Comparing DRR and PCA

Guido Kraemer

2016-09-15

This is an example application to compare the accuracy and computational speed of DRR for different parameters to PCA.

Load libraries

library(DRR)

Read in data

data(iris)

in_data <- iris[,1:4]

npoints <- nrow(in_data)
nvars <- ncol(in_data)
for (i in seq_len(nvars)) in_data[[i]] <- as.numeric(in_data[[i]])
my_data <- scale(in_data[sample(npoints),], scale = FALSE)

Fit the dimensionality reductions.

t0 <- system.time(pca   <- prcomp(my_data, center = FALSE, scale. = FALSE))
t1 <- system.time(drr.1 <- drr(my_data))
t2 <- system.time(drr.2 <- drr(my_data, fastkrr = 2))
t3 <- system.time(drr.3 <- drr(my_data, fastkrr = 5))
t4 <- system.time(drr.4 <- drr(my_data, fastkrr = 2, fastcv = TRUE))

Plot the data

Calculate RMSE

rmse <- matrix(NA_real_, nrow = 5, ncol = nvars, dimnames = list(c("pca", "drr.1", 
    "drr.2", "drr.3", "drr.4"), seq_len(nvars)))

for (i in seq_len(nvars)) {
    pca_inv <- pca$x[, 1:i, drop = FALSE] %*% t(pca$rotation[, 1:i, drop = FALSE])
    rmse["pca", i] <- sqrt(sum((my_data - pca_inv)^2))
    rmse["drr.1", i] <- sqrt(sum((my_data - drr.1$inverse(drr.1$fitted.data[, 
        1:i, drop = FALSE]))^2))
    rmse["drr.2", i] <- sqrt(sum((my_data - drr.2$inverse(drr.2$fitted.data[, 
        1:i, drop = FALSE]))^2))
    rmse["drr.3", i] <- sqrt(sum((my_data - drr.3$inverse(drr.3$fitted.data[, 
        1:i, drop = FALSE]))^2))
    rmse["drr.4", i] <- sqrt(sum((my_data - drr.4$inverse(drr.4$fitted.data[, 
        1:i, drop = FALSE]))^2))
}

The Results

More blocks for fastkrr speed up calculation, too are bad for accuracy.

RMSE

##              1        2        3            4
## pca   7.166770 3.899313 1.884524 1.732772e-14
## drr.1 5.469965 3.458503 1.709825 1.675732e-14
## drr.2 5.478541 3.487811 1.645224 1.674559e-14
## drr.3 5.552791 3.499912 1.668842 1.674177e-14
## drr.4 5.570917 3.690015 1.642986 1.674143e-14

Processing time

##       user.self sys.self elapsed
## pca       0.000    0.000   0.001
## drr.1    30.412   51.860  24.329
## drr.2    20.200   34.372  15.491
## drr.3    39.788   67.140  32.411
## drr.4    22.648   21.956  19.565