# R/CCA.R In PMA2: Penalized Multivariate Analysis

#### Documented in CCACCA.permuteprint.CCA

# This contains what used to be in CGH.SparseCCA.R and MultiSparseCCA.R

#' Perform sparse canonical correlation analysis using the penalized matrix
#' decomposition.
#'
#' Given matrices X and Z, which represent two sets of features on the same set
#' of samples, find sparse u and v such that u'X'Zv is large.  For X and Z, the
#' samples are on the rows and the features are on the columns. X and Z must
#' have same number of rows, but may (and usually will) have different numbers
#' of columns. The columns of X and/or Z can be unordered or ordered. If
#' unordered, then a lasso penalty will be used to obtain the corresponding
#' canonical vector. If ordered, then a fused lasso penalty will be used; this
#' will result in smoothness.
#'
#' This function is useful for performing an integrative analysis of two sets
#' of measurements taken on the same set of samples: for instance, gene
#' expression and CGH measurements on the same set of patients. It takes in two
#' data sets, called x and z, each of which have (the same set of) samples on
#' the rows. If z is a matrix of CGH data with *ordered* CGH spots on the
#' columns, then use typez="ordered". If z consists of unordered columns, then
#' use typez="standard". Similarly for typex.
#'
#' This function performs the penalized matrix decomposition on the data matrix
#' $X'Z$. Therefore, the results should be the same as running the PMD function
#' on t(x)\%*\% z. However, when ncol(x)>>nrow(x) and ncol(z)>>nrow(z) then
#' using the CCA function is much faster because it avoids computation of
#' $X'Z$.
#'
#' The CCA criterion is as follows: find unit vectors $u$ and $v$ such that
#' $u'X'Zv$ is maximized subject to constraints on $u$ and $v$.  If
#' typex="standard" and typez="standard" then the constraints on $u$ and $v$
#' are lasso ($L_1$). If typex="ordered" then the constraint on $u$ is a fused
#' lasso penalty (promoting sparsity and smoothness). Similarly if
#' typez="ordered".
#'
#' When type x is "standard": the L1 bound of u is penaltyx*sqrt(ncol(x)).
#'
#' When typex is "ordered": penaltyx controls the amount of sparsity and
#' smoothness in u, via the fused lasso penalty: $lambda sum_j |u_j| + lambda #' sum_j |u_j - u_(j-1)|$. If NULL, then it will be chosen adaptively from the
#' data.
#'
#' @aliases CCA print.CCA
#' @param x Data matrix; samples are rows and columns are features. Cannot
#' contain missing values.
#' @param z Data matrix; samples are rows and columns are features.  Cannot
#' contain missing values.
#' @param typex Are the columns of x unordered (type="standard") or ordered
#' (type="ordered")? If "standard", then a lasso penalty is applied to u, to
#' enforce sparsity. If "ordered" (generally used for CGH data), then a fused
#' lasso penalty is applied, to enforce both sparsity and smoothness.
#' @param typez Are the columns of z 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.
#' @param penaltyx The penalty to be applied to the matrix x, i.e. the penalty
#' that results in the canonical vector u. If typex is "standard" then the L1
#' bound on u is penaltyx*sqrt(ncol(x)). In this case penaltyx must be between
#' 0 and 1 (larger L1 bound corresponds to less penalization). If "ordered"
#' then it's the fused lasso penalty lambda, which must be non-negative (larger
#' lambda corresponds to more penalization).
#' @param penaltyz The penalty to be applied to the matrix z, i.e. the penalty
#' that results in the canonical vector v. If typez is "standard" then the L1
#' bound on v is penaltyz*sqrt(ncol(z)). In this case penaltyz must be between
#' 0 and 1 (larger L1 bound corresponds to less penalization). If "ordered"
#' then it's the fused lasso penalty lambda, which must be non-negative (larger
#' lambda corresponds to more penalization).
#' @param K The number of u's and v's desired; that is, the number of canonical
#' vectors to be obtained.
#' @param niter How many iterations should be performed? Default is 15.
#' @param v The first K columns of the v matrix of the SVD of X'Z. If NULL,
#' then the SVD of X'Z will be computed inside the CCA 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 (since that process can
#' be time-consuming if X and Z both have high dimension).
#' @param trace Print out progress?
#' @param standardize Should the columns of x and z be centered (to have mean
#' zero) and scaled (to have standard deviation 1)? Default is TRUE.
#' @param xnames An optional vector of column names for x.
#' @param znames An optional vector of column names for z.
#' @param chromx Used only if typex is "ordered"; allows user to specify a
#' vector of length ncol(x) giving the chromosomal location of each CGH spot.
#' This is so that smoothness will be enforced within each chromosome, but not
#' between chromosomes.
#' @param chromz Used only if typez is "ordered"; allows user to specify a
#' vector of length ncol(z) giving the chromosomal location of each CGH spot.
#' This is so that smoothness will be enforced within each chromosome, but not
#' between chromosomes.
#' @param upos If TRUE, then require elements of u to be positive. FALSE by
#' default. Can only be used if type is "standard".
#' @param uneg If TRUE, then require elements of u to be negative. FALSE by
#' default.  Can only be used if type is "standard".
#' @param vpos If TRUE, require elements of v to be positive. FALSE by default.
#' Can only be used if type is "standard".
#' @param vneg If TRUE, require elements of v to be negative. FALSE by default.
#' Can only be used if type is "standard".
#' @param outcome If you would like to incorporate a phenotype into CCA
#' analysis - that is, you wish to find features that are correlated across the
#' two data sets and also correlated with a phenotype - then use one of
#' "survival", "multiclass", or "quantitative" to indicate outcome type.
#' Default is NULL.
#' @param y If outcome is not NULL, then this is a vector of phenotypes - one
#' for each row of x and z. If outcome is "survival" then these are survival
#' times; must be non-negative. If outcome is "multiclass" then these are class
#' labels (1,2,3,...). Default NULL.
#' @param cens If outcome is "survival" then these are censoring statuses for
#' each observation. 1 is complete, 0 is censored. Default NULL.
#' @return \item{u}{u is output. If you asked for multiple factors then each
#' column of u is a factor. u has dimension nxK if you asked for K factors.}
#' \item{v}{v is output. If you asked for multiple factors then each column of
#' v is a factor. v has dimension pxK if you asked for K factors.} \item{d}{A
#' vector of length K, which can alternatively be computed as the diagonal of
#' the matrix $u'X'Zv$.} \item{v.init}{The first K factors of the v matrix of
#' the SVD of x'z. This is saved in case this function will be re-run later.}
#' @references
#' Ali Mahzarnia, Alexander Badea (2022)
#' \emph{Joint Estimation of Vulnerable Brain Networks and Alzheimer’s Disease Risk Via Novel Extension of Sparse Canonical Correlation at bioRxiv.} \cr
#' @examples
#'
#' # first, do CCA with type="standard"
#' # A simple simulated example
#' set.seed(3189)
#' u <- matrix(c(rep(1,25),rep(0,75)),ncol=1)
#' v1 <- matrix(c(rep(1,50),rep(0,450)),ncol=1)
#' v2 <- matrix(c(rep(0,50),rep(1,50),rep(0,900)),ncol=1)
#' x <- u%*%t(v1) + matrix(rnorm(100*500),ncol=500)
