| Title: | Matching and meta-clustering in flow cytometry |
|---|---|
| Description: | Matching cell populations and building meta-clusters and templates from a collection of FC samples. |
| Authors: | Ariful Azad |
| Maintainer: | Ariful Azad <[email protected]> |
| License: | Artistic-2.0 |
| Version: | 1.43.0 |
| Built: | 2024-10-30 07:51:02 UTC |
| Source: | https://github.com/bioc/flowMatch |
Matching cell populations and building meta-clusters and templates from a collection of FC samples.
| Package: | flowMatch |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2013-08-01 |
| License: | GPL (>= 2) |
| LazyLoad: | yes |
Ariful Azad <[email protected]>
Azad, Ariful and Pyne, Saumyadipta and Pothen, Alex (2012), Matching phosphorylation response patterns of antigen-receptor-stimulated T cells via flow cytometry; BMC Bioinformatics, 13 (Suppl 2), S10.
Azad, Ariful and Langguth, Johannes and Fang, Youhan and Qi, Alan and Pothen, Alex (2010), Identifying rare cell populations in comparative flow cytometry; Algorithms in Bioinformatics, Springer, 162-175.
## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template)## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template)
An object of class "Cluster" represents a cluster or a cell population. We model a cluster with a normal distribution. An object of class "Cluster" therefore represents a cluster with a mean vector, a covariance matrix and the size of the cluster.
An object of class Cluster is usually created when constructing an object of class ClusteredSample.
Unless you know exactly what you are doing, creating an object of class "Cluster" using new or using the constructor is discouraged.
An object of class "Cluster" can be created using the following constructorCluster(size, center, cov, cluster.id = NA_integer_, sample.id=NA_integer_)
The arguments of the constructor bear usual meaning as described in the value section above.
An object of class "Cluster" contains the following slots:
size:An integer denoting the number of points (cells) present in the cluster.
center:A numeric vector denoting the center of the cluster.
cov:A matrix denoting the covariances of the underlying normal distribution of the cluster.
cluster.id:The index of the cluster (relative to other clusters in same sample). Default is NA_integer_ .
sample.id:The index of sample in which the cluster belongs to. Default is NA_integer_ .
All the slot accessor functions take an object of class Cluster. I show usage of the first accessor function. Other functions can be called similarly.
get.size:Returns the number of cells in the cluster.
Usage: get.size(object)
here object is a Cluster object.
get.center:Returns the center of the cluster.
get.cov:Returns the covariances matrix of the cluster.
get.cluster.id:Returns the index of the cluster (relative to other clusters in same sample).
get.sample.id:Returns the index of sample in which the cluster belongs to.
sample.id<-:Set the index of sample in which the cluster belongs to.
Display details about the Cluster object.
Return descriptive summary for each Cluster object.
Usage: summary(Cluster)
Ariful Azad
## An object of class "Cluster"" is usually created when constructing a "ClusteredSample". ## Unless you know exactly what you are doing, creating an object of class "Cluster" ## using new or using the constructor is discouraged. ## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## and retrive the parameters of the first cluster ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) center1 = km$centers[1,] # compute the covariance matrix of the first cluster cov1 = cov(sample[km$cluster==1,]) size1 = length(which(km$cluster==1)) ## ------------------------------------------------ ## Create an object of class "Cluster" ## and show summary ## ------------------------------------------------ clust = Cluster(size=size1, center=center1, cov=cov1) summary(clust)## An object of class "Cluster"" is usually created when constructing a "ClusteredSample". ## Unless you know exactly what you are doing, creating an object of class "Cluster" ## using new or using the constructor is discouraged. ## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## and retrive the parameters of the first cluster ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) center1 = km$centers[1,] # compute the covariance matrix of the first cluster cov1 = cov(sample[km$cluster==1,]) size1 = length(which(km$cluster==1)) ## ------------------------------------------------ ## Create an object of class "Cluster" ## and show summary ## ------------------------------------------------ clust = Cluster(size=size1, center=center1, cov=cov1) summary(clust)
An object of class "ClusteredSample" represents a partitioning of a sample into clusters. We model a flow cytometry sample with a mixture of cell populations where a cell population is a normally distributed cluster. An object of class "ClusteredSample" therefore stores a list of clusters and other necessary parameters.
An object of class "ClusteredSample" can be created using the following constructorClusteredSample(labels, centers=list(), covs=list(), sample=NULL, sample.id=NA_integer_)
labels A vector of integers (from 1:num.clusters) indicating the cluster to which each point is allocated. This is usually obtained from a clustering algorithm.
centers A list of length num.clusters storing the centers of the clusters. The ith entry of the list centers[[i]] stores the center of the ith cluster. If not specified, the constructor estimates centers from sample.
covs A list of length num.clusters storing the covariance matrices of the clusters. The ith entry of the list cov[[i]] stores the covariance matrix of the ith cluster. If not specified, the constructor estimates cov from sample.
sample A matrix, data frame of observations, or object of class flowFrame. Rows correspond to observations and columns correspond to variables. It must be passed to the constructor if either centers or cov is unspecified; then centers or cov is estimated from sample.
sample.id The index of the sample (relative to other samples of a cohort).
