Author: Guido Kraemer
Date: 2018-01-05

# Comparing DRR and PCA

#### Guido Kraemer

#### 2018-01-05

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

## 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 1.379328e-14
    ## drr.1 5.549355 3.427558 1.700925 1.357570e-14
    ## drr.2 5.508291 3.193501 1.638346 1.358499e-14
    ## drr.3 5.555269 3.485765 1.734136 1.356369e-14
    ## drr.4 5.631050 2.302263 1.473392 1.353796e-14

### Processing time

    ##       user.self sys.self elapsed
    ## pca       0.000    0.000   0.001
    ## drr.1    22.604   14.104  20.295
    ## drr.2    13.796    9.024  12.317
    ## drr.3    27.340   16.756  24.402
    ## drr.4    19.244    7.484  17.991