R/SOPC.R

In SOPC: The Sparse Online Principal Component Estimation Algorithm

#' The sparse online principal component can not only process online data sets, but also obtain a sparse solution of online data sets.
#'
#' @param data is a highly correlated online data set
#' @param m is the number of principal component
#' @param gamma is a sparse parameter
#' @param eta is the proportion of online data to total data
#'
#' @return Aso,Dso
#' @export
#' @importFrom stats cor cov
#' @importFrom elasticnet spca
#' @examples
#' require(elasticnet)
#' SOPC(PSA,3,0.03,0.6)
SOPC<-function(data,m,gamma,eta){
X<-scale(data)
S<-cov(X)
eig<-eigen(S)
p<-nrow(S)
n<-nrow(X)
n0<-round(eta*n)
Xbar<-colMeans(X[1:n0,])
S0<-cov(X[1:n0,])
lambda=eigen(S0)$values[1:m]
V<-eigen(S0)$vectors[,1:m]
paras<-rep(gamma,1*m,m)
Sd<-S0

iter1=0
for (i in (n0+1):n) {
iter1=iter1+1
Xcenter<-t(X[i,])
Sd<-((i-1)/i)*Sd+(1/i)*t(Xcenter)%*%Xcenter
lambda<-eigen(Sd)$values
spc<-spca(Sd,K=m,type="Gram",max.iter=0,sparse="penalty",trace=FALSE,para=paras)
V<-spc$loadings
}
lambda2<-lambda[1:m]
V2<-V[,1:m]
Aso<-matrix(0,nrow=p,ncol=m)
for (j in 1:m){
  Aso[,j]<-sqrt(lambda2[j])*V2[,j]
  }
Aso;table(Aso==0)
h2<-diag(Aso%*%t(Aso))
Dso<-diag(S-h2)
return(list(Aso=Aso,Dso=Dso))
}