An object of class "ClusteredSample" contains the following slots:
num.clusters The number of clusters in the sample.
labels A vector of integers (from range 1:num.clusters) indicating the cluster to which each point is assigned to. For example, labels[i]=j means that the ith element (cell) is assigned to the jth cluster.
dimensionDimensionality of the sample (number of columns in data matrix).
clustersA list of length num.clusters storing the cell populations. Each cluster is stored as an object of class Cluster.
size Number of cells in the sample (summation of all cluster sizes).
sample.idinteger, denoting the index of the sample (relative to other samples of a cohort). Default is NA_integer_
All the slot accessor functions take an object of class ClusteredSample. I show usage of the first accessor function. Other functions can be called similarly.
get.size:Returns the number of cells in the sample (summation of all cluster sizes).
Usage: get.size(object)
here object is a ClusteredSample object.
get.num.clusters Returns the number of clusters in the sample.
get.labels Returns the cluster labels for each cell. For example, labels[i]=j means that the ith element (cell) is assigned to the jth cluster.
get.dimensionReturns the dimensionality of the sample (number of columns in data matrix).
get.clustersReturns the list of clusters in this sample. Each cluster is stored as an object of class Cluster.
get.sample.idReturns the index of the sample (relative to other samples of a cohort).
Display details about the ClusteredSample object.
Return descriptive summary for the ClusteredSample object.
Usage: summary(ClusteredSample)
We plot a sample by bivariate scatter plots where different clusters are shown in different colors.
Usage:
plot(sample, ClusteredSample, ...)
the arguments of the plot function are:
sample: A matrix, data.frame or an object of class flowFrame representing an FC sample.
ClusteredSample: An object of class ClusteredSample storing the clustering of the sample.
... Other usual plotting related parameters.
Ariful Azad
## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object (Option 1 ) ## without specifying centers and covs ## we need to pass FC sample for paramter estimation ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) ## ------------------------------------------------ ## Create ClusteredSample object (Option 2) ## specifying centers and covs ## no need to pass the sample ## ------------------------------------------------ centers = list() covs = list() num.clusters = nrow(km$centers) for(i in 1:num.clusters) { centers[[i]] = km$centers[i,] covs[[i]] = cov(sample[cluster.labels==i,]) } # Now we do not need to pass sample ClusteredSample(labels=cluster.labels, centers=centers, covs=covs) ## ------------------------------------------------ ## Show summary and plot a clustered sample ## ------------------------------------------------ summary(clustSample) plot(sample, clustSample)## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object (Option 1 ) ## without specifying centers and covs ## we need to pass FC sample for paramter estimation ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) ## ------------------------------------------------ ## Create ClusteredSample object (Option 2) ## specifying centers and covs ## no need to pass the sample ## ------------------------------------------------ centers = list() covs = list() num.clusters = nrow(km$centers) for(i in 1:num.clusters) { centers[[i]] = km$centers[i,] covs[[i]] = cov(sample[cluster.labels==i,]) } # Now we do not need to pass sample ClusteredSample(labels=cluster.labels, centers=centers, covs=covs) ## ------------------------------------------------ ## Show summary and plot a clustered sample ## ------------------------------------------------ summary(clustSample) plot(sample, clustSample)
An object of class "ClusterMatch" represents matching of cluster/meta-clusters across a pair of FC samples/templates. A cluster (meta-cluster) from a sample (template) can match to zero, one or more than one cluster (meta-clusters) in another sample (template).
An object of class "ClusterMatch" is usually created by calling the function match.clusters:
match.clusters(object1, object2, dist.type='Mahalanobis', unmatch.penalty=999999).
Here, object1 and object2 are two objects of class ClusteredSample or Template between which the clusters or meta-clusters are matched. See the example section and also the match.clusters function for more details.
Unless you know exactly what you are doing, creating an object of class "ClusterMtach" using new or using the constructor is discouraged.
Let S1 and S2 be two FC samples or templates with k1 and k2 clusters or meta-clusters respectively. Then the matching of clusters (meta-clusters) across S1 and S2 is represented by an object of class "ClusterMatch" that contains the following slots:
match12:A list of length k1 where match12[[i]] stores the indices of clusters (meta-clusters) from S2 matched to the i-th clustrer (meta-cluster) of S1. match12[[i]]=NULL if the i-th cluster (meta-cluster) of S1 remains unmatched, otherwise, it stores a vector of matched clusters (meta-clusters) from S2.
match21:A list of length k2 where match21[[i]] stores the indices of clusters (meta-clusters) from S1 matched to the i-th clustrer (meta-cluster) of S2. match21[[i]]=NULL if the i-th cluster (meta-cluster) of S2 remains unmatched, otherwise, it stores a vector of matched clusters (meta-clusters) from S1.
matching.cost:The cost of matching clusters (meta-clusters) across the samples. It is equal to the summation of dissimilarities of the matched clusters (meta-clusters) and penalty for the unmatched clusters (meta-clusters).
unmatch.penalty:A numeric value denoting the penalty for leaving a cluster (meta-cluster) unmatched. If we set it to a a very large value then no cluster (meta-cluster) remains unmatched giving an edge cover solution.
All the slot accessor functions take an object of class ClusterMatch. I show usage of the first accessor function. Other functions can be called similarly.
get.match12:Returns the matching from cluster in sample 1 to clusters in sample 2. See the slot description for details.
