# metamer v0.2.0

0

0th

Percentile

## Create Data with Identical Statistics

Creates data with identical statistics (metamers) using an iterative algorithm proposed by Matejka & Fitzmaurice (2017) <DOI:10.1145/3025453.3025912>.

# metamer

Implements the algorithm proposed by Matejka & Fitzmaurice (2017) to create metamers (datasets with identical statistical properties but very different graphs).

In colour theory, metamers) are colours that have very different wavelength distribution but are perceived as equal by out visual system. This happens because out eyes essentially summarise a continuous distribution of wavelength by just 3 numbers: the amount that each type of cone cell is exited. Colour metamerism is how artists can reproduce so many colours with a few pigments, or how PC monitors use only 3 lights to show colourful pictures.

(from the excellent Color: From Hexcodes to Eyeballs by Jamie Wong)

Statistical transformations such as mean, standard deviation and correlation behave very similarly in that they summarise data with just a few numbers for the benefit of our limited cognitive capacity. Thus, statistical metamers are sets of data that share some statistical properties.

This article explores statistical metamerism in more detail.

## Installation

You can install metamer with:

install.packages("metamer")

or install the development version with:

# install.packages("devtools")
devtools::install_github("eliocamp/metamer")

## Example

You can construct metamers from a starting dataset and a vector of statistical properties to remain constant (by default, up to 2 significant figures).

library(metamer)
# install.packages("datasauRus")
start <- subset(datasauRus::datasaurus_dozen, dataset == "dino")
start$dataset <- NULL # And we want to preserve means and correlation mean_cor <- delayed_with(mean(x), mean(y), cor(x, y)) N <- 20000 set.seed(42) # To make results reproducible metamers <- metamerize(start, preserve = mean_cor, N = N) print(metamers) #> List of 12791 metamers We found 12791 metamers. Let’s see the final one, with the starting dataset as background. library(ggplot2) ggplot(metamers[[length(metamers)]], aes(x, y)) + geom_point(data = start, color = "red", alpha = 0.5, size = 0.4) + geom_point() We can check that the statistical properties have been preserved up to 2 significant figures: cbind(dino = signif(mean_cor(start), 2), last = signif(mean_cor(metamers[[length(metamers)]]), 2)) #> dino last #> [1,] 54.000 54.000 #> [2,] 48.000 48.000 #> [3,] -0.064 -0.064 However, a semi random cloud of points is not that interesting, so we can specify a minimizing function so that the result is similar to another dataset. metamerize will start from the last metamer of the previous run if the data argument is a list of metamers and append the result. target1 <- subset(datasauRus::datasaurus_dozen, dataset == "x_shape") target1$dataset <- NULL
metamers <- metamerize(metamers,
minimize = mean_dist_to(target1),
N = N)

Now the result is a bit more impressive.

ggplot(metamers[[length(metamers)]], aes(x, y)) +
geom_point(data = start, color = "red", alpha = 0.5, size = 0.4) +
geom_point()

We can animate the whole thing. Since 19552 metamers is overkill, first we keep only 200 of them.

library(gganimate)
metamers_anim <- trim(metamers, 30*2)

ggplot(as.data.frame(metamers_anim), aes(x, y)) +
geom_point() +
transition_manual(.metamer)
#> nframes and fps adjusted to match transition

You can freehand your own starting or target data with the draw_data() utility, that will open a shiny interface. You might need to install shiny and miniUI with install.packages(c("shiny", "miniUI")).

Metamerizing operations can be chained while changing the minimizing function.

library(magrittr)
target2 <- subset(datasauRus::datasaurus_dozen, dataset == "star")
target2\$dataset <- NULL

metamers <- metamerize(start,
preserve = mean_cor,
minimize = mean_dist_to(target1),
N = N) %>%
set_minimize(mean_dist_to(target2)) %>%
metamerize(N = N) %>%
set_minimize(mean_dist_to(start)) %>%
metamerize(N = N)

And the full sequence

trim(metamers, 30*3) %>%
as.data.frame() %>%
ggplot(aes(x, y)) +
geom_point() +
transition_manual(.metamer)

## Functions in metamer

 Name Description draw_data Freehand drawing mean_dist_to Mean minimum distance mean_self_proximity Inverse of the mean self distance metamer-package metamer: Create Data with Identical Statistics delayed_with Apply expressions to data.frames densify Increase resolution of data set_minimize Set metamer_list attributes trim Trim a metamer_list metamerize Create metamers moments_n Compute moments No Results!