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.
propensityClustering(
adjacency,
decompositionType = c("CPBA", "Pure Propensity"),
objectiveFunction = c("Poisson", "L2norm"),
fastUpdates = TRUE,
blocks = NULL,
initialClusters = NULL,
nClusters = NULL,
maxBlockSize = if (fastUpdates) 5000 else 1000,
clustMethod = "average",
cutreeDynamicArgs = list(deepSplit = 2, minClusterSize = 20,
verbose = 0),
dropUnassigned = TRUE,
unassignedLabel = 0,
verbose = 2,
indent = 0)List with the following components:
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.
Propensities (or conformities) of each node.
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).
Intermodular adjacencies or the conformities between clusters.
Factorizability of the data.
The L2 Norm or the loglikelihood depending on l2bool.
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.
A distance structure representing the lower triangle of the symmetric matrix of the tail probabilities under the Poisson distribution.
Blocks. A vector with one component for each node giving the block label for each node. The blocks are labeled 1,2,3,...
The initial clusters. A copy of the input if given, otherwise the automatically determined initial clutering.
The hierarchical clustering dendrogram (tree) used to determine initial clusters. Only present if the initial clusters were not supplied by the user.
Adjacency matrix of the network: a square, symmetric, non-negative matrix giving the connection strengths between pairs of nodes. Missing data are not allowed.
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.
Objective function. Available choices are "Poisson" and "L2norm".
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).
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.
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.
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.
Maximum block size.
Hierarchical clustering method. Recognized options are "average", "complete", and "single".
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.
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.
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.
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.
Indentation of the printed diagnostic messages. 0 means no indentation, each unit adds two spaces.
John Michael Ranola, Peter Langfelder, Kenneth Lange, Steve Horvath
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).
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. MC Syst Biol. 2013 Mar 14;7:21. doi: 10.1186/1752-0509-7-21.
CPBADecomposition for propensity decomposition;
hclust for the hierarchical clustering function,
cutreeDynamic for the dynamic tree cut to identify clusters in a dendrogram
# 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)
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