#' z <- u%*%t(v2) + matrix(rnorm(100*1000),ncol=1000)
#' # Can run CCA with default settings, and can get e.g. 3 components
#' out <- CCA(x,z,typex="standard",typez="standard",K=3)
#' print(out,verbose=TRUE) # To get less output, just print(out)
#' # Or can use CCA.permute to choose optimal parameter values
#' perm.out <- CCA.permute(x,z,typex="standard",typez="standard",nperms=7)
#' print(perm.out)
#' out <- CCA(x,z,typex="standard",typez="standard",K=1,
#' 	   penaltyx=perm.out$bestpenaltyx,penaltyz=perm.out$bestpenaltyz,
#' 	   v=perm.out$v.init) #' print(out) #' #' #' @references #' Ali Mahzarnia, Alexander Badea (2022) #' \emph{Joint Estimation of Vulnerable Brain Networks and Alzheimer’s Disease Risk Via Novel Extension of Sparse Canonical Correlation at bioRxiv.} \cr #' @export CCA CCA <- function(x, z, typex=c("standard", "ordered"), typez=c("standard","ordered"), penaltyx=NULL, penaltyz=NULL, K=1, niter=15, v=NULL, trace=TRUE, standardize=TRUE, xnames=NULL, znames=NULL, chromx=NULL, chromz=NULL, upos=FALSE, uneg=FALSE, vpos=FALSE, vneg=FALSE, outcome=NULL, y=NULL, cens=NULL, UVperms=NA, allpenaltyxs=NA){ if(ncol(x)<2) stop("Need at least two features in dataset x.") if(ncol(z)<2) stop("Need at least two features in dataset z.") if(upos && uneg) stop("At most one of upos and uneg should be TRUE!") if(vpos && vneg) stop("At most one of vpos and vneg should be TRUE!") if(typez=="ordered" && (vpos||vneg)) stop("Cannot require elements of v to be positive or negative if typez is ordered") if(typex=="ordered" && (upos||uneg)) stop("Cannot require elements of u to be positive or negative if typex is ordered") typex <- match.arg(typex) typez <- match.arg(typez) call <- match.call() if(sum(is.na(x))+sum(is.na(z)) > 0) stop("Cannot have NAs in x or z") if(nrow(x)!=nrow(z)) stop("x and z must have same number of rows") if(standardize){ sdx <- apply(x,2,sd) sdz <- apply(z,2,sd) if(min(sdx)==0) stop("Cannot standardize because some of the columns of x have std. dev. 0") if(min(sdz)==0) stop("Cannot standardize because some of the columns of z have std. dev. 0") x <- scale(x,TRUE,sdx) z <- scale(z,TRUE,sdz) } if(!is.null(outcome)){ pheno.out <- CCAPhenotypeZeroSome(x,z,y,qt=.8, cens=cens, outcome=outcome, typex=typex, typez=typez) x <- pheno.out$x
z <- pheno.out$z } if(typex=="standard" && !is.null(chromx)) warning("Chromx has no effect for type standard") if(typez=="standard" && !is.null(chromz)) warning("Chromz has no effect for type standard") v <- CheckVs(v,x,z,K) if(is.null(penaltyx)){ if(typex=="standard") penaltyx <- .3#pmax(1.001,.3*sqrt(ncol(x)))/sqrt(ncol(x)) if(typex=="ordered") penaltyx <- ChooseLambda1Lambda2(as.numeric(CheckVs(NULL,z,x,1))) # v[,1] used to be NULL } if(is.null(penaltyz)){ if(typez=="standard") penaltyz <- .3#pmax(1.001,.3*sqrt(ncol(z)))/sqrt(ncol(z)) if(typez=="ordered") penaltyz <- ChooseLambda1Lambda2(as.numeric(CheckVs(NULL,x,z,1))) # ChooseLambda1Lambda2(as.numeric(v[,1])) } if(!is.null(penaltyx)){ if(typex=="standard" && (penaltyx<0 || penaltyx>1)) stop("Penaltyx must be between 0 and 1 when typex is standard.") if(typex=="ordered" && penaltyx<0) stop("Penaltyx must be non-negative when typex is standard.") } if(!is.null(penaltyz)){ if(typez=="standard" && (penaltyz<0 || penaltyz>1)) stop("Penaltyz must be between 0 and 1 when typez is standard.") if(typez=="ordered" && penaltyz<0) stop("Penaltyz must be non-negative when typez is standard.") } out <- CCAAlgorithm(x=x,z=z,v=v,typex=typex,typez=typez,penaltyx=penaltyx,penaltyz=penaltyz,K=K,niter=niter,trace=trace,chromx=chromx,chromz=chromz,upos=upos,uneg=uneg,vpos=vpos,vneg=vneg) if(!is.na(UVperms)[1]) { lambdaindex=which(penaltyx==allpenaltyxs) if (length(lambdaindex)==0) { stop("The list of joint regularization parameters used in the permutation does not include that of the input in this function. You may need to choose a tuning parameter from the current list perm.out$penaltyxs,
or re-run the permutation with your current
input penaltyx and penaltyz included in the
list before running this part, the CCA!")}
savedu=matrix(NA, dim(x)[2], length( UVperms  ));
savedv=matrix(NA, dim(z)[2], length(  UVperms ));
for (i in 1: length( UVperms  ))
{ temps=UVperms[[i]]
tempsuv=temps[[lambdaindex]];
savedu[,i]=tempsuv[[1]] ;
savedv[,i]= tempsuv[[2]];
}
SDu=apply(savedu,1, sd, na.rm = TRUE);
SDv=apply(savedv,1, sd, na.rm = TRUE);
out$SDu=SDu; out$SDv=SDv;
tempstdu=out$u; tempstdv=out$v;
tempstdu[tempstdu!=0]=tempstdu[tempstdu!=0]/SDu[tempstdu!=0];
tempstdv[tempstdv!=0]=tempstdv[tempstdv!=0]/SDv[tempstdv!=0];
out$standardu=tempstdu; out$standardv=tempstdv;
if( sum(abs(out$standardu)==Inf)>0 | sum(abs(out$standardu)==Inf)>0 )
{cat("The Inf in standardized U or V i.e. standardu or standardv indicates that the estimated U or
V for that component is nonzero and that its estimated standard deviation through all permutations is zero.Therefore, that component is the most significant among all. If a component of U or V is estimated zero, the associated standardu or standardv component is zero. \n")}
utemp=out$u ; vtemp=out$v
pvalsu=matrix(1, length(utemp) )
for (i in 1:length(utemp)) {
if (utemp[i]<0)  { pvalsu[i]=mean(utemp[i]>savedu[i,])    }
if (utemp[i]>0)  { pvalsu[i]=mean(utemp[i]<savedu[i,])    }
}
pvalsv=matrix(1, length(vtemp) )
for (i in 1:length(vtemp)) {
if (vtemp[i]<0)  { pvalsv[i]=mean(vtemp[i]>savedv[i,])    }
if (vtemp[i]>0)  { pvalsv[i]=mean(vtemp[i]<savedv[i,])    }
}
out$pvalsu=pvalsu ; out$pvalsv=pvalsv ;
}
out$outcome <- outcome out$call <- call
out$xnames <- xnames out$znames <- znames
out$typex<-typex out$typez<-typez
out$penaltyx<-penaltyx out$penaltyz<-penaltyz
out$K <- K out$niter <- niter
out$upos <- upos out$uneg <- uneg
out$vpos <- vpos out$vneg <- vneg
out$xnames <- xnames out$znames <- znames
out$v.init <- v out$cors <- numeric(K)
for(k in 1:K){
if(sum(out$u[,k]!=0)>0 && sum(out$v[,k]!=0)>0) out$cors[k] <- cor(x%*%out$u[,k],z%*%out$v[,k]) } class(out) <- "CCA" return(out) } #' @method print CCA #' @export print.CCA <- function(x,verbose=FALSE,...){ cat("Call: ") dput(x$call)
cat("\n\n")
cat("Num non-zeros u's: ", apply(x$u!=0,2,sum), "\n") cat("Num non-zeros v's: ", apply(x$v!=0,2,sum), "\n")
cat("Type of x: ", x$typex,"\n") cat("Type of z: ", x$typez,"\n")
if(x$typex=="standard") cat("Penalty for x: L1 bound is ", x$penaltyx, "\n")
if(x$typez=="standard") cat("Penalty for z: L1 bound is ", x$penaltyz, "\n")
if(x$typex=="ordered") cat("Penalty for x: Lambda is ", x$penaltyx, "\n")
if(x$typez=="ordered") cat("Penalty for z: Lambda is ", x$penaltyz, "\n")
if(x$upos) cat("U's constrained to be positive", fill=TRUE) if(x$uneg) cat("U's constrained to be negative", fill=TRUE)
if(x$vpos) cat("V's constrained to be positive", fill=TRUE) if(x$vneg) cat("V's constrained to be negative", fill=TRUE)
if(!is.null(x$outcome)) cat("Outcome used: ", x$outcome, fill=TRUE)
cat("Cor(Xu,Zv): ", x$cors, fill=TRUE) if(verbose){ for(k in 1:x$K){
cat("\n Component ", k, ":\n")
u <- x$u[,k] v <- x$v[,k]
if(is.null(x$xnames)) x$xnames <- 1:length(u)
if(is.null(x$znames)) x$znames <- 1:length(v)
cat(fill=T)
us <- cbind(x$xnames[u!=0], round(u[u!=0],3)) dimnames(us) <- list(1:sum(u!=0), c("Row Feature Name", "Row Feature Weight")) vs <- cbind(x$znames[v!=0], round(v[v!=0],3))
dimnames(vs) <- list(1:sum(v!=0), c("Column Feature Name", "Column Feature Weight"))
print(us, quote=FALSE, sep="\t")
cat(fill=T)
print(vs, quote=FALSE, sep="\t")
}
}
}

