propensityClustering {PropClust}

Propensity clustering

Description

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.

Usage

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)

Arguments

adjacency

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. MC Syst Biol. 2013 Mar 14;7:21. doi: 10.1186/1752-0509-7-21.

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)