# Applicability domain methods for binary data

## Introduction

library(applicable)

Similarity statistics can be used to compare data sets where all of the predictors are binary. One of the most common measures is the Jaccard index.

For a training set of size n, there are n similarity statistics for each new sample. These can be summarized via the mean statistic or a quantile. In general, we want similarity to be low within the training set (i.e., a diverse training set) and high for new samples to be predicted.

To analyze the Jaccard metric, applicable provides the following methods:

• apd_similarity: analyzes samples in terms of similarity scores. For a training set of n samples, a new sample is compared to each, resulting in n similarity scores. These can be summarized into the median similarity.

• autoplot: shows the cumulative probability versus the unique similarity values in the training set.

• score: scores new samples using similarity methods. In particular, it calculates the similarity scores and if add_percentile = TRUE, it also estimates the percentile of the similarity scores.

## Example

The example data is from two QSAR data sets where binary fingerprints are used as predictors.

data(qsar_binary)

Let us construct the model:

jacc_sim <- apd_similarity(binary_tr)
jacc_sim
#> Applicability domain via similarity
#> Reference data were 67 variables collected on 4330 data points.
#> New data summarized using the mean.

As we can see below, this is a fairly diverse training set:

library(ggplot2)

# Plot the empirical cumulative distribution function for the training set
autoplot(jacc_sim)

We can compare the similarity between new samples and the training set:

# Summarize across all training set similarities
mean_sim <- score(jacc_sim, new_data = binary_unk)
mean_sim
#> # A tibble: 5 x 2
#>   similarity similarity_pctl
#>        <dbl>           <dbl>
#> 1     0.376            49.8
#> 2     0.284            13.5
#> 3     0.218             6.46
#> 4     0.452           100
#> 5     0.0971            5.59

Samples 3 and 5 are definitely extrapolations based on these predictors. In other words, the new samples are not similar to the training set and so predictions on them may not be very reliable.