CCAAlgorithm <- function(x,z,v,typex,typez,penaltyx,penaltyz,K,niter,trace,chromx,chromz,upos,uneg,vpos,vneg){
if(typez!="ordered"){
if(K>1) v.init <- v[apply(z^2,2,sum)!=0,]
if(K==1) v.init <- v[apply(z^2,2,sum)!=0]
} else {
v.init <- v
}
v.init <- matrix(v.init,ncol=K)
u=v=d=NULL
xres <- x; zres <- z
if(typex!="ordered") xres <- x[,apply(x^2,2,sum)!=0]
if(typez!="ordered") zres <- z[,apply(z^2,2,sum)!=0]
for(k in 1:K){
if(vpos && sum(abs(v.init[v.init[,k]>0,k]))<sum(abs(v.init[v.init[,k]<0,k]))) v.init[,k] <- -v.init[,k]
if(vneg && sum(abs(v.init[v.init[,k]<0,k]))<sum(abs(v.init[v.init[,k]>0,k]))) v.init[,k] <- -v.init[,k]
out <- SparseCCA(xres,zres,v.init[,k],typex,typez,penaltyx, penaltyz,niter,trace, upos, uneg, vpos, vneg,chromx,chromz)
coef <- out$d d <- c(d, coef) xres <- rbind(xres, sqrt(coef)*t(out$u))
zres <- rbind(zres, -sqrt(coef)*t(out$v)) u <- cbind(u, out$u)
v <- cbind(v, out$v) } ubig <- u vbig <- v if(typex!="ordered"){ ubig <- matrix(0,nrow=ncol(x),ncol=K) ubig[apply(x^2,2,sum)!=0,] <- u } if(typez!="ordered"){ vbig <- matrix(0,nrow=ncol(z),ncol=K) vbig[apply(z^2,2,sum)!=0,] <- v } return(list(u=ubig,v=vbig,d=d)) } fastsvd <- function(x,z){ # fast svd of t(x)%*%z, where ncol(x)>>nrow(x) and same for z xx=x%*%t(x) xx2=msqrt(xx) y=t(z)%*%xx2 a=try(svd(y), silent=TRUE) iter <- 1 if(inherits(a,"try-error") && iter<10){ a=try(svd(y), silent=TRUE) iter <- iter+1 } if(iter==10) stop("too many tries.") v=a$u
d=a$d zz=z%*%t(z) zz2=msqrt(zz) y=t(x)%*%zz2 a=try(svd(y), silent=TRUE) iter <- 1 if(inherits(a,"try-error") && iter<10){ a=try(svd(y), silent=TRUE) iter <- iter+1 } if(iter==10) stop("too many tries.") u=a$u
return(list(u=u,v=v,d=d))
}

