Package 'PropClust'

Cluster and Propensity-based Approximation decomposition for adajcency matrixes.

Description

Given an adjacency matrix and cluster assignments, this function calculates either the conformity factors or the propensities of each node.

Usage

CPBADecomposition(adjacency,
                  clustering,
                  nClusters = NULL,
                  objectiveFunction = c("Poisson", "L2norm"),
                  dropUnassigned = TRUE,
                  unassignedLabel = 0,
                  unassignedMethod = "average",
                  accelerated = TRUE,
                  parallel = FALSE)

Arguments

adjacency	A square symmetric matrix giving either the number of connections between two nodes (for Poisson objective function) or the weighted connections (between 0 and 1) between each pair of nodes.
clustering	A vector with element per node containing the cluster assignments for each node. If a single cluster decomposition is desired, an alternative is to set nClusters=1 (see below).
nClusters	If the user wishes to input trivial clustering to calculate a "pure propensity" decomposition, this variable can be set to 1. Any other non-NULL value is considered invalid; use clusters to specify a non-trivial clustering.
objectiveFunction	Specifies the objective function for the Cluster and Propensity-based Approximation. Valid choices are (unique abbreviations of) "Poisson" and "L2norm".
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 clustering 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.
unassignedMethod	If dropUnassigned is FALSE, this argument sepcifies the method to assign unassigned objects to the nearest cluster. Valid values are (unique abbreviations) of "average", "single", and "complete". In analogy with hierarchical clustering, each node will be assigned to the cluster with which it has the highest average, maximum, and minimum adjacency, respectively.
accelerated	Logical: should an accelerated algorithm be used? In general the accelerated method is preferable.
parallel	Logical: should parallel calculation be used? At present the parallel calculation is not fully implemented and the function falls back to standard accelerated calculation, with a warning.

Details

If a single cluster is specified, the approximation is known as "Pure Propensity".

If unassigned nodes are present in the clustering and they are dropped before the CPBA calculation, their propensities, mean values and tail p-values are returned as NA.

Value

Returns the following list of items.

Propensity	Gives the propensities (or conformities) of each node.
IntermodularAdjacency	Gives the intermodular adjacencies or the conformities between clusters.
Factorizability	Gives the factorizability of the data.
L2Norm or Loglik	The L2 Norm (for L2 norm objective function) or the log-likelihood (for Poisson objetive function).
ExpectedAdjancency	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.
EdgePvalues	A distance structure representing the lower triangle of the symmetric matrix of the tail probabilities under the Poisson distribution.

Author(s)

John Michael Ranola, Peter Langfelder, Steve Horvath, Kenneth Lange

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

propensityClustering

Examples

nNodes=50
nClusters=5
#We would like to use L2Norm instead of Loglikelihood
objective = "L2norm"

ADJ<-matrix(runif(nNodes*nNodes),ncol=nNodes)
for(i in 1:(length(ADJ[1,])-1)){
		for(j in i:length(ADJ[,1])){
			ADJ[i,j]=ADJ[j,i]
		}
	}

for(i in 1:length(ADJ[1,])) ADJ[i,i]=0 

Results<-propensityClustering(
              adjacency = ADJ,
              objectiveFunction = objective,
              initialClusters = NULL,
              nClusters = nClusters,
              fastUpdates = FALSE)

Results2<-CPBADecomposition(adjacency = ADJ, clustering = Results$Clustering, 
                            objectiveFunction = objective)

Results3<-propensityClustering( adjacency = ADJ,
              objectiveFunction = objective,
              initialClusters = NULL,
              nClusters = nClusters,
              fastUpdates = TRUE)

---

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)

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