# MultiCCA: Perform sparse multiple canonical correlation analysis. In PMA: Penalized Multivariate Analysis

 MultiCCA R Documentation

## Perform sparse multiple canonical correlation analysis.

### Description

Given matrices \$X1,...,XK\$, which represent K sets of features on the same set of samples, find sparse \$w1,...,wK\$ such that \$sum_(i<j) (wi' Xi' Xj wj)\$ is large. If the columns of Xk are ordered (and type="ordered") then wk will also be smooth. For \$X1,...,XK\$, the samples are on the rows and the features are on the columns. \$X1,...,XK\$ must have same number of rows, but may (and usually will) have different numbers of columns.

### Usage

``````MultiCCA(
xlist,
penalty = NULL,
ws = NULL,
niter = 25,
type = "standard",
ncomponents = 1,
trace = TRUE,
standardize = TRUE
)
``````

### Arguments

 `xlist` A list of length K, where K is the number of data sets on which to perform sparse multiple CCA. Data set k should be a matrix of dimension \$n x p_k\$ where \$p_k\$ is the number of features in data set k. `penalty` The penalty terms to be used. Can be a single value (if the same penalty term is to be applied to each data set) or a K-vector, indicating a different penalty term for each data set. There are 2 possible interpretations for the penalty terms: If type="standard" then this is an L1 bound on wk, and it must be between 1 and \$sqrt(p_k)\$ (\$p_k\$ is the number of features in matrix Xk). If type="ordered" then this is the parameter for the fused lasso penalty on wk. `ws` A list of length K. The kth element contains the first ncomponents columns of the v matrix of the SVD of Xk. If NULL, then the SVD of \$X1,...,XK\$ will be computed inside the MultiCCA function. However, if you plan to run this function multiple times, then save a copy of this argument so that it does not need to be re-computed. `niter` How many iterations should be performed? Default is 25. `type` Are the columns of \$x1,...,xK\$ unordered (type="standard") or ordered (type="ordered")? If "standard", then a lasso penalty is applied to v, to enforce sparsity. If "ordered" (generally used for CGH data), then a fused lasso penalty is applied, to enforce both sparsity and smoothness. This argument can be a vector of length K (if different data sets are of different types) or it can be a single value "ordered"/"standard" (if all data sets are of the same type). `ncomponents` How many factors do you want? Default is 1. `trace` Print out progress? `standardize` Should the columns of \$X1,...,XK\$ be centered (to have mean zero) and scaled (to have standard deviation 1)? Default is TRUE.

### Value

 `ws` A list of length K, containg the sparse canonical variates found (element k is a \$p_k x ncomponents\$ matrix). `ws.init` A list of length K containing the initial values of ws used, by default these are the v vector of the svd of matrix Xk.

### References

Witten D. M., Tibshirani R., and Hastie, T. (2009) A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis, Biostatistics, Gol 10 (3), 515-534, Jul 2009

MultiCCA.permute,CCA, CCA.permute

### Examples

``````
# Generate 3 data sets so that first 25 features are correlated across
# the data sets...
set.seed(123)
u <- matrix(rnorm(50),ncol=1)
v1 <- matrix(c(rep(.5,25),rep(0,75)),ncol=1)
v2 <- matrix(c(rep(1,25),rep(0,25)),ncol=1)
v3 <- matrix(c(rep(.5,25),rep(0,175)),ncol=1)

x1 <- u%*%t(v1) + matrix(rnorm(50*100),ncol=100)
x2 <- u%*%t(v2) + matrix(rnorm(50*50),ncol=50)
x3 <- u%*%t(v3) + matrix(rnorm(50*200),ncol=200)

xlist <- list(x1, x2, x3)

# Run MultiCCA.permute w/o specifying values of tuning parameters to
# try.
# The function will choose the lambda for the ordered data set.
# Then permutations will be used to select optimal sum(abs(w)) for
# standard data sets.
# We assume that x1 is standard, x2 is ordered, x3 is standard:
perm.out <- MultiCCA.permute(xlist, type=c("standard", "ordered",
"standard"))
print(perm.out)
plot(perm.out)
out <- MultiCCA(xlist, type=c("standard", "ordered", "standard"),
penalty=perm.out\$bestpenalties, ncomponents=2, ws=perm.out\$ws.init)
print(out)
# Or if you want to specify tuning parameters by hand:
# this time, assume all data sets are standard:
perm.out <- MultiCCA.permute(xlist, type="standard",
penalties=cbind(c(1.1,1.1,1.1),c(2,3,4),c(5,7,10)), ws=perm.out\$ws.init)
print(perm.out)
plot(perm.out)

# Making use of the fact that the features are ordered:
out <- MultiCCA(xlist, type="ordered", penalty=.6)
par(mfrow=c(3,1))
PlotCGH(out\$ws[[1]], chrom=rep(1,ncol(x1)))
PlotCGH(out\$ws[[2]], chrom=rep(2,ncol(x2)))
PlotCGH(out\$ws[[3]], chrom=rep(3,ncol(x3)))

``````

PMA documentation built on May 29, 2024, 12:04 p.m.