msqrt <- function(x){
eigenx <- eigen(x)
return(eigenx$vectors%*%diag(sqrt(pmax(0,eigenx$values)))%*%t(eigenx$vectors)) } SparseCCA <- function(x,y,v,typex,typez,penaltyx, penaltyz,niter,trace, upos, uneg, vpos, vneg,chromx,chromz){ vold <- rnorm(length(v)) u <- rnorm(ncol(x)) for(i in 1:niter){ if(sum(is.na(u))>0 || sum(is.na(v))>0){ v <- rep(0, length(v)) vold <- v } if(sum(abs(vold-v))>1e-6){ if(trace) cat(i,fill=F) # Update u # unew <- rep(NA, ncol(x)) if(typex=="standard"){ #argu <- t(x)%*%(y%*%v) argu <- matrix(y%*%v,nrow=1)%*%x if(upos) argu <- pmax(argu,0) if(uneg) argu <- pmin(argu,0) lamu <- BinarySearch(argu,penaltyx*sqrt(ncol(x))) su <- soft(argu,lamu) u <- matrix(su/l2n(su), ncol=1) }else if(typex=="ordered"){ yv <- y%*%v if(is.null(chromx)) chromx <- rep(1, ncol(x)) for(j in unique(chromx)){ xyv <- as.numeric(t(yv)%*%x[,chromx==j])#as.numeric(t(x[,chromx==j])%*%yv) if(penaltyx!=0){ coefs <- FLSA(xyv/l2n(xyv),lambda1=penaltyx,lambda2=penaltyx) # diagfl.out <- diag.fused.lasso.new(xyv/l2n(xyv), lam1=penaltyx) # lam2ind <- which.min(abs(diagfl.out$lam2-penaltyx))
#            coefs <- diagfl.out$coef[,lam2ind] } if(penaltyx==0){ coefs <- xyv/l2n(xyv) } unew[chromx==j] <- coefs } u <- unew if(sum(is.na(u))==0 && sum(abs(u))>0) u <- u/l2n(u) u <- matrix(u,ncol=1) } # Done updating u # # Update v # vnew <- rep(NA, ncol(y)) if(typez=="standard"){ vold <- v #argv <- (t(u)%*%t(x))%*%y argv <- matrix(x%*%u,nrow=1)%*%y if(vpos) argv <- pmax(argv,0) if(vneg) argv <- pmin(argv,0) lamv <- BinarySearch(argv,penaltyz*sqrt(ncol(y))) sv <- soft(argv, lamv) v <- matrix(sv/l2n(sv),ncol=1) } else if (typez=="ordered"){ xu <- x%*%u if(is.null(chromz)) chromz <- rep(1, ncol(y)) for(j in unique(chromz)){ yxu <- as.numeric(t(xu)%*%y[,chromz==j])#as.numeric(t(y[,chromz==j])%*%xu) if(penaltyz!=0){ coefs <- FLSA(yxu/l2n(yxu),lambda1=penaltyz,lambda2=penaltyz) # diagfl.out <- diag.fused.lasso.new(yxu/l2n(yxu), lam1=penaltyz) # lam2ind <- which.min(abs(diagfl.out$lam2-penaltyz))
#            coefs <- diagfl.out$coef[,lam2ind] } if(penaltyz==0){ coefs <- yxu/l2n(yxu) } vnew[chromz==j] <- coefs } v <- vnew if(sum(is.na(v))==0 && sum(abs(v))>0) v <- v/l2n(v) v <- matrix(v,ncol=1) } # Done updating v # } } if(trace) cat(fill=T) # Update d # d <- sum((x%*%u)*(y%*%v)) # Done updating d # if(sum(is.na(u))>0 || sum(is.na(v))>0){ u <- matrix(rep(0,ncol(x)),ncol=1) v <- matrix(rep(0,ncol(y)),ncol=1) d <- 0 } return(list(u=u,v=v,d=d)) } CheckVs <- function(v,x,z,K){ # If v is NULL, then get v as appropriate. ##print(list(v=v, x = x, z = z, K = K)) if(!is.null(v) && !is.matrix(v)) v <- matrix(v,nrow=ncol(z)) if(!is.null(v) && ncol(v)<K) v <- NULL if(!is.null(v) && ncol(v)>K) v <- matrix(v[,1:K],ncol=K) if(is.null(v) && ncol(z)>nrow(z) && ncol(x)>nrow(x)){ v <- try(matrix(fastsvd(x,z)$v[,1:K],ncol=K), silent=TRUE)
attempt <- 1
while(("try-error" %in% class(v))  && attempt < 10){
v <- try(matrix(fastsvd(x,z)$v[,1:K],ncol=K), silent=TRUE) attempt <- attempt+1 } if(attempt==10) stop("Problem computing SVD.") } else if (is.null(v) && (ncol(z)<=nrow(z) || ncol(x)<=nrow(x))){ attempt <- 1 v <- try(matrix(svd(t(x)%*%z)$v[,1:K],ncol=K), silent=TRUE)
while(("try-error" %in% class(v)) && attempt<10){
v <- try(matrix(svd(t(x)%*%z)$v[,1:K],ncol=K), silent=TRUE) attempt <- attempt+1 } if(attempt==10) stop("Problem computing SVD.") } return(v) } ftrans <- function(a){ return(log((1+a)/(1-a))) } CCA.permute.both <- function(x,z,typex, typez,penaltyxs,penaltyzs,niter, v,trace,nperms,standardize,chromx,chromz,upos,uneg, vpos,vneg,outcome,y,cens, SD=FALSE){ call <- match.call() if(standardize){ x <- scale(x,TRUE,TRUE) z <- scale(z,TRUE,TRUE) } v <- CheckVs(v,x,z,1) ccperms=nnonzerous.perms=nnonzerovs.perms=matrix(NA, length(penaltyxs), nperms) ccs=nnonzerous=nnonzerovs=numeric(length(penaltyxs)) UVperms=vector("list", length = nperms); for(i in 1:nperms){ if(trace && .Platform$OS.type!="windows") cat("\n Permutation ",i," out of ", nperms, " ")
#   #  if(trace && .Platform$OS.type=="windows" && i==1) pb <- winProgressBar(title="Doing Permutations", min=0, max=1, initial=(i/nperms)) # # if(trace && .Platform$OS.type=="windows" && i>1) setWinProgressBar(pb, value=(i/nperms))
sampz <- sample(1:nrow(z))
sampx <- sample(1:nrow(x))
if (SD==TRUE) { UVlambdas=vector("list", length = length(penaltyxs)); } ###
for(j in 1:length(penaltyxs)){
if(SD==TRUE){templist=vector("list", length = 2);}###
if(trace && .Platform$OS.type!="windows") cat(j,fill=FALSE) if(i==1){ out <- CCA(x,z,typex=typex,typez=typez,penaltyx=penaltyxs[j], penaltyz=penaltyzs[j],y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromz=chromz,chromx=chromx) nnonzerous[j] <- sum(out$u!=0)
nnonzerovs[j] <- sum(out$v!=0) if(mean(out$u==0)!=1 && mean(out$v==0)!=1){ ccs[j] <- cor(x%*%out$u,z%*%out$v) } else { ccs[j] <- 0 } } out <- CCA(x[sampx,],z[sampz,],typex=typex,typez=typez,penaltyx=penaltyxs[j], penaltyz=penaltyzs[j],y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromz=chromz,chromx=chromx) nnonzerous.perms[j,i] <- sum(out$u!=0)
nnonzerovs.perms[j,i] <- sum(out$v!=0) if(SD==TRUE){templist[[1]]=out$u;templist[[2]]=out$v; } ### if(mean(out$u==0)!=1 && mean(out$v==0)!=1){ ccperms[j,i] <- cor(x[sampx,]%*%out$u,z[sampz,]%*%out$v) } else { ccperms[j,i] <- 0 } if(SD==TRUE){ UVlambdas[[j]]=templist;}### } if(SD==TRUE){ UVperms[[i]]=UVlambdas;}### } #SDs=NA; #if(SD==TRUE){dataSD=as.data.frame(do.call(rbind, UVperms)); SDs=apply(array(unlist(m), c(3, 3, 3)), c(1,2), sd)} # if(trace && .Platform$OS.type=="windows") close(pb)
cc.norm <- ftrans(ccs)
ccperm.norm <- ftrans(ccperms)
zstats <- (cc.norm - rowMeans(ccperm.norm))/(apply(ccperm.norm,1,sd) + .05)
# 0.05 added to the denominator to avoid getting zstat of INFINITY
if(trace) cat(fill=T)
pvals <- apply(sweep(ccperms,1,ccs,"-")>=0,1,mean)
results <- list(zstats=zstats,
penaltyxs=penaltyxs, penaltyzs=penaltyzs,bestpenaltyx=penaltyxs[which.max(zstats)],
bestpenaltyz=penaltyzs[which.max(zstats)], cors=ccs, corperms=ccperms, ft.cors=cc.norm,
ft.corperms=rowMeans(ccperm.norm),nnonzerous=nnonzerous,nnonzerovs=nnonzerovs,
nnonzerous.perm=rowMeans(nnonzerous.perms),nnonzerovs.perm=rowMeans(nnonzerovs.perms),
call=call,v.init=v,pvals=pvals,nperms=nperms,chromz=chromz,
chromx=chromx,typex=typex,typez=typez, pvalbestz=pvals[which.max(zstats)],UVperms=UVperms )
return(results)
}

