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.

```library(DRR)
set.seed(123)
```

```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])
```

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