Usage: get.match12(object)
here object is a ClusterMatch object.
get.match21:Returns the matching from cluster in sample 2 to clusters in sample 1. See the slot description for details.
get.matching.cost:Returns the total cost of matching clusters (meta-clusters) across the pair samples/templates.
get.unmatch.penalty:Returns the penalty for leaving a cluster (meta-cluster) unmatched.
Display details about the ClusterMatch object.
Return descriptive summary of the matching of clusters (meta-clusters) across a pair of samples (templates). Shows both list and matrix format.
Usage: summary(ClusterMatch)
Ariful Azad
match.clusters, ClusteredSample, Template
## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') ## ------------------------------------------------ ## Computing matching of clusteres ## An object of class "ClusterMatch" is returned ## ------------------------------------------------ mec = match.clusters(clustSample1, clustSample2, dist.type="Mahalanobis", unmatch.penalty=99999) ## show the matching summary(mec) ## ********************************************************************** ## ************** Now matching meta-clusters across templates *********** ## ********************************************************************** ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) ## ------------------------------------------------ ## Match meta-clusters across templates ## ------------------------------------------------ mec = match.clusters(template1, template2, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec) ## ------------------------------------------------ ## Another example of matching meta-clusters & clusters ## across a template and a sample ## ------------------------------------------------ mec = match.clusters(template1, clustSample1, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec)## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') ## ------------------------------------------------ ## Computing matching of clusteres ## An object of class "ClusterMatch" is returned ## ------------------------------------------------ mec = match.clusters(clustSample1, clustSample2, dist.type="Mahalanobis", unmatch.penalty=99999) ## show the matching summary(mec) ## ********************************************************************** ## ************** Now matching meta-clusters across templates *********** ## ********************************************************************** ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) ## ------------------------------------------------ ## Match meta-clusters across templates ## ------------------------------------------------ mec = match.clusters(template1, template2, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec) ## ------------------------------------------------ ## Another example of matching meta-clusters & clusters ## across a template and a sample ## ------------------------------------------------ mec = match.clusters(template1, clustSample1, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec)
Create an object of class Template summarizes a group of samples belonging to same biological-class with a class-template. A template is represented by a collection of meta-clusters (MetaCluster) created from samples of same class. An object of class Template therefore stores a list of MetaCluster objects and other necessary parameters.
create.template(clustSamples, dist.type = "Mahalanobis", unmatch.penalty=999999, template.id = NA_integer_)create.template(clustSamples, dist.type = "Mahalanobis", unmatch.penalty=999999, template.id = NA_integer_)
clustSamples |
A list of |
dist.type |
character, indicating the method with which the dissimilarity between a pair of clusters is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean'. If this argument is not passed then 'Mahalanobis' distance is used by default. |
unmatch.penalty |
A numeric value denoting the penalty for leaving a cluster unmatched. This parameter should be already known or be estimated empirically estimated from data (see the reference for a discussion). Default is set to a very high value so that no cluster remains unmatched. |
template.id |
integer, denoting the index of the template (relative to other template). Default is NA_integer_ |
An object of class Template summarizes a group of samples belonging to same biological-class with a class-specific template. A template is represented by a collection of meta-clusters (MetaCluster) created from samples of same class. An object of class Template therefore stores a list of MetaCluster objects and other necessary parameters.
dist.sample returns a numeric value representing dissimilarity between a pair of samples. This value is equal to the summation of dissimilarities of the matched clusters and penalty for the unmatched clusters.
Ariful Azad
Azad, Ariful and Pyne, Saumyadipta and Pothen, Alex (2012), Matching phosphorylation response patterns of antigen-receptor-stimulated T cells via flow cytometry; BMC Bioinformatics, 13 (Suppl 2), S10.
## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template) ## option-2: plot contours of each cluster of the meta-clusters with defined color plot(template, color.mc=c('blue','black','green3','red')) ## option-3: plot contours of the meta-clusters with defined color plot(template, plot.mc=TRUE, color.mc=c('blue','black','green3','red')) ## option-4: plot contours of each cluster of the meta-clusters with different colors for different samples plot(template, colorbysample=TRUE)## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template) ## option-2: plot contours of each cluster of the meta-clusters with defined color plot(template, color.mc=c('blue','black','green3','red')) ## option-3: plot contours of the meta-clusters with defined color plot(template, plot.mc=TRUE, color.mc=c('blue','black','green3','red')) ## option-4: plot contours of each cluster of the meta-clusters with different colors for different samples plot(template, colorbysample=TRUE)
Calculate the dissimilarity between a pair of cell populations (clusters) from the distributions of the clusters.
dist.cluster(cluster1,cluster2, dist.type = 'Mahalanobis')dist.cluster(cluster1,cluster2, dist.type = 'Mahalanobis')
cluster1 |
an object of class |
cluster2 |
an object of class |
dist.type |
character, indicating the method with which the dissimilarity between a pair of clusters is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean'. |
Consider two p-dimensional, normally distributed clusters with centers and covariance matrices . Assume the size of the clusters are n1 and n2 respectively. We compute the dissimilarity d12 between the clusters as follows:
If dist.type='Mahalanobis': we compute the dissimilarity d12 with the Mahalanobis distance between the distributions of the clusters.
