initialClusters
Optional specification of initial clusters. If given, must be a vector with length equal the number of
columns in
adjacency, each entry giving the cluster label for the corresponding node.
If not given, initial clusters will be determined automatically. The method depends on whether
nClusters (see below) is specified.
nClusters
Optional specification of the number of clusters. Note that specifying nClusters
changes the cluster initialization method. If nodes are split into blocks, the number of clusters in each
block will equal nClusters, and the total number of clusters will be nClusters times the
number of blocks.
maxBlockSize
Maximum block size.
clustMethod
Hierarchical clustering method. Recognized options are "average", "complete", and
"single".
cutreeDynamicArgs
Arguments (options) for the cutreeDynamic
function from package dynamicTreeCut used in the initial clustering step. Arguments dendro and
distM are set automatically; the rest can be set by the user to fine-tune the process of initial
cluster identification.
dropUnassigned
Logical: should unassigned nodes be excluded from the clustering? Unassigned nodes
can be present in initial clustering or blocks (if given), and internal pre-partitioning and initial
clustering can also lead to unassigned nodes. If dropUnassigned is TRUE, these nodes are
excluded from the calls to propensityClustering.
Otherwise these nodes will be assigned to the nearest
cluster within each block and be clustered using propensityClustering in each block.
unassignedLabel
Label in input blocks and initialClustering that is reserved for
unassigned objects. For clusterings with numeric lables this is typically (but not always) 0. Note that this
must a valid value - missing value NA will not work.
verbose
Level of verbosity of printed diagnostic messages. 0 means silent (except for progress
reports from the underlying propensity clustering function), higher values will lead to more detailed
progress messages.
indent
Indentation of the printed diagnostic messages. 0 means no indentation, each unit adds two
spaces.
Details
If initialClusters are not given, they are determined from the adjancency in one of the following
two ways: if
nClusters is not specified, the initialization uses hierarchical
clustering followed by the Dynamic Tree Cut (see cutreeDynamic). Arguments and
options for the cutreeDynamic can be specified using the argument
cutreeDynamicArgs. Some nodes may be left unassigned and their handling is described below.
If nClusters is specified, an internal initialization algorithm based on
connectivities is used. This second algorithm assigns all nodes to a cluster.
If dropUnassigned is TRUE, nodes left unassigned by the clustering procedure are excluded from
the following calculations. If dropUnassigned is FALSE, nodes left unassigned by the
clustering procedure are assigned to their nearest cluster, using the clustering dissimilarity measure
specified in clustMethod.
In the next step, if the total number of nodes exceeds maximum block size, the initial clusters (either
given or those automatically determined by hierarchical clustering) are split into blocks.
Clusters bigger than maximum block size
maxBlockSize are put
into separate blocks (one cluster per block). Clusters smaller than maximum block size are placed into
blocks such that the block size does not exceed maxBlockSize and such that clusters with high
between-cluster adjacency are placed in the same block, if possible. The between-cluster adjacency is
consistent with clustMethod.
Note that for the purposes of splitting data into blocks, hierarchical clustering is always used. If the
internal initialization of clusters is used, it is applied within each block and idependently of all other
blocks.
Next, propensity clustering
is applied to each block. More precisely, propensity clustering is
applied to the subset of nodes in each block that is assigned to an initial cluster. Some nodes may not be
assigned to initial clusters and these nodes are excluded from propensity clustering.
Once propensity clustering on all blocks is finished, propensity decomposition is calculated on the entire
network (excluding unassigned nodes).
Value
List with the following components:
Clustering
The final clustering. A vector of length equal to the number of nodes (columns in
adjacency) givig the cluster labels for each node. Clusters are labeled 1,2,3,...
Label 0 is reserved for unassigned nodes.
Propensity
Propensities (or conformities) of each node.
NodeWasConsidered
Logical vector with one entry per node. TRUE if the node was part of the
propensity clustering and decomposition (recall that unassigned nodes are excluded).
IntermodularAdjacency
Intermodular adjacencies or the conformities between clusters.
Factorizability
Factorizability of the data.
L2Norm or Loglik
The L2 Norm or the loglikelihood depending on l2bool.
MeanValues
A distance structure representing the lower triangle of the symmetric matrix of estimated
values of the adjacency matrix using the Propensity and IntermodularAdjacency.
If the Poisson updates are used,
the returned values are the estimate means of the distribution.
TailPvalues
A distance structure representing the lower triangle of the symmetric matrix of
the tail probabilities under the Poisson distribution.
Blocks
Blocks. A vector with one component for each node giving the block label for each node. The
blocks are labeled 1,2,3,...
InitialClusters
The initial clusters. A copy of the input if given, otherwise the automatically
determined initial clutering.
InitialTree
The hierarchical clustering dendrogram (tree) used to determine initial clusters. Only
present if the initial clusters were not supplied by the user.
Author(s)
John Michael Ranola, Peter Langfelder, Kenneth Lange, Steve Horvath
References
Ranola et. al. (2010) A Poisson Model for Random Multigraphs. Bioinformatics 26(16):2004-2001.
Ranola JM, Langfelder P, Lange K, Horvath S (2013) Cluster and propensity based approximation of a network.
BMC Bioinformatics, in press.
See Also
CPBADecomposition for propensity decomposition;
hclust for the hierarchical clustering function,
cutreeDynamic for the dynamic tree cut to identify clusters in a dendrogram
Examples
# Simulate 50 nodes in 5 clusters
nNodes=50
nClusters=5
# We would like to use L2Norm instead of Loglikelihood
objective = "L2norm"
ADJ<-matrix(runif(nNodes*nNodes),ncol=nNodes)
ADJ = (ADJ + t(ADJ))/2;
diag(ADJ) = 0;
results<-propensityClustering(
adjacency = ADJ,
objectiveFunction = objective,
initialClusters = NULL,
nClusters = nClusters,
fastUpdates = FALSE)
table(results$Clustering)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(PropClust)
Loading required package: flashClust
Attaching package: 'flashClust'
The following object is masked from 'package:stats':
hclust
Loading required package: dynamicTreeCut
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/PropClust/propensityClustering.Rd_%03d_medium.png", width=480, height=480)
> ### Name: propensityClustering
> ### Title: Propensity clustering
> ### Aliases: propensityClustering
> ### Keywords: cluster misc
>
> ### ** Examples
>
>
> # Simulate 50 nodes in 5 clusters
> nNodes=50
> nClusters=5
> # We would like to use L2Norm instead of Loglikelihood
> objective = "L2norm"
>
> ADJ<-matrix(runif(nNodes*nNodes),ncol=nNodes)
>
> ADJ = (ADJ + t(ADJ))/2;
>
> diag(ADJ) = 0;
>
> results<-propensityClustering(
+ adjacency = ADJ,
+ objectiveFunction = objective,
+ initialClusters = NULL,
+ nClusters = nClusters,
+ fastUpdates = FALSE)
..determining blocks..
..running propensityClustering in each block with non-trivial clustering..
..running propensityClustering in block 1
CLUSTERS QUICK INITIALIZED
CLUSTER ITERATION
[1] 1
CLUSTER ITERATION
[1] 2
CLUSTER ITERATION
[1] 3
..running final propensity decomposition..
..done (propensityClustering).
>
> table(results$Clustering)
1 2 3 4 5
8 10 12 11 9
>
>
>
>
>
> dev.off()
null device
1
>