#' @method plot CCA.permute
#' @export
plot.CCA.permute <- function(x,...){
penaltyxs <- x$penaltyxs penaltyzs <- x$penaltyzs
if(length(penaltyxs)==1 && length(penaltyzs)==1) stop("Cannot plot output of CCA.permute if only 1 tuning parameter was considered.")
ccs <- x$cors nperms <- x$nperms
zstats <- x$zstats ccperms <- x$corperms
on.exit(par(oldpar))
par(mfrow=c(2,1))
if(length(unique(penaltyxs))==1 && length(unique(penaltyzs))>1){
plot(penaltyzs, ccs, main="Correlations For Real/Permuted Data", xlab="Penalty on data set 2", ylab="Correlations", ylim=range(ccperms,ccs))
points(penaltyzs, ccs, type="l")
for(i in 1:nperms) points(penaltyzs, ccperms[,i], col="green")
plot(penaltyzs,zstats,main="Z-Statistics", xlab="Penalty on data set 2", ylab="Z-statistic")
lines(penaltyzs,zstats)
}
if(length(unique(penaltyzs))==1 && length(unique(penaltyxs))>1){
plot(penaltyxs, ccs, main="Correlations For Real/Permuted Data", xlab="Penalty on data set 1", ylab="Correlations", ylim=range(ccperms,ccs))
points(penaltyxs, ccs, type="l")
for(i in 1:nperms) points(penaltyxs, ccperms[,i], col="green")
plot(penaltyxs,zstats,main="Z-Statistics", xlab="Penalty on data set 1", ylab="Z-statistic")
lines(penaltyxs,zstats)
}
if(length(unique(penaltyzs))>1 && length(unique(penaltyxs))>1 && sum(penaltyxs!=penaltyzs)>0){
plot(1:length(penaltyxs), ccs, main="Correlations For Real/Permuted Data", xlab="Index of Tuning Parameters Considered", ylab="Correlations", ylim=range(ccperms,ccs))
points(1:length(penaltyxs), ccs, type="l")
for(i in 1:nperms) points(1:length(penaltyxs), ccperms[,i], col="green")
plot(1:length(penaltyxs),zstats,main="Z-Statistics", xlab="Index of Tuning Parameters Considered", ylab="Z-statistic")
lines(1:length(penaltyxs),zstats)
}
if(length(unique(penaltyzs))>1 && length(unique(penaltyxs))>1 && sum(penaltyxs!=penaltyzs)==0){
plot(penaltyxs, ccs, main="Correlations For Real/Permuted Data", xlab="Penalty on data sets 1 and 2", ylab="Correlations", ylim=range(ccperms,ccs))
points(penaltyxs, ccs, type="l")
for(i in 1:nperms) points(penaltyxs, ccperms[,i], col="green")
plot(penaltyxs,zstats,main="Z-Statistics", xlab="Penalty on data sets 1 and 2", ylab="Z-statistic")
lines(penaltyxs,zstats)
}
}

CCA.permute.zonly<- function(x,z,typex,typez,penaltyx,penaltyzs,niter,v,trace,nperms,standardize,chromx,chromz,upos,uneg,vpos,vneg,outcome,y,cens, SD=FALSE){
call <- match.call()
if(standardize){
x <- scale(x,TRUE,TRUE)
z <- scale(z, TRUE, TRUE)
}
v <- CheckVs(v,x,z,1)
ccperms=nnonzerous.perms=nnonzerovs.perms=matrix(NA, length(penaltyzs), nperms)
ccs=nnonzerous=nnonzerovs=numeric(length(penaltyzs))
storevs <- NULL
UVperms=vector("list", length = nperms);
for(i in 1:nperms){
if(trace && .Platform$OS.type!="windows") cat("\n Permutation ",i," out of ", nperms, " ") # #if(trace && .Platform$OS.type=="windows" && i==1) pb <- winProgressBar(title="Doing Permutations", min=0, max=1, initial=(i/nperms))
#     #if(trace && .Platform$OS.type=="windows" && i>1) setWinProgressBar(pb, value=(i/nperms)) sampz <- sample(1:nrow(z)) sampx <- sample(1:nrow(x)) if (SD==TRUE) { UVlambdas=vector("list", length = length(penaltyzs)); } ### for(j in 1:length(penaltyzs)){ if(trace && .Platform$OS.type!="windows") cat(j,fill=FALSE)
if(SD==TRUE){templist=vector("list", length = 2);}###

if(i==1){
out <- CCA(x,z,typex=typex,typez=typez,penaltyx=penaltyx, penaltyz=penaltyzs[j],y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromz=chromz,chromx=chromx)
nnonzerous[j] <- sum(out$u!=0) nnonzerovs[j] <- sum(out$v!=0)
if(mean(out$u==0)!=1 && mean(out$v==0)!=1){
ccs[j] <- cor(x%*%out$u,z%*%out$v)
} else {
ccs[j] <- 0
}
storevs <- cbind(storevs, out$v) } out <- CCA(x[sampx,],z[sampz,],typex=typex,typez=typez,penaltyx=penaltyx, penaltyz=penaltyzs[j],y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromx=chromx,chromz=chromz) nnonzerous.perms[j,i] <- sum(out$u!=0)
nnonzerovs.perms[j,i] <- sum(out$v!=0) if(SD==TRUE){templist[[1]]=out$u;templist[[2]]=out$v; } ### if(mean(out$u==0)!=1 && mean(out$v==0)!=1){ ccperms[j,i] <- cor(x[sampx,]%*%out$u,z[sampz,]%*%out$v) } else { ccperms[j,i] <- 0 } if(SD==TRUE){ UVlambdas[[j]]=templist;}### } if(SD==TRUE){ UVperms[[i]]=UVlambdas;}### } # if(trace && .Platform$OS.type=="windows") close(pb)
cc.norm <- ftrans(ccs)
ccperm.norm <- ftrans(ccperms)
zstats <- (cc.norm - rowMeans(ccperm.norm))/(apply(ccperm.norm,1,sd) + .05)
if(trace) cat(fill=T)
pvals <- apply(sweep(ccperms,1,ccs,"-")>=0,1,mean)
results <- list(zstats=zstats,typex=typex,typez=typez,
penaltyxs=rep(penaltyx,length(penaltyzs)),penaltyzs=penaltyzs,
bestpenaltyx=penaltyx,bestpenaltyz=penaltyzs[which.max(zstats)],
cors=ccs, corperms=ccperms, ft.cors=cc.norm,ft.corperms=rowMeans(ccperm.norm),
nnonzerous=nnonzerous,nnonzerovs=nnonzerovs, nnonzerous.perm=rowMeans(nnonzerous.perms),nnonzerovs.perm=rowMeans(nnonzerovs.perms),call=call,v.init=v, pvals=pvals,nperms=nperms,chromx=chromx,chromz=chromz,
storevs=storevs, outcome=outcome, pvalbestz=pvals[which.max(zstats)], UVperms=UVperms )
return(results)
}

CCA.permute.justone <- function(x,z,typex,typez,penaltyx,penaltyz,niter,v,
trace,nperms,standardize,chromx,chromz,upos,uneg,vpos,vneg,
outcome,y,cens,SD=FALSE){
call <- match.call()
if(standardize){
x <- scale(x,TRUE,TRUE)
z <- scale(z, TRUE, TRUE)
}
v <- CheckVs(v,x,z,1)
storevs <- NULL
UVperms=vector("list", length = nperms);
for(i in 1:nperms){
if(trace && .Platform$OS.type!="windows") cat("\n Permutation ",i," out of ", nperms, " ") # #if(trace && .Platform$OS.type=="windows" && i==1) pb <- winProgressBar(title="Doing Permutations", min=0, max=1, initial=(i/nperms))
#     #if(trace && .Platform$OS.type=="windows" && i>1) setWinProgressBar(pb, value=(i/nperms)) if (SD==TRUE) { UVlambdas=vector("list", length = length(penaltyx)); } ### sampz <- sample(1:nrow(z)) sampx <- sample(1:nrow(x)) if(i==1){ out <- CCA(x,z,typex=typex,typez=typez,penaltyx=penaltyx, penaltyz=penaltyz,y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromz=chromz,chromx=chromx) ccperms=nnonzerous.perms=nnonzerovs.perms=rep(NA, nperms) nnonzerou <- sum(out$u!=0)
nnonzerov <- sum(out$v!=0) if(mean(out$u==0)!=1 && mean(out$v==0)!=1){ cc <- cor(x%*%out$u,z%*%out$v) } else { cc <- 0 } storevs <- cbind(storevs, out$v)

}
if(SD==TRUE){templist=vector("list", length = 2);}###

out <- CCA(x[sampx,],z[sampz,],typex=typex,typez=typez,penaltyx=penaltyx, penaltyz=penaltyz,y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromx=chromx,chromz=chromz)
if(SD==TRUE){templist[[1]]=out$u;templist[[2]]=out$v; } ###
if(SD==TRUE){ UVlambdas[[1]]=templist;}###

nnonzerous.perms[i] <- sum(out$u!=0) nnonzerovs.perms[i] <- sum(out$v!=0)
if(mean(out$u==0)!=1 && mean(out$v==0)!=1){
ccperms[i] <- cor(x[sampx,]%*%out$u,z[sampz,]%*%out$v)
} else {
ccperms[i] <- 0
}
if(SD==TRUE){ UVperms[[i]]=UVlambdas;}###