If dist.type='KL': we compute the dissimilarity d12 with the Symmetrized Kullback-Leibler divergence between the distributions of the clusters. Note that KL-divergence is not symmetric in its original form. We converted it symmetric by averaging both way KL divergence. The symmetrized KL-divergence is not a metric because it does not satisfy triangle inequality.
If dist.type='Euclidean': we compute the dissimilarity d12 with the Euclidean distance between the centers of the clusters.
The dimension of the clusters must be same.
dist.cluster returns a numeric value denoting the dissimilarities between a pair of cell populations (clusters).
Ariful Azad
McLachlan, GJ (1999) Mahalanobis distance; Journal of Resonance 4(6), 20–26.
Abou–Moustafa, Karim T and De La Torre, Fernando and Ferrie, Frank P (2010) Designing a Metric for the Difference between Gaussian Densities; Brain, Body and Machine, 57–70.
mahalanobis.dist, symmetric.KL, dist.matrix
## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) clust1 = get.clusters(clustSample)[[1]] clust2 = get.clusters(clustSample)[[2]] dist.cluster(clust1, clust2, dist.type='Mahalanobis') dist.cluster(clust1, clust2, dist.type='KL') dist.cluster(clust1, clust2, dist.type='Euclidean')## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) clust1 = get.clusters(clustSample)[[1]] clust2 = get.clusters(clustSample)[[2]] dist.cluster(clust1, clust2, dist.type='Mahalanobis') dist.cluster(clust1, clust2, dist.type='KL') dist.cluster(clust1, clust2, dist.type='Euclidean')
Calculate a matrix storing the dissimilarities between each pair of clusters (meta-clusters) across a pair of samples (templates) S1 and S2. (i,j)th entry of the matrix stores dissimilarity between i-th cluster (meta-cluster) from S1 and the j-th cluster (meta-cluster) from S2.
dist.matrix(object1,object2, dist.type = 'Mahalanobis')dist.matrix(object1,object2, dist.type = 'Mahalanobis')
object1 |
an object of class |
object2 |
an object of class |
dist.type |
character, indicating the method with which the dissimilarity between a pair of clusters (meta-clusters) is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean', with the default is set to 'Mahalanobis' distance. |
Consider two FC samples/templates S1 and S2 with k1 and k2 clusters/meta-clusters. The dissimilarity between each pair of cluster (meta-clusters) across S1 and S2 is computed and stored in a (k1 x k2) matrix. The dissimilarity between i-th cluster (meta-cluster) from S1 and j-th cluster (meta-cluster) from S2 is computed using function dist.cluster.
dist.matrix function returns a (k1 x k2) matrix where k1 and k2 are the number of clusters (meta-clusters) in the first and the second samples (templates) respectively. (i,j)th entry of the matrix contains the dissimilarity between the i-th cluster (meta-cluster) from sample1 (template1) and the j-th cluster (meta-cluster) from sample2 (template2).
Ariful Azad
## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute the Mahalanobis distance between ## each pair of clsuters and save it in a matrix ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') print(DM)## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute the Mahalanobis distance between ## each pair of clsuters and save it in a matrix ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') print(DM)
Compute the dissimilarity between a pair of clustered FC samples by using Mixed Edge Cover (MEC) algorithm.
dist.sample(clustSample1, clustSample2, dist.type='Mahalanobis', unmatch.penalty=999999)dist.sample(clustSample1, clustSample2, dist.type='Mahalanobis', unmatch.penalty=999999)
clustSample1 |
an object of class |
clustSample2 |
an object of class |
dist.type |
character, indicating the method with which the dissimilarity between a pair of clusters is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean'. |
unmatch.penalty |
A numeric value denoting the penalty for leaving a cluster unmatched. This parameter should be already known or be estimated empirically estimated from data (see the reference for a discussion). Default is set to a very high value so that no cluster remains unmatched. |
We used a robust version of matching called Mixed Edge Cover (MEC) to match clusters across a pair of samples. MEC allows a cluster to be matched with zero, one or more than one clusters in a paired sample. The cost of an MEC solution is equal to the summation of dissimilarities of the matched clusters and penalty for the unmatched clusters. The MEC algorithm finds an optimal solution by minimizing the cost of MEC, which is then used as dissimilarity between a pair of samples.
dist.sample returns a numeric value representing dissimilarity between a pair of samples. This value is equal to the summation of dissimilarities of the matched clusters and penalty for the unmatched clusters.
Ariful Azad
Azad, Ariful and Langguth, Johannes and Fang, Youhan and Qi, Alan and Pothen, Alex (2010), Identifying rare cell populations in comparative flow cytometry; Algorithms in Bioinformatics, Springer, 162-175.
