flowClust {flowClust} | R Documentation |
This function performs automated clustering for identifying cell populations in flow cytometry data. The approach is based on the t mixture model with the Box-Cox transformation, which provides a unified framework to handle outlier identification and data transformation simultaneously.
flowClust(x, expName="Flow Experiment", varNames=NULL, K, B=500, tol=1e-5, nu=4, lambda=1, trans=TRUE, min.count=10, max.count=10, min=NULL, max=NULL, level=0.9, u.cutoff=NULL, z.cutoff=0, randomStart=FALSE)
x |
A numeric vector, matrix, data frame of observations, or object of class flowFrame . Rows correspond to observations and columns correspond to variables. |
expName |
A character string giving the name of the experiment. |
varNames |
A character vector specifying the variables (columns) to be included in clustering. When it is left unspecified, all the variables will be used. |
K |
An integer indicating the number of clusters. |
B |
The maximum number of EM iterations. |
tol |
The tolerance used to assess the convergence of the EM. |
nu |
The degrees of freedom used for the t distribution. Default is 4. |
lambda |
The initial transformation to be applied to the data. |
trans |
A logical value indicating whether the Box-Cox transformation parameter is estimated from the data. |
min.count |
An integer specifying the threshold count for filtering data points from below. The default is 10, meaning that if 10 or more data points are smaller than or equal to min , they will be excluded from the analysis. If min is NULL , then the minimum of data as per each variable will be used. To suppress filtering, set it as -1. |
max.count |
An integer specifying the threshold count for filtering data points from above. Interpretation is similar to that of min.count . |
min |
The lower boundary set for data filtering. Note that it is a vector of length equal to the number of variables (columns), implying that a different value can be set as per each variable. |
max |
The upper boundary set for data filtering. Interpretation is similar to that of min . |
level |
A numeric value between 0 and 1 specifying the threshold quantile level used to call a point an outlier. The default is 0.9, meaning that any point outside the 90% quantile region will be called an outlier. |
u.cutoff |
Another criterion used to identify outliers. If this is NULL , then level will be used. Otherwise, this specifies the threshold (e.g., 0.5) for u, a quantity used to measure the degree of “outlyingness” based on the Mahalanobis distance. Please refer to Lo et al. (2008) for more details. |
z.cutoff |
A numeric value between 0 and 1 underlying a criterion which may be used together with level /u.cutoff to identify outliers. A point with the probability of assignment z (i.e., the posterior probability that a data point belongs to the cluster assigned) smaller than z.cutoff will be called an outlier. The default is 0, meaning that assignment will be made no matter how small the associated probability is, and outliers will be identified solely based on the rule set by level or cutoff . |
randomStart |
A logical value indicating whether a random parition of the data is applied for initialization. The default is FALSE , which means hierarchical clustering is used instead. |
Estimation of the unknown parameters (including the Box-Cox parameter) is done via an Expectation-Maximization (EM) algorithm. At each EM iteration, Brent's algorithm is used to find the optimal value of the Box-Cox transformation parameter. Conditional on the transformation parameter, all other estimates can be obtained in closed form. Please refer to Lo et al. (2008) for more details.
The flowClust package makes extensive use of the GSL as well as BLAS. If an optimized BLAS library is provided when compiling the package, the flowClust package will be able to run multi-threaded processes.
Various operations have been defined for the object returned from flowClust
. These include:
Subsetting operations: | %in% , Subset and split |
Slot retrieval operations: | ruleOutliers , Map , posterior , importance , uncertainty and getEstimates |
Graphical operations: | plot , density and hist |
In addition, to facilitate the integration with the flowCore package for processing flow cytometry data, the flowClust
operation can be done through a method pair (tmixFilter
and filter
) such that various methods defined in flowCore can be applied on the object created from the filtering operation.
