Comparing DRR and PCA

In DRR: Dimensionality Reduction via Regression

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

Load libraries

library(DRR)
set.seed(123)

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, verbose = FALSE))
t2 <- system.time(drr.2 <- drr(my_data, fastkrr = 2, verbose = FALSE))
t3 <- system.time(drr.3 <- drr(my_data, fastkrr = 5, verbose = FALSE))
t4 <- system.time(drr.4 <- drr(my_data, fastkrr = 2, fastcv = TRUE,
                               verbose = FALSE))

Plot the data

pairs(my_data,           gap = 0, main = "iris")
pairs(pca$x,             gap = 0, main = "pca")
pairs(drr.1$fitted.data, gap = 0, main = "drr.1")
pairs(drr.2$fitted.data, gap = 0, main = "drr.2")
pairs(drr.3$fitted.data, gap = 0, main = "drr.3")
pairs(drr.4$fitted.data, gap = 0, main = "drr.4")

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

print(rmse)

Processing time

print(rbind(pca = t0, drr.1 = t1, drr.2 = t2, drr.3 = t3, drr.4 = t4)[, 1:3])

DRR documentation built on Feb. 12, 2020, 5:59 p.m.