ClusteredSample, match.clusters
## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute dissimilarity between two clustered samples ## using the mixed edge cover algorithm ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) D = dist.sample(clustSample1, clustSample2, dist.type='Mahalanobis', unmatch.penalty=999999)## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute dissimilarity between two clustered samples ## using the mixed edge cover algorithm ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) D = dist.sample(clustSample1, clustSample2, dist.type='Mahalanobis', unmatch.penalty=999999)
Compute the dissimilarity between a pair of FC templates by using Mixed Edge Cover (MEC) algorithm.
dist.template(template1, template2, dist.type='Mahalanobis', unmatch.penalty=999999)dist.template(template1, template2, dist.type='Mahalanobis', unmatch.penalty=999999)
template1 |
an object of class |
template2 |
an object of class |
dist.type |
character, indicating the method with which the dissimilarity between a pair of meta-clusters is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean'. |
unmatch.penalty |
A numeric value denoting the penalty for leaving a meta-cluster unmatched. This parameter should be already known or be estimated empirically estimated from data (see the reference for a discussion). Default is set to a very high value so that no meta-cluster remains unmatched. |
We used a robust version of matching called Mixed Edge Cover (MEC) to match meta-clusters across a pair of templates. MEC allows a meta-cluster to be matched with zero, one or more than one meta-clusters in a paired template. The cost of an MEC solution is equal to the summation of dissimilarities of the matched meta-clusters and penalty for the unmatched meta-clusters. The MEC algorithm finds an optimal solution by minimizing the cost of MEC, which is then used as dissimilarity between a pair of templates.
dist.template returns a numeric value representing dissimilarity between a pair of templates. This value is equal to the summation of dissimilarities of the matched meta-clusters and penalty for the unmatched meta-clusters.
Ariful Azad
Azad, Ariful and Langguth, Johannes and Fang, Youhan and Qi, Alan and Pothen, Alex (2010), Identifying rare cell populations in comparative flow cytometry; Algorithms in Bioinformatics, Springer, 162-175.
## ------------------------------------------------ ## load data and retrieve two templates ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) D = dist.template(template1, template2, dist.type='Mahalanobis', unmatch.penalty=999999)## ------------------------------------------------ ## load data and retrieve two templates ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) D = dist.template(template1, template2, dist.type='Mahalanobis', unmatch.penalty=999999)
Compute the Mahalanobis distance between a pair of normally distributed clusters.
mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)
mean1 |
mean vector of length |
mean2 |
mean vector of length |
cov1 |
|
cov2 |
|
n1 |
number of cells (points) in cluster 1. |
n2 |
number of cells (points) in cluster 2. |
Consider two p-dimensional, normally distributed clusters with centers and covariance matrices . Assume the size of the clusters are n1 and n2 respectively.
We compute the Mahalanobis distance d12 between the clusters as follows:
The dimension of the clusters must be same.
mahalanobis.dist returns a numeric value measuring the Mahalanobis distance between a pair of normally distributed clusters.
Ariful Azad
McLachlan, GJ (1999) Mahalanobis distance; Journal of Resonance 4(6), 20–26.
## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) mean1 = get.center(get.clusters(clustSample)[[1]]) mean2 = get.center(get.clusters(clustSample)[[2]]) cov1 = get.cov(get.clusters(clustSample)[[1]]) cov2 = get.cov(get.clusters(clustSample)[[2]]) n1 = get.size(get.clusters(clustSample)[[1]]) n2 = get.size(get.clusters(clustSample)[[2]]) mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) mean1 = get.center(get.clusters(clustSample)[[1]]) mean2 = get.center(get.clusters(clustSample)[[2]]) cov1 = get.cov(get.clusters(clustSample)[[1]]) cov2 = get.cov(get.clusters(clustSample)[[2]]) n1 = get.size(get.clusters(clustSample)[[1]]) n2 = get.size(get.clusters(clustSample)[[2]]) mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)
This function computes a matching of cluster/meta-clusters across a pair of FC samples/templates. A cluster (meta-cluster) from a sample (template) can match to zero, one or more than one clusters (meta-clusters) in another sample (template).
match.clusters(object1, object2, dist.type='Mahalanobis', unmatch.penalty=999999) match.clusters.dist(d.matrix,unmatch.penalty=999999)match.clusters(object1, object2, dist.type='Mahalanobis', unmatch.penalty=999999) match.clusters.dist(d.matrix,unmatch.penalty=999999)
object1 |
an object of class |
object2 |
an object of class |
dist.type |
character, indicating the method with which the dissimilarity between a pair of clusters (meta-clusters) is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean', with the default is set to 'Mahalanobis' distance. |
d.matrix |
a matrix used only in the second defination ( |
unmatch.penalty |
numeric value denoting the penalty for leaving a cluster (meta-cluster) unmatched. This parameter should be already known or be estimated empirically estimated from data (see the reference for a discussion). Default is set to a very high value so that no cluster (meta-cluster) remains unmatched. |
We used a robust version of matching called Mixed Edge Cover (MEC) to match clusters (meta-clusters) across a pair of samples (templates). MEC allows a cluster (meta-cluster) to be matched with zero, one or more than one clusters (meta-clusters) across a pair of samples (template). The cost of an MEC solution is equal to the summation of dissimilarities of the matched clusters (meta-clusters) and penalty for the unmatched clusters (meta-clusters). The MEC algorithm finds an optimal solution by minimizing the cost of MEC.
match.clusters returns an object of class ClusterMatch representing matching of clusters (meta-clusters) across a pair of FC samples (templates). A cluster (meta-cluster) from a sample (template) can match to zero, one or more than one cluster (meta-clusters) in another sample (template).