An object of class flowClust
containing the following slots, where K is the number of clusters, N is the number of observations and P is the number of variables:
expName |
Content of the expName argument. |
varNames |
Content of the varNames argument if provided; generated if available otherwise. |
K |
An integer showing the number of clusters. |
mu |
A matrix of size K x P, containing the estimates of the K mean vectors. |
sigma |
An array of dimension K x P x P, containing the estimates of the K covariance matrices. |
w |
A vector of length K, containing the estimates of the K cluster proportions. |
z |
A matrix of size N x K, containing the posterior probabilities of cluster memberships. The probabilities in each row sum up to one. |
u |
A matrix of size N x K, containing the “weights” (the contribution for computing cluster mean and covariance matrix) of each data point in each cluster. Since this quantity decreases monotonically with the Mahalanobis distance, it can also be interpreted as the level of “outlyingness” of a data point. |
label |
A vector of size N, showing the cluster membership according to the initial partition (i.e., hierarchical clustering if randomStart is FALSE ). Filtered observations will be labelled as NA . |
uncertainty |
A vector of size N, containing the uncertainty about the cluster assignment. Uncertainty is defined as 1 minus the posterior probability that a data point belongs to the cluster to which it is assigned. |
ruleOutliers |
A numeric vector of size 3, storing the rule used to call outliers. The first element is 0 if the criterion is set by the level argument, or 1 if it is set by u.cutoff . The third element copies the content of the z.cutoff argument. For instance, if points will be called outliers if they lie outside the 90% quantile region or have assignment probabilities less than 0.5, then ruleOutliers is c(0, 0.9, 0.5) . If points will be called outliers only if their “weights” in the assigned clusters are less than 0.5 regardless of the assignment probabilities, then ruleOutliers becomes c(1, 0.5, 0) . |
flagOutliers |
A logical vector of size N, showing whether each data point is called an outlier or not based on the rule defined by level /u.cutoff and z.cutoff . |
rm.min |
Number of points filtered from below. |
rm.max |
Number of points filtered from above. |
lambda |
The Box-Cox transformation parameter estimate. |
nu |
The degrees of freedom used for the t distribution. |
logLike |
The log-likelihood of the fitted mixture model. |
BIC |
The Bayesian Information Criterion for the fitted mixture model. |
ICL |
The Integrated Completed Likelihood for the fitted mixture model. |
Raphael Gottardo <raph@stat.ubc.ca>, Kenneth Lo <c.lo@stat.ubc.ca>
Lo, K., Brinkman, R. R. and Gottardo, R. (2008) Automated Gating of Flow Cytometry Data via Robust Model-based Clustering. Cytometry A 73, 321-332.
summary
, plot
, density
, hist
, Subset
, split
, ruleOutliers
, Map
, SimulateMixture
data(rituximab) ### cluster the data using FSC.H and SSC.H res1 <- flowClust(rituximab, varNames=c("FSC.H", "SSC.H"), K=1) ### remove outliers before proceeding to the second stage # %in% operator returns a logical vector indicating whether each # of the observations lies within the cluster boundary or not rituximab2 <- rituximab[rituximab %in% res1,] # a shorthand for the above line rituximab2 <- rituximab[res1,] # Subset has an optional select argument to select columns Subset(rituximab, res1, select=c("FSC.H", "SSC.H", "FL1.H", "FL3.H")) ### cluster the data using FL1.H and FL3.H (with 3 clusters) res2 <- flowClust(rituximab2, varNames=c("FL1.H", "FL3.H"), K=3) show(res2) summary(res2) # to demonstrate the use of the split method split(rituximab2, res2) split(rituximab2, res2, split=list(sc1=c(1,2), sc2=3)) # to show the cluster assignment of observations table(Map(res2)) # to show the cluster centres (i.e., the mean parameter estimates # transformed back to the original scale) getEstimates(res2)$locations ### demonstrate the use of various plotting methods # a scatterplot plot(res2, data=rituximab2, level=0.8) # a contour / image plot res2.den <- density(res2, data=rituximab2) plot(res2.den) plot(res2.den, type="image", nlevels=100) # a histogram (1-D density) plot hist(res2, data=rituximab2, subset="FL1.H") # the following line illustrates how to select a subset of data # to perform cluster analysis through the min and max arguments; # also note the use of level to specify a rule to call outliers # other than the default flowClust(rituximab2, varNames=c("FL1.H", "FL3.H"), K=3, B=100, min=c(0,0), max=c(400,800), level=0.95, z.cutoff=0.5)