SDADcv <- function (x, ...) UseMethod("SDADcv")
SDADcv.default <- function(X, Y, folds, Om, gam, lams, mu, q, PGsteps, PGtol, maxits, tol, feat, quiet, initTheta, ...){
#
# HERE WE NEED A DESCRIPTION
# Use Roxygen2 to create the desired documentation
#
# TODO: handle Y as a factor an generate dummy matrix
# Get dimensions of input matrices
# Note: PGtol is a vector with abs(index 1) and rel(index 2) tolerances
# Inconsistency with SDAD on norm of beta, here 1e-12, 1e-15 in SDAD
dimX <- dim(X)
n <- dimX[1]
p <- dimX[2]
K <- dim(Y)[2]
# If n is not divisible by K, duplicate some records for the sake of
# cross validation.
pad <- 0
if(n %% folds > 0){
pad <- ceiling(n/folds)*folds - n
# Add the duplicates, such that number of data points is
# divisible by the number of folds
X <- rbind(X,X[1:pad,])
Y <- rbind(Y,Y[1:pad,])
}
# Get the new number of rows
n <- dim(X)[1]
# Randomly permute rows of X
prm <- sample(1:n,n,replace=FALSE)
X <- X[prm,]
Y <- Y[prm,]
# Sort lambdas in descending order
lams <- lams[order(lams,decreasing = FALSE)]
###
# Initialization of cross-validation indices
###
# Number of validation samples
nv <- n/folds
# Initial validation indices
vinds <- 1:nv
# Initial training indices
tinds <- (nv+1):n
# Number of params to test
nlam <- length(lams)
# Validation scores
scores <- q*p*matrix(1,nrow = folds, ncol = nlam)
# Misclassification rate for each classifier
mc <- matrix(0,nrow = folds, ncol = nlam)
for(f in 1:folds){
# Initialization
# Extract X and Y from training data
Xt <- X[tinds,]
Yt <- Y[tinds,]
# Extract validation data
Xv <- X[vinds,]
Yv <- Y[vinds,]
# Normalize
Xt_norm <- accSDA::normalize(Xt)
Xt <- Xt_norm$Xc # Use the centered and scaled data
Xv <- accSDA::normalizetest(Xv,Xt_norm)
# Get dimensions of training matrices
nt <- dim(Xt)[1]
p <- dim(Xt)[2]
# Centroid matrix of training data
C <- diag(diag((1/(t(Yt)%*%Yt))))%*%t(Yt)%*%Xt
# Check if Om is diagonal. If so, use matrix inversion lemma in linear
# system solves.
if(norm(diag(diag(Om))-Om,type = "F") < 1e-15){
if(dim(Om)[1] != p){
warning("Columns dropped in normalization to a total of p, setting Om to diag(p)")
Om <- diag(p)
}
# Flag to use Sherman-Morrison-Woodbury to translate to
# smaller dimensional linear system solves.
SMW <- 1
# Easy to invert diagonal part of Elastic net coefficient matrix.
M <- mu + 2*gam*diag(Om)
Minv = 1/M
# Cholesky factorization for smaller linear system.
RS = chol(diag(nt) + 2*Xt%*%((Minv/nt)*t(Xt)));
} else{ # Use Cholesky for solving linear systems in ADMM step
# Flag to not use SMW
SMW <- 0
A <- mu*diag(p) + 2*(t(Xt)%*%Xt/nt + gam*Om)
R2 <- chol(A)
}
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# Matrices for theta update.
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
D <- (1/nt)*(t(Yt)%*%Yt)
R <- chol(D) # Cholesky factorization of D.
###
# Validation loop
###
if(!quiet){
print("-------------------------------------------")
print(paste("Fold number:",f))
print("-------------------------------------------")
}
B <- array(0,c(p,q,nlam))
###
# Loop through the validation parameters
###
for(ll in 1:nlam){
# Initialize B and Q
Q <- matrix(1,K,q)
#-------------------------------------------------
# Call Alternating Direction Method to solve SDA
#-------------------------------------------------
# For j=1,2,...,q compute the SDA pair (theta_j, beta_j)
for(j in 1:q){
# Initialization
# Compute Qj (K by j, first j-1 scoring vectors, all-ones last col)
Qj <- Q[,1:j]
# Precompute Mj = I-Qj*Qj'*D
Mj <- function(u){
return(u-Qj%*%(t(Qj)%*%(D%*%u)))
}
# Initialize theta
theta <- matrix(stats::runif(K),nrow=K,ncol=1)
theta <- Mj(theta)
if(j == 1 & !missing(initTheta)){
theta=initTheta
}
theta <- theta/as.numeric(sqrt(crossprod(theta,D%*%theta)))
# Initialize coefficient vector for elastic net step
d <- 2*t(Xt)%*%(Yt%*%(theta/nt))
# Initialize beta
if(SMW == 1){
btmp <- Xt%*%(Minv*d)/nt
beta <- (Minv*d) - 2*Minv*(t(Xt)%*%(solve(RS,solve(t(RS),btmp))))
}else{
beta <- solve(R2,solve(t(R2),d))