Ariful Azad
Azad, Ariful and Langguth, Johannes and Fang, Youhan and Qi, Alan and Pothen, Alex (2010), Identifying rare cell populations in comparative flow cytometry; Algorithms in Bioinformatics, Springer, 162-175.
dist.matrix, ClusteredSample, Template
## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ********************************************************************** ## ************** first matching clusters across samples **************** ## ********************************************************************** ## ------------------------------------------------ ## retrieve and cluster two samples using kmeans algorithm ## ------------------------------------------------ sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') ## ------------------------------------------------ ## Computing matching of clusteres ## An object of class "ClusterMatch" is returned ## ------------------------------------------------ ## directly from the ClusteredSample objects: approach 1 mec = match.clusters(clustSample1, clustSample2, dist.type="Mahalanobis", unmatch.penalty=99999) ## from the dissimilarity matrix: approach 2 mec = match.clusters.dist(DM, unmatch.penalty=99999) ## show the matching summary(mec) ## ********************************************************************** ## ************** Now matching meta-clusters across templates *********** ## ********************************************************************** ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) ## ------------------------------------------------ ## Match meta-clusters across templates ## ------------------------------------------------ mec = match.clusters(template1, template2, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec) ## ------------------------------------------------ ## Another example of matching meta-clusters & clusters ## across a template and a sample ## ------------------------------------------------ mec = match.clusters(template1, clustSample1, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec)## ------------------------------------------------ ## load data and retrieve two samples ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ********************************************************************** ## ************** first matching clusters across samples **************** ## ********************************************************************** ## ------------------------------------------------ ## retrieve and cluster two samples using kmeans algorithm ## ------------------------------------------------ sample1 = exprs(hd.flowSet[[1]]) sample2 = exprs(hd.flowSet[[2]]) clust1 = kmeans(sample1, centers=4, nstart=20) clust2 = kmeans(sample2, centers=4, nstart=20) cluster.labels1 = clust1$cluster cluster.labels2 = clust2$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSample2 = ClusteredSample(labels=cluster.labels2, sample=sample2) ## compute the dissimilarity matrix DM = dist.matrix(clustSample1, clustSample2, dist.type='Mahalanobis') ## ------------------------------------------------ ## Computing matching of clusteres ## An object of class "ClusterMatch" is returned ## ------------------------------------------------ ## directly from the ClusteredSample objects: approach 1 mec = match.clusters(clustSample1, clustSample2, dist.type="Mahalanobis", unmatch.penalty=99999) ## from the dissimilarity matrix: approach 2 mec = match.clusters.dist(DM, unmatch.penalty=99999) ## show the matching summary(mec) ## ********************************************************************** ## ************** Now matching meta-clusters across templates *********** ## ********************************************************************** ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:10) # read 10 samples and cluster them { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create two templates each from five samples ## ------------------------------------------------ template1 = create.template(clustSamples[1:5]) template2 = create.template(clustSamples[6:10]) ## ------------------------------------------------ ## Match meta-clusters across templates ## ------------------------------------------------ mec = match.clusters(template1, template2, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec) ## ------------------------------------------------ ## Another example of matching meta-clusters & clusters ## across a template and a sample ## ------------------------------------------------ mec = match.clusters(template1, clustSample1, dist.type="Mahalanobis", unmatch.penalty=99999) summary(mec)
An object of class "MetaCluster" represents a collection of biologically similar clusters from a set of FC samples. A meta-cluster is formed by matching clusters across samples and merging the matched clusters. An object of class "ClusteredSample" stores the estimated parameter of the whole meta-cluster as well as a list of clusters participating in the meta-cluster.
An object of class MetaCluster is usually created when constructing an object of class Template.
Unless you know exactly what you are doing, creating an object of class "MetaCluster" using new or using the constructor is discouraged.
An object of class "MetaCluster" can be created using the following constructorMetaCluster(clusters) where the argument "clusters" is a list of object of class Cluster from which the meta-cluster is created.
An object of class "MetaCluster" contains the following slots:
num.clustersThe number of clusters in the meta-cluster.
clustersA list of length num.clusters storing the clusters (cell populations) participating in this meta-cluster. Each cluster is stored as an object of class Cluster.
size Number of cells in the meta-cluster (summation of all cluster sizes).
centerA numeric vector denoting the center of the meta-cluster.
covA matrix denoting the covariances of the underlying normal distribution of the meta-cluster.
All the slot accessor functions take an object of class MetaCluster. I show usage of the first accessor function. Other functions can be called similarly.
get.size:The number of cells in the meta-cluster(summation of all cluster sizes).
Usage: get.size(object)
here object is a MetaCluster object.
get.num.clustersReturns the number of clusters in the meta-cluster.
get.clustersReturns the list of clusters (cell populations) participating in this meta-cluster. Each cluster is stored as an object of class Cluster.
get.size Returns the number of cells in the meta-cluster (summation of all cluster sizes).
get.centerReturns the center of the meta-cluster.
get.covReturns the covariances matrix of the meta-cluster.
Display details about the Metacluster object.
Return descriptive summary for the MetaCluster object.
Usage: summary(MetaCluster)
We plot a meta-cluster as a contour plot of the distribution of the underlying clusters or the combined meta-cluster.
We consider cells in clusters or in the meta-cluster are normally distributed and represent the distribution with ellipsoid.
The axes of an ellipsoid is estimated from the eigen values and eigen vectors of the covariance matrix ("Applied Multivariate Statistical Analysis" by R. Johnson and D. Wichern, 5th edition, Prentice hall).
We then plot the bi-variate projection of the ellipsoid as 2-D ellipses.