}
#   if(trace && .Platform$OS.type=="windows") close(pb) cc.norm <- ftrans(cc) ccperm.norms <- ftrans(ccperms) zstat <- (cc.norm - mean(ccperm.norms))/(sd(ccperm.norms) + .05) if(trace) cat(fill=T) cc <- as.numeric(cc) ccperms <- as.numeric(ccperms) pval <- mean(ccperms>=cc) results <- list(zstats=zstat,typex=typex,typez=typez,penaltyxs=penaltyx, penaltyzs=penaltyz, bestpenaltyx=penaltyx,bestpenaltyz=penaltyz, cors=cc, corperms=ccperms, ft.cors=cc.norm, ft.corperms=mean(ccperm.norms),nnonzerous=nnonzerou,nnonzerovs=nnonzerov, nnonzerous.perm=mean(nnonzerous.perms),nnonzerovs.perm=mean(nnonzerovs.perms) ,call=call,v.init=v, pvals=pval,nperms=nperms,chromx=chromx, chromz=chromz,storevs=storevs, outcome=outcome, pvalbestz=pval,UVperms=UVperms) return(results) } CCA.permute.xonly<- function(x,z,typex,typez,penaltyxs,penaltyz,niter, v,trace,nperms=25,standardize,chromx,chromz, upos,uneg,vpos,vneg,outcome,y,cens, SD=FALSE){ call <- match.call() if(standardize){ x <- scale(x,TRUE,TRUE) z <- scale(z, TRUE, TRUE) } v <- CheckVs(v,x,z,1) ccperms=nnonzerous.perms=nnonzerovs.perms=matrix(NA, length(penaltyxs), nperms) ccs=nnonzerous=nnonzerovs=numeric(length(penaltyxs)) storevs <- NULL UVperms=vector("list", length = nperms); for(i in 1:nperms){ if(trace && .Platform$OS.type!="windows") cat("\n Permutation ",i," out of ", nperms, " ")
#     #if(trace && .Platform$OS.type=="windows" && i==1) pb <- winProgressBar(title="Doing Permutations", min=0, max=1, initial=(i/nperms)) # #if(trace && .Platform$OS.type=="windows" && i>1) setWinProgressBar(pb, value=(i/nperms))
if (SD==TRUE) { UVlambdas=vector("list", length = length(penaltyxs)); } ###
sampz <- sample(1:nrow(z))
sampx <- sample(1:nrow(x))
for(j in 1:length(penaltyxs)){
if(trace && .Platform$OS.type!="windows") cat(j,fill=FALSE) if(i==1){ out <- CCA(x,z,typex=typex,typez=typez,penaltyx=penaltyxs[j], penaltyz=penaltyz,y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromz=chromz,chromx=chromx) nnonzerous[j] <- sum(out$u!=0)
nnonzerovs[j] <- sum(out$v!=0) if(mean(out$u==0)!=1 && mean(out$v==0)!=1){ ccs[j] <- cor(x%*%out$u,z%*%out$v) } else { ccs[j] <- 0 } storevs <- cbind(storevs, out$v)
}
if(SD==TRUE){templist=vector("list", length = 2);}###

out <- CCA(x[sampx,],z[sampz,],typex=typex,typez=typez,penaltyx=penaltyxs[j], penaltyz=penaltyz,y=y,outcome=outcome,cens=cens,niter=niter,v=v,trace=FALSE, upos=upos, uneg=uneg, vpos=vpos, vneg=vneg, standardize=FALSE,chromx=chromx,chromz=chromz)
nnonzerous.perms[j,i] <- sum(out$u!=0) nnonzerovs.perms[j,i] <- sum(out$v!=0)
if(SD==TRUE){templist[[1]]=out$u;templist[[2]]=out$v; } ###

if(mean(out$u==0)!=1 && mean(out$v==0)!=1){
ccperms[j,i] <- cor(x[sampx,]%*%out$u,z[sampz,]%*%out$v)
} else {
ccperms[j,i] <- 0
}
if(SD==TRUE){ UVlambdas[[j]]=templist;}###

