Returns reduces data after PCA with desired percent of variance retained.

pca_var.R

pca_var <- function(X, percent) {
        #Normalize data before start
        X = scale(X)
        
        #Covariance matrix
        Sigma = (1 / nrow(X)) * t(X) %*% X
        
        #Singular value decomposition of covariance matrix
        Sigma_svd <- svd(Sigma)
        
        #Get minimum number of vectors to retain desired percent of variation
        k = which(cumsum(Sigma_svd$d)/sum(Sigma_svd$d) >= percent)[1]
        
        #Take this number of vectors
        Ureduce <- Sigma_svd$u[, 1:k]
        
        #Compute reduced version of data
        Z = X %*% Ureduce
        
        return(Z)
}