Usage:
plot(mc, alpha=.05, plot.mc=FALSE, ...)
the arguments of the plot function are:
mc An object of class MetaCluster for which the plot function is invoked.
alpha (1-alpha)*100% quantile of the distribution of the clusters or meta-cluster is plotted.
plot.mc TRUE/FALSE, when TRUE the functions draws contour of the combined meta-cluster and when FALSE the function draws the contours of the individual clusters.
... Other usual plotting related parameters.
Ariful Azad
Azad, Ariful and Pyne, Saumyadipta and Pothen, Alex (2012), Matching phosphorylation response patterns of antigen-receptor-stimulated T cells via flow cytometry; BMC Bioinformatics, 13 (Suppl 2), S10.
## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, cluster it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and retrieve the meta-clusters ## ------------------------------------------------ template = create.template(clustSamples) #retrieve meta-clusters from template mc = get.metaClusters(template)[[1]] summary(mc) # plot all participating cluster in this meta-cluster plot(mc) # plot the outline of the combined meta-cluster plot(mc, plot.mc=TRUE)## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, cluster it and store the ## clustered samples in a list ## ------------------------------------------------ cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and retrieve the meta-clusters ## ------------------------------------------------ template = create.template(clustSamples) #retrieve meta-clusters from template mc = get.metaClusters(template)[[1]] summary(mc) # plot all participating cluster in this meta-cluster plot(mc) # plot the outline of the combined meta-cluster plot(mc, plot.mc=TRUE)
Compute the Symmetrized Kullback-Leibler divergence between a pair of normally distributed clusters.
symmetric.KL(mean1, mean2, cov1, cov2)symmetric.KL(mean1, mean2, cov1, cov2)
mean1 |
mean vector of length |
mean2 |
mean vector of length |
cov1 |
|
cov2 |
|
Consider two p-dimensional, normally distributed clusters with centers and covariance matrices . We compute the KL divergence d12 between the clusters as follows:
The dimension of the clusters must be same.
Note that KL-divergence is not symmetric in its original form. We converted it symmetric by averaging both way KL divergence. The symmetrized KL-divergence is not a metric because it does not satisfy triangle inequality.
symmetric.KL returns a numeric value measuring the Symmetrized Kullback-Leibler divergence between a pair of normally distributed clusters.
Ariful Azad
Abou–Moustafa, Karim T and De La Torre, Fernando and Ferrie, Frank P (2010) Designing a Metric for the Difference between Gaussian Densities; Brain, Body and Machine, 57–70.
mahalanobis.dist, dist.cluster
## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) mean1 = get.center(get.clusters(clustSample)[[1]]) mean2 = get.center(get.clusters(clustSample)[[2]]) cov1 = get.cov(get.clusters(clustSample)[[1]]) cov2 = get.cov(get.clusters(clustSample)[[2]]) n1 = get.size(get.clusters(clustSample)[[1]]) n2 = get.size(get.clusters(clustSample)[[2]]) symmetric.KL(mean1, mean2, cov1, cov2)## ------------------------------------------------ ## load data and retrieve a sample ## ------------------------------------------------ library(healthyFlowData) data(hd) sample = exprs(hd.flowSet[[1]]) ## ------------------------------------------------ ## cluster sample using kmeans algorithm ## ------------------------------------------------ km = kmeans(sample, centers=4, nstart=20) cluster.labels = km$cluster ## ------------------------------------------------ ## Create ClusteredSample object ## and compute mahalanobis distance between two clsuters ## ------------------------------------------------ clustSample = ClusteredSample(labels=cluster.labels, sample=sample) mean1 = get.center(get.clusters(clustSample)[[1]]) mean2 = get.center(get.clusters(clustSample)[[2]]) cov1 = get.cov(get.clusters(clustSample)[[1]]) cov2 = get.cov(get.clusters(clustSample)[[2]]) n1 = get.size(get.clusters(clustSample)[[1]]) n2 = get.size(get.clusters(clustSample)[[2]]) symmetric.KL(mean1, mean2, cov1, cov2)
An object of class "Template" summarizes a group of samples belonging to same biological-class with a class-template. A template is represented by a collection of meta-clusters (MetaCluster) created from samples of same class. An object of class "Template" therefore stores a list of MetaCluster objects and other necessary parameters.
An object of class "Template" can be created using the function create.template : create.template(clustSamples, dist.type = "Mahalanobis", unmatch.penalty=999999, template.id = NA_integer_).
The arguments to the create.template function is described below:
clustSamples: A list of ClusteredSample objects from which the template is created. The working examples describe how this objects are created by clustering FC samples.
dist.type: character, indicating the method with which the dissimilarity between a pair of clusters is computed. Supported dissimilarity measures are: 'Mahalanobis', 'KL' and 'Euclidean'. If this argument is not passed then 'Mahalanobis' distance is used by default.
unmatch.penalty: A numeric value denoting the penalty for leaving a cluster unmatched. This parameter should be already known or be estimated empirically estimated from data (see the reference for a discussion). Default is set to a very high value so that no cluster remains unmatched.
template.id: integer, denoting the index of the template (relative to other template). Default is NA_integer_
num.metaclusters:The number of meta-clusters in the template.
metaClusters:A list of length num.metaclusters storing the meta-clusters. Each meta-cluster is stored as an object of class MetaCluster.
dimension:Dimensionality of the samples from which the template is created.
size:Number of cells in the template (summation of all meta-cluster sizes).
tree: A list (similar to an hclust object) storing the hierarchy of the samples in a template.
template.id:integer, denoting the index of the template (relative to other templates). Default is NA_integer_
All the slot accessor functions take an object of class Template. I show usage of the first accessor function. Other functions can be called similarly.
get.size:Number of cells in the template (summation of all meta-cluster sizes).