}
if(SD==TRUE){ UVperms[[i]]=UVlambdas;}###

}
#   if(trace && .Platform$OS.type=="windows") close(pb) cc.norm <- ftrans(ccs) ccperm.norm <- ftrans(ccperms) zstats <- (cc.norm - rowMeans(ccperm.norm))/(apply(ccperm.norm,1,sd) + .05) if(trace) cat(fill=T) pvals <- apply(sweep(ccperms,1,ccs,"-")>=0,1,mean) results <- list(zstats=zstats,typex=typex, typez=typez,penaltyxs=penaltyxs, penaltyzs=rep(penaltyz, length(penaltyxs)), bestpenaltyx=penaltyxs[which.max(zstats)], bestpenaltyz=penaltyz, cors=ccs, corperms=ccperms, ft.cors=cc.norm, ft.corperms=rowMeans(ccperm.norm), nnonzerous=nnonzerous,nnonzerovs=nnonzerovs, nnonzerous.perm=rowMeans(nnonzerous.perms), nnonzerovs.perm=rowMeans(nnonzerovs.perms),call=call,v.init=v, pvals=pvals,nperms=nperms, chromx=chromx,chromz=chromz,storevs=storevs, outcome=outcome, pvalbestz=pvals[which.max(zstats)], UVperms=UVperms) return(results) } #' Select tuning parameters for sparse canonical correlation analysis using the #' penalized matrix decomposition. #' #' This function can be used to automatically select tuning parameters for #' sparse CCA using the penalized matrix decompostion. For each data set x and #' z, two types are possible: (1) type "standard", which does not assume any #' ordering of the columns of the data set, and (2) type "ordered", which #' assumes that columns of the data set are ordered and thus that corresponding #' canonical vector should be both sparse and smooth (e.g. CGH data). #' #' For X and Z, the samples are on the rows and the features are on the #' columns. #' #' The tuning parameters are selected using a permutation scheme. For each #' candidate tuning parameter value, the following is performed: (1) The #' samples in X are randomly permuted nperms times, to obtain matrices #'$X*_1,X*_2,...$. (2) Sparse CCA is run on each permuted data set$(X*_i,Z)$#' to obtain factors$(u*_i, v*_i)$. (3) Sparse CCA is run on the original data #' (X,Z) to obtain factors u and v. (4) Compute$c*_i=cor(X*_i u*_i,Z v*_i)$#' and$c=cor(Xu,Zv)$. (5) Use Fisher's transformation to convert these #' correlations into random variables that are approximately normally #' distributed. Let Fisher(c) denote the Fisher transformation of c. (6) #' Compute a z-statistic for Fisher(c), using #'$(Fisher(c)-mean(Fisher(c*)))/sd(Fisher(c*))$. The larger the z-statistic, #' the "better" the corresponding tuning parameter value. #' #' This function also gives the p-value for each pair of canonical variates #' (u,v) resulting from a given tuning parameter value. This p-value is #' computed as the fraction of$c*_i$'s that exceed c (using the notation of #' the previous paragraph). #' #' Using this function, only the first left and right canonical variates are #' considered in selection of the tuning parameter. #' #' Note that x and z must have same number of rows. This function #' performs just a one-dimensional search in tuning parameter space, #' even if penaltyxs and penaltyzs both are vectors: the pairs #' (penaltyxs[1],penaltyzs[1]), #' (penaltyxs[2],penaltyzs[2]),.... are considered. #' @param x Data matrix; samples are rows and columns are features. #' @param z Data matrix; samples are rows and columns are features. Note that x #' and z must have the same number of rows, but may (and generally will) have #' different numbers of columns. #' @param typex Are the columns of x 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. #' @param typez Are the columns of z 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. #' @param penaltyxs The set of x penalties to be considered. If #' typex="standard", then the L1 bound on u is penaltyxs*sqrt(ncol(x)). If #' "ordered", then it's the lambda for the fused lasso penalty. The user can #' specify a single value or a vector of values. If penaltyxs is a vector and #' penaltyzs is a vector, then the vectors must have the same length. If NULL, #' then the software will automatically choose a single lambda value if type is #' "ordered", or a grid of (L1 bounds)/sqrt(ncol(x)) if type is "standard". #' @param penaltyzs The set of z penalties to be considered. If #' typez="standard", then the L1 bound on v is penaltyzs*sqrt(ncol(z)). If #' "ordered", then it's the lambda for the fused lasso penalty. The user can #' specify a single value or a vector of values. If penaltyzs is a vector and #' penaltyzs is a vector, then the vectors must have the same length. If NULL, #' then the software will automatically choose a single lambda value if type is #' "ordered", or a grid of (L1 bounds)/sqrt(ncol(z)) if type is "standard". #' @param niter How many iterations should be performed each time CCA is #' called? Default is 3, since an approximate estimate of u and v is acceptable #' in this case, and otherwise this function can be quite time-consuming. #' @param v The first K columns of the v matrix of the SVD of X'Z. If NULL, #' then the SVD of X'Z will be computed inside this 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 (since that process can be #' time-consuming if X and Z both have high dimension). #' @param trace Print out progress? #' @param nperms How many times should the data be permuted? Default is 25. A #' large value of nperms is very important here, since the formula for #' computing the z-statistics requires a standard deviation estimate for the #' correlations obtained via permutation, which will not be accurate if nperms #' is very small. #' @param standardize Should the columns of X and Z be centered (to have mean #' zero) and scaled (to have standard deviation 1)? Default is TRUE. #' @param chromx Used only if typex="ordered"; a vector of length ncol(x) that #' allows you to specify which chromosome each CGH spot is on. If NULL, then it #' is assumed that all CGH spots are on same chromosome. #' @param chromz Used only if typex="ordered"; a vector of length ncol(z) that #' allows you to specify which chromosome each CGH spot is on. If NULL, then it #' is assumed that all CGH spots are on same chromosome. #' @param upos If TRUE, then require all elements of u to be positive in sign. #' Default is FALSE. Can only be used if type is standard. #' @param uneg If TRUE, then require all elements of u to be negative in sign. #' Default is FALSE. Can only be used if type is standard. #' @param vpos If TRUE, then require all elements of v to be positive in sign. #' Default is FALSE. Can only be used if type is standard. #' @param vneg If TRUE, then require all elements of v to be negative in sign. #' Default is FALSE. Can only be used if type is standard. #' @param outcome If you would like to incorporate a phenotype into CCA #' analysis - that is, you wish to find features that are correlated across the #' two data sets and also correlated with a phenotype - then use one of #' "survival", "multiclass", or "quantitative" to indicate outcome type. #' Default is NULL. #' @param y If outcome is not NULL, then this is a vector of phenotypes - one #' for each row of x and z. If outcome is "survival" then these are survival #' times; must be non-negative. If outcome is "multiclass" then these are class #' labels. Default NULL. #' @param cens If outcome is "survival" then these are censoring statuses for #' each observation. 1 is complete, 0 is censored. Default NULL. #' @return \item{zstat}{The vector of z-statistics, one per element of #' sumabss.} \item{pvals}{The vector of p-values, one per element of sumabss.} #' \item{bestpenaltyx}{The x penalty that resulted in the highest z-statistic.} #' \item{bestpenaltyz}{The z penalty that resulted in the highest z-statistic.} #' \item{cors}{The value of cor(Xu,Zv) obtained for each value of sumabss.} #' \item{corperms}{The nperms values of cor(X*u*,Zv*) obtained for each value #' of sumabss, where X* indicates the X matrix with permuted rows, and u* and #' v* are the output of CCA using data (X*,Z).} \item{ft.cors}{The result of #' applying Fisher transformation to cors.} \item{ft.corperms}{The result of #' applying Fisher transformation to corperms.} \item{nnonzerous}{Number of #' non-zero u's resulting from applying CCA to data (X,Z) for each value of #' sumabss.} \item{nnonzerouv}{Number of non-zero v's resulting from applying #' CCA to data (X,Z) for each value of sumabss.} \item{v.init}{The first factor #' of the v matrix of the SVD of x'z. This is saved in case this function (or #' the CCA function) will be re-run later.} #' @seealso \link{PMD},\link{CCA} #' #' @references #' Ali Mahzarnia, Alexander Badea (2022) #' \emph{Joint Estimation of Vulnerable Brain Networks and Alzheimer’s Disease Risk Via Novel Extension of Sparse Canonical Correlation at bioRxiv.} \cr #' @examples #' #' # See examples in CCA function #' #' @export CCA.permute CCA.permute <- function(x,z,typex=c("standard", "ordered"), typez=c("standard","ordered"), penaltyxs=NULL, penaltyzs=NULL, niter=3,v=NULL,trace=TRUE,nperms=25, standardize=TRUE, chromx=NULL, chromz=NULL,upos=FALSE, uneg=FALSE, vpos=FALSE, vneg=FALSE, outcome=NULL, y=NULL, cens=NULL, SD=FALSE){ if(ncol(x)<2) stop("Need at least 2 features in data set x.") if(ncol(z)<2) stop("Need at least 2 features in data set z.") u <- NULL typex <- match.arg(typex) typez <- match.arg(typez) call <- match.call() if(!is.null(penaltyxs) && !is.null(penaltyzs) && length(penaltyxs)>1 && length(penaltyzs)>1 && length(penaltyxs)!=length(penaltyzs)) stop("Penaltyxs and Penaltyzs must be same length, or one must have length 1. This is because tuning parameters are considered in pairs.") if(is.null(penaltyxs) && typex=="ordered"){ u <- CheckVs(NULL,z,x,1) penaltyxs <- c(ChooseLambda1Lambda2(as.numeric(u))) warning("Since type of x is ordered, the penalty for x was chosen w/o permutations.") } if(is.null(penaltyzs) && typez=="ordered"){ v <- CheckVs(v,x,z,1) penaltyzs <- c(ChooseLambda1Lambda2(as.numeric(v))) warning("Since type of z is ordered, the penalty for z was chosen w/o permutations.") } if(is.null(penaltyxs)) penaltyxs <- seq(.1,.7,len=10) if(is.null(penaltyzs)) penaltyzs <- seq(.1,.7,len=10) if(typex=="ordered" && (upos||uneg)) stop("If type=ordered then you cannot require elements of u to be positive or negative!") if(typez=="ordered" && (vpos||vneg)) stop("If type=ordered then you cannot require elements of v to be positive or negative!") if(length(unique(penaltyxs))==1 && length(unique(penaltyzs))==1){ out <- CCA.permute.justone(x=x,z=z,typex=typex,typez=typez,penaltyx=penaltyxs[1],penaltyz=penaltyzs[1],niter=niter,v=v,trace=trace,nperms=nperms,standardize=standardize,chromx=chromx,chromz=chromz,upos=upos,uneg=uneg,vpos=vpos,vneg=vneg,outcome=outcome,y=y,cens=cens, SD=SD) } if(length(penaltyxs)==1 && length(penaltyzs)>1) out <- CCA.permute.zonly(x=x,z=z,typex=typex,typez=typez,penaltyx=penaltyxs,penaltyzs=penaltyzs,niter=niter,v=v,trace=trace,nperms=nperms,standardize=standardize,chromx=chromx,chromz=chromz,upos=upos,uneg=uneg,vpos=vpos,vneg=vneg,outcome=outcome,y=y,cens=cens, SD=SD) if(length(penaltyxs)>1 && length(penaltyzs)==1) out <- CCA.permute.xonly(x=x,z=z,typex=typex,typez=typez,penaltyxs=penaltyxs,penaltyz=penaltyzs,niter=niter,v=v,trace=trace,nperms=nperms,standardize=standardize,chromx=chromx,chromz=chromz,upos=upos,uneg=uneg,vpos=vpos,vneg=vneg,outcome=outcome,y=y,cens=cens, SD=SD) if(length(penaltyzs)>1 && length(penaltyxs)>1) out <- CCA.permute.both(x=x,z=z,typex=typex,typez=typez,penaltyxs=penaltyxs, penaltyzs=penaltyzs,niter=niter,v=v,trace=trace, nperms=nperms,standardize=standardize,chromx=chromx, chromz=chromz,upos=upos,uneg=uneg,vpos=vpos,vneg=vneg, outcome=outcome,y=y,cens=cens, SD=SD) out$call <- call
out$upos <- upos out$uneg <- uneg
out$vpos <- vpos out$vneg <- vneg
if (SD=="TRUE") {out$UVperms =out$UVperms;}
class(out) <- "CCA.permute"
return(out)
}