}
###
# Alternating direction method to update (theta,beta)
###
for(its in 1:maxits){
# Update beta using alternating direction method of multipliers.
b_old <- beta
if(SMW == 1){
# Use SMW-based ADMM
betaOb <- ADMM_EN_SMW(Minv, Xt, RS, d, beta, lams[ll], mu, PGsteps, PGtol, TRUE, rep(1,p))
beta <- betaOb$y
} else{
betaOb <- ADMM_EN2(R2, d, beta, lams[ll], mu, PGsteps, PGtol, TRUE, rep(1,p))
beta <- betaOb$y
}
# Update theta using the projected solution
if(norm(beta, type="2") > 1e-12){
# Update theta
b <- t(Yt)%*%(Xt%*%beta)
y <- solve(t(R),b)
z <- solve(R,y)
tt <- Mj(z)
t_old <- theta
theta <- tt/sqrt(as.numeric(t(tt)%*%D%*%tt))
# Update changes
db <- norm(beta-b_old, type="2")/norm(beta, type="2")
dt <- norm(theta-t_old, type="2")/norm(theta, type="2")
} else{
# Update b and theta
beta <- beta*0
theta <- theta*0
db <- 0
dt <- 0
}
if(max(db,dt) < tol){
# Converged
break
}
}
# Make the first argument be positive, this is to make the results
# more reproducible and consistent.
if(theta[1] < 0){
theta <- (-1)*theta
beta <- (-1)*beta
}
# Update Q and B
Q[,j] <- theta
B[,j,ll] <- beta
}
#------------------------------------------------------------
# Get classification statistics for (Q,B)
#------------------------------------------------------------
# Project validation data
PXtest <- Xv%*%B[,,ll]
# Project centroids
PC <- C%*%B[,,ll]
# Compute distances to the centroid for each projected test observation
dists <- matrix(0,nv,K)
for(i in 1:nv){
for(j in 1:K){
dists[i,j] <- norm(PXtest[i,] - PC[j,], type="2")
}
}
# Label test observation according to the closest centroid to its projection.
predicted_labels <- t(apply(dists, 1, function(x) c(min(x),which.min(x))))
predicted_labels <- predicted_labels[,2] # Select the indices
# Form predicted Y
Ypred <- matrix(0,nv,K)
for(i in 1:nv){
Ypred[i,predicted_labels[i]] <- 1
}
# Fraction misclassified
mc[f,ll] <- (0.5*norm(Yv-Ypred,type="F")^2)/nv
###
# Validation scores
###
B_loc <- matrix(B[,,ll],p,q)
sum_B_loc_nnz <- sum(B_loc != 0)
# if fraction nonzero features less than feat.
if( 1 <= sum_B_loc_nnz & sum_B_loc_nnz <= q*p*feat){
# Use misclassification rate as validation score.
scores[f,ll] <- mc[f,ll]
} else if(sum_B_loc_nnz > q*p*feat){
# Solution is not sparse enough, use most sparse as measure of quality instead.
scores[f,ll] <- sum_B_loc_nnz
}
# Display iteration stats
if(!quiet){
print(paste("f:", f, "| ll:", ll, "| lam:", lams[ll], "| feat:",
sum_B_loc_nnz/(q*p), "| mc:", mc[f,ll], "| score:", scores[f,ll]))
}
} # End of for ll in 1:nlam
#--------------------------------------------
# Update training/validation split
#--------------------------------------------
# Extract new validation indices
tmp <- tinds[1:nv]
if(nv+1 > nt){
# Special case for 2-fold CV
tinds <- vinds
vinds <- tmp
} else{
tinds <- c(tinds[(nv+1):nt],vinds)
# Update validation indices
vinds <- tmp
}
} # End of folds loop
###
# Find the best solution
###
# Average CV scores
avg_score <- colMeans(scores)
# Choose lambda with best average score
lbest <- which.min(avg_score)
lambest <- lams[lbest]
###
# Solve with lambda = lam(lbest)
###
print(paste("Finished Training: lam =", lambest))
# Use the full training set to obtain parameters
Xt <- X[1:(n-pad),]
Yt <- Y[1:(n-pad),]
# Normalize
Xt_norm <- accSDA::normalize(Xt)
Xt <- Xt_norm$Xc # Use the centered and scaled data
# Get best Q and B on full training data
resBest <- SDAD(Xt, Yt, Om, gam, lambest, mu, q, PGsteps, PGtol, maxits, tol)
# Create an object of class SDAPcv to return, might add more to it later
retOb <- structure(
list(call = match.call(),
B = resBest$B,
Q = resBest$Q,
lbest = lbest,
lambest = lambest,
scores = scores),
class = "SDADcv")
return(retOb)
}
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