Usage: get.size(object)
here object is a Template object.
get.num.metaclusters:Returns the number of meta-clusters in the template.
get.metaClusters:Returns a list of length num.metaclusters storing the meta-clusters. Each meta-cluster is stored as an object of class MetaCluster.
get.dimension:Returns the dimensionality of the samples from which the template is created.
get.tree:Returns a hclust object storing the hierarchy of the samples in a template.
get.template.id:Returns the index of the template (relative to other templates).
Display details about the Template object.
Return descriptive summary for each MetaCluster of a Template.
Usage: summary(Template)
We plot a template as a collection of bivariate contour plots of its meta-clusters.
To plot each meta-cluster we consider the clusters within the meta-cluster normally distributed and represent each cluster with an ellipsoid. The axes of an ellipsoid is estimated from the eigen values and eigen vectors of the covariance matrix of a cluster ("Applied Multivariate Statistical Analysis" by R. Johnson and D. Wichern, 5th edition, Prentice hall). We then plot the bivariate projection of the ellipsoid as 2-D ellipses.
Usage:
plot(template, alpha=.05, plot.mc=FALSE, color.mc=NULL, colorbysample=FALSE, ...)
the arguments of the plot function are:
template: An object of class Template for which the plot function is invoked.
alpha: (1-alpha)*100% quantile of the distribution of the clusters or meta-cluster is plotted.
plot.mc: TRUE/FALSE, when TRUE the functions draws contour of the combined meta-cluster and when FALSE the function draws the contours of the individual clusters.
color.mc: A character vector of length num.metaclusters denoting the colors to be used to draw the contours. The ith color of this vector is used to draw the ellipses denoting clusters in the ith meta-cluster or the combined ith meta-cluster (depending on the argument plot.mc). By default an empty vector is passed and then an arbitrary color is used to draw each meta-cluster.
colorbysample: TRUE/FALSE, when TRUE the functions draws clusters from same samples in a single color and when FALSE the function draws meta-clusters in a single color.
... : Other usual plotting related parameters.
Plot the hierarchy of samples established while creating the template-tree. See template.tree
Ariful Azad
Azad, Ariful and Pyne, Saumyadipta and Pothen, Alex (2012), Matching phosphorylation response patterns of antigen-receptor-stimulated T cells via flow cytometry; BMC Bioinformatics, 13 (Suppl 2), S10.
MetaCluster, ClusteredSample, create.template, template.tree
## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template) ## option-2: plot contours of each cluster of the meta-clusters with defined color plot(template, color.mc=c('blue','black','green3','red')) ## option-3: plot contours of the meta-clusters with defined color plot(template, plot.mc=TRUE, color.mc=c('blue','black','green3','red')) ## option-4: plot contours of each cluster of the meta-clusters with different colors for different samples plot(template, colorbysample=TRUE)## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template) ## plot the template in terms of the meta-clusters ## option-1 (default): plot contours of each cluster of the meta-clusters plot(template) ## option-2: plot contours of each cluster of the meta-clusters with defined color plot(template, color.mc=c('blue','black','green3','red')) ## option-3: plot contours of the meta-clusters with defined color plot(template, plot.mc=TRUE, color.mc=c('blue','black','green3','red')) ## option-4: plot contours of each cluster of the meta-clusters with different colors for different samples plot(template, colorbysample=TRUE)
All samples within a template are organized as binary tree. This function plots the hierarchy of samples established while creating a template-tree.
template.tree(object, ...)template.tree(object, ...)
object |
An object of class |
... |
Other usual plotting related parameters. |
Returns a tree object of class hclust storing the hierarchy of the samples in the template.
Ariful Azad
Azad, Ariful and Pyne, Saumyadipta and Pothen, Alex (2012), Matching phosphorylation response patterns of antigen-receptor-stimulated T cells via flow cytometry; BMC Bioinformatics, 13 (Suppl 2), S10.
## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template)## ------------------------------------------------ ## load data ## ------------------------------------------------ library(healthyFlowData) data(hd) ## ------------------------------------------------ ## Retrieve each sample, clsuter it and store the ## clustered samples in a list ## ------------------------------------------------ set.seed(1234) # for reproducable clustering cat('Clustering samples: ') clustSamples = list() for(i in 1:length(hd.flowSet)) { cat(i, ' ') sample1 = exprs(hd.flowSet[[i]]) clust1 = kmeans(sample1, centers=4, nstart=20) cluster.labels1 = clust1$cluster clustSample1 = ClusteredSample(labels=cluster.labels1, sample=sample1) clustSamples = c(clustSamples, clustSample1) } ## ------------------------------------------------ ## Create a template from the list of clustered samples and plot functions ## ------------------------------------------------ template = create.template(clustSamples) summary(template) ## plot the tree denoting the hierarchy of the samples in a template tree = template.tree(template)