#' @method print CCA.permute
#' @export
print.CCA.permute <- function(x,...){
cat("Call: ")
dput(x$call) cat("\n") cat("Type of x: ", x$typex,"\n")
cat("Type of z: ", x$typez,"\n") if(x$upos) cat("U's constrained to be positive", fill=TRUE)
if(x$uneg) cat("U's constrained to be negative", fill=TRUE) if(x$vpos) cat("V's constrained to be positive", fill=TRUE)
if(x$vneg) cat("V's constrained to be negative", fill=TRUE) if(!is.null(x$outcome)) cat("Outcome used: ", x$outcome, fill=TRUE) if(length(x$penaltyxs)>1 && length(x$penaltyzs)>1){ tab <- round(cbind(x$penaltyxs,x$penaltyzs, x$zstats,x$pvals,x$cors,rowMeans(x$corperms),x$ft.cors,x$ft.corperms,x$nnonzerous,x$nnonzerovs),3) # if(x$typex=="ordered" && x$typez=="ordered") dimnames(tab) <- list(1:length(x$penaltyxs), c("X Lambda", "Z Lambda","Z-Stat","P-Value","Cors","Cors Perm", "FT(Cors)", "FT(Cors Perm)", "# U's non-zero", "# V's non-zero"))
#    if(x$typex=="standard" && x$typez=="ordered") dimnames(tab) <- list(1:length(x$penaltyxs), c("X L1 Bound", "Z Lambda","Z-Stat","P-Value","Cors","Cors Perm", "FT(Cors)", "FT(Cors Perm)", "# U's non-zero", "# V's non-zero")) # if(x$typex=="ordered" && x$typez=="standard") dimnames(tab) <- list(1:length(x$penaltyxs), c("X Lambda", "Z L1 Bound","Z-Stat","P-Value","Cors","Cors Perm", "FT(Cors)", "FT(Cors Perm)", "# U's non-zero", "# V's non-zero"))
#    if(x$typex=="standard" && x$typez=="standard") dimnames(tab) <- list(1:length(x$penaltyxs), c("X L1 Bound", "Z L1 Bound","Z-Stat","P-Value","Cors","Cors Perm", "FT(Cors)", "FT(Cors Perm)", "# U's non-zero", "# V's non-zero")) dimnames(tab) <- list(1:length(x$penaltyxs), c("X Penalty", "Z Penalty", "Z-Stat", "P-Value", "Cors", "Cors Perm", "FT(Cors)", "FT(Cors Perm)", "# U's Non-Zero", "# Vs Non-Zero"))
print(tab)
if(x$typex=="standard") cat("Best L1 bound for x: ", x$bestpenaltyx,fill=TRUE)
if(x$typex=="ordered") cat("Best lambda for x: ", x$bestpenaltyx,fill=TRUE)
if(x$typez=="standard") cat("Best L1 bound for z: ", x$bestpenaltyz,fill=TRUE)
if(x$typez=="ordered") cat("Best lambda for z: ", x$bestpenaltyz,fill=TRUE)
} else {
cat("P-value is ", x$pvals, fill=TRUE) cat("Z-stat is ", x$zstats, fill=TRUE)
cat("Correlation is ", x$cors, fill=TRUE) cat("Average correlation of permuted data is ", mean(x$corperms),fill=TRUE)
}
}

CCAPhenotypeZeroSome <- function(x,z,y,qt=.8,cens=NULL,outcome=c("quantitative", "survival", "multiclass"), typex,typez){
outcome <- match.arg(outcome)
if(outcome=="quantitative"){
score.x <- quantitative.func(t(x)[,!is.na(y)],y[!is.na(y)])$tt score.z <- quantitative.func(t(z)[,!is.na(y)],y[!is.na(y)])$tt
} else if (outcome=="survival"){
score.x <- cox.func(t(x)[,!is.na(y)],y[!is.na(y)],cens[!is.na(y)])$tt score.z <- cox.func(t(z)[,!is.na(y)],y[!is.na(y)],cens[!is.na(y)])$tt
} else if (outcome=="multiclass"){
score.x <- multiclass.func(t(x)[,!is.na(y)],y[!is.na(y)])$tt score.z <- multiclass.func(t(z)[,!is.na(y)],y[!is.na(y)])$tt
}
if(typex=="standard"){
keep.x <- abs(score.x)>=quantile(abs(score.x),qt)
} else if(typex=="ordered"){
lam <- ChooseLambda1Lambda2(as.numeric(score.x))
flsa.out <- FLSA(as.numeric(score.x),lambda1=lam, lambda2=lam)
#    diagfl.out <- diag.fused.lasso.new(as.numeric(score.x), lam1=lam)
#    lam2ind <- which.min(abs(diagfl.out$lam2-lam)) # flsa.out <- diagfl.out$coef[,lam2ind]
on.exit(par(oldpar))
par(mfrow=c(2,1))
keep.x <- abs(flsa.out)>=quantile(abs(flsa.out), qt)
if(mean(keep.x)==1 | mean(keep.x)==0) keep.x <- (abs(score.x) >= quantile(abs(score.x), qt))
}
if(typez=="standard"){
keep.z <- abs(score.z)>=quantile(abs(score.z),qt)
} else if(typez=="ordered"){
lam <- ChooseLambda1Lambda2(as.numeric(score.z))
flsa.out <- FLSA(as.numeric(score.z),lambda1=lam, lambda2=lam)
#    diagfl.out <- diag.fused.lasso.new(as.numeric(score.z), lam1=lam)
#    lam2ind <- which.min(abs(diagfl.out$lam2-lam)) # flsa.out <- diagfl.out$coef[,lam2ind]
on.exit(par(oldpar))
par(mfrow=c(2,1))
keep.z <- abs(flsa.out)>=quantile(abs(flsa.out), qt)
if(mean(keep.z)==1 | mean(keep.z)==0) keep.z <- (abs(score.z) >= quantile(abs(score.z), qt))
}
xnew <- x
xnew[,!keep.x] <- 0
znew <- z
znew[,!keep.z] <- 0
return(list(x=xnew,z=znew))
}


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PMA2 documentation built on May 12, 2022, 9:06 a.m.