kerntools

The goal of kerntools is to provide R tools for working with a family of Machine Learning methods called kernel methods. It can be used to complement other R packages like kernlab. Right now, kerntools implements several kernel functions for treating non-negative and real vectors, real matrices, categorical and ordinal variables, sets, and strings. Several tools for studying the resulting kernel matrix or to compare two kernel matrices are available. These diagnostic tools may be used to infer the kernel(s) matrix(ces) suitability in training models. This package also provides functions for computing the feature importance of Support Vector Machines (SVMs) models, and display customizable kernel Principal Components Analysis (PCA) plots. For convenience, widespread performance measures and feature importance barplots are available for the user.

Installation

Installation and loading

Installing kerntools is easy. In the R console:

install.packages("kerntools")

Once the package is installed, it can be loaded anytime typing:

library(kerntools)

Dependencies

kerntools requires R (>= 2.10). Currently, it also relies on the following packages:

• dplyr
• ggplot2
• kernlab
• methods
• reshape2
• stringi

Usually, if some of these packages are missing in your library, they will be installed automatically when kerntools is installed.

A quick example: kernel PCA

Imagine that you want to perform a (kernel) PCA plot but your dataset consist of categorical variables. This can be done very easily with kerntools! First, you chose an appropriate kernel for your data (in this example, the Dirac kernel for categorical variables), and then you pass the output of the Dirac() function to the kPCA() function.

head(showdata)
#>   Favorite.color   Favorite.actress     Favorite.actor    Favorite.show
#> 1            red      Sophie Turner      Josh O'Connor        The crown
#> 2          black         Soo Ye-jin           Hyun Bin       Bridgerton
#> 3            red Lorraine Ashbourne       Henry Cavill       Bridgerton
#> 4           blue      Sophie Turner       Alvaro Morte La casa de papel
#> 5            red      Sophie Turner Michael K Williams         The wire
#> 6         yellow      Sophie Turner      Kit Harington  Game of Thrones
#>   Liked.new.show
#> 1            Yes
#> 2             No
#> 3            Yes
#> 4             No
#> 5            Yes
#> 6             No
KD <- Dirac(showdata[,1:4])
dirac_kpca <- kPCA(KD,plot=c(1,2),title="Survey", name_leg = "Liked the show?", 
                   y=showdata$Liked.new.show, ellipse=0.66)
dirac_kpca$plot

You can customize your kernel PCA plot: apart from picking which principal components you want to display (in the example: PC1 and PC2), you may want to add a title, or a legend, or use different colors to represent an additional variable of interest, so you can check patterns on your data. To see in detail how to customize a kPCA() plot, please refer to the documentation. The projection matrix is also returned (dirac_kpca$projection), so you may use it for further analyses and/or creating your own plot.

Main kerntools features

Right now, kerntools can deal effortlessly with the following kinds of data:

• Real vectors: Linear, RBF and Laplacian kernels.
• Real matrices: Frobenius kernel.
• Counts or frequencies (non-negative numbers): Bray-Curtis and Ruzicka (quantitative Jaccard) kernels.
• Compositional data (relative frequencies or proportions): Compositional-Linear and Aitchison kernels.
• Categorical data: Overlap / Dirac kernel.
• Sets: Intersect and Jaccard kernels.
• Ordinal data and rankings: Kendall’s tau kernel.
• Strings, sequences and short texts: Spectrum kernel.
• Bag-of-words (text documents, sometimes images): Chi-squared kernel.

Several tools for visualizing and comparing kernel matrices are provided.

Regarding kernel PCA, kerntools allows the user to:

• Compute a kernel PCA from any kernel matrix, be it computed with kerntools or provided by the user.
• Display customizable PCA plots
• (When possible) Compute and display the contribution of variables to each principal component.
• Compare two or more PCAs generated from the same set of samples using Co-inertia and Procrustes analysis.

When using some specific kernels, kerntools computes the importance of each variable or feature in a Support Vector Machine (SVM) model. kerntools does not train SVMs or other prediction models, but it can recover the feature importance of models fitted with other packages (for instance kernlab). These importances can be sorted and summarized in a customizable barplot.

Finally, the following performance measures for regression, binary and multi-class classification are implemented:

• Regression: Normalized Mean Squared Error
• Classification: accuracy, specificity, sensitivity, precision and F1 with (optional) confidence intervals, computed using normal approximation or bootstrapping.

Example data

kerntools contains a categorical toy dataset called showdata and a real-world count dataset called soil.

Documentation

Vignette

To see detailed and step-by-step examples that illustrate the main cases of use of kerntools, please have a look to the vignettes:

browseVignettes(kerntools)

The basic vignette covers the typical kerntools workflow. Thorough documentation about the kernel functions implemented in this package is in the “Kernel functions” vignette. If you want instead to know more about kernel PCA and Coinertia analysis, you can refer to the corresponding vignette too.

Additional help

Remember that detailed, argument-by-argument documentation is available for each function:

help(kPCA) ## or the specific name of the function
?kPCA

The documentation of the example datasets is available in an analogous way, typing:

help(showdata)
?showdata

More about kernels

To know more about kernel functions, matrices and methods, you can consult the following reference materials:

• Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (Vol. 4, No. 4, p. 738). Chapter 6, pp. 291-323. New York: springer.

• Müller, K. R., Mika, S., Tsuda, K., & Schölkopf, K. (2018) An introduction to kernel-based learning algorithms. In Handbook of neural network signal processing (pp. 4-1). CRC Press.

• Shawe-Taylor, J., & Cristianini, N. (2004). Kernel methods for pattern analysis. Cambridge university press.