Type:	Package
Title:	Kernel Functions and Tools for Machine Learning Applications
Version:	1.2.0
Description:	Kernel functions for diverse types of data (including, but not restricted to: nonnegative and real vectors, real matrices, categorical and ordinal variables, sets, strings), plus other utilities like kernel similarity, kernel Principal Components Analysis (PCA) and features' importance for Support Vector Machines (SVMs), which expand other 'R' packages like 'kernlab'.
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown, spelling, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Imports:	dplyr, ggplot2, kernlab, methods, reshape2, stats, stringi
VignetteBuilder:	knitr
Depends:	R (≥ 2.10)
Language:	en-US
URL:	https://github.com/elies-ramon/kerntools, https://elies-ramon.github.io/kerntools/
BugReports:	https://github.com/elies-ramon/kerntools/issues
NeedsCompilation:	no
Packaged:	2025-02-19 14:52:02 UTC; syko
Author:	Elies Ramon [aut, cre, cph]
Maintainer:	Elies Ramon <eramon@everlyrusher.com>
Repository:	CRAN
Date/Publication:	2025-02-19 15:10:02 UTC

kerntools: Kernel Functions and Tools for Machine Learning Applications

Description

Kernel functions for diverse types of data (including, but not restricted to: nonnegative and real vectors, real matrices, categorical and ordinal variables, sets, strings), plus other utilities like kernel similarity, kernel Principal Components Analysis (PCA) and features' importance for Support Vector Machines (SVMs), which expand other 'R' packages like 'kernlab'.

Author(s)

Maintainer: Elies Ramon eramon@everlyrusher.com (ORCID) [copyright holder]

See Also

Useful links:

• https://github.com/elies-ramon/kerntools

• https://elies-ramon.github.io/kerntools/

• Report bugs at https://github.com/elies-ramon/kerntools/issues

Accuracy

Description

'Acc()' computes the accuracy between the output of a classification model and the actual values of the target. It can also compute the weighted accuracy, which is useful in imbalanced classification problems. The weighting is applied according to the class frequencies in the target. In balanced problems, weighted Acc = Acc.

Usage

Acc(ct, weighted = FALSE)

Arguments

Value

Accuracy of the model (a single value).

Examples

y <- c(rep("a",3),rep("b",2))
y_pred <- c(rep("a",2),rep("b",3))
ct <- table(y,y_pred)
Acc(ct)
Acc(ct,weighted=TRUE)

Accuracy of a random model

Description

'Acc_rnd()' computes the expected accuracy of a random classifier based on the class frequencies of the target. This measure can be used as a benchmark when contrasted to the accuracy (in test) of a given prediction model.

Usage

Acc_rnd(target, freq = FALSE)

Arguments

Value

Expected accuracy of a random classification model (a single value).

Examples

# Expected accuracy of a random model:
target <- c(rep("a",5),rep("b",2))
Acc_rnd(target)
# This is the same than:
freqs <- c(5/7,2/7)
Acc_rnd(freqs,freq=TRUE)

Confidence Interval using Bootstrap

Description

'Boots_CI()' computes the Confidence Interval (CI) of a performance measure (for instance, accuracy) via bootstrapping.

Usage

Boots_CI(target, pred, index = "acc", nboots, confidence = 95, ...)

Arguments

Value

A vector containing the bootstrap estimate of the performance and its CI.

Examples

y <- c(rep("a",30),rep("b",20))
y_pred <- c(rep("a",20),rep("b",30))
# Computing Accuracy with their 95%CI
Boots_CI(target=y, pred=y_pred, index="acc", nboots=1000, confidence=95)

Kernels for count data

Description

Ruzicka and Bray-Curtis are kernel functions for absolute or relative frequencies and count data. Both kernels have as input a matrix or data.frame with dimension NxD and N>1, D>1, containing strictly non-negative real numbers. Samples should be in the rows. Thus, when working with relative frequencies, 'rowSums(X)' should be 1 (or 100, or another arbitrary number) for all rows (samples) of the dataset.

Usage

BrayCurtis(X)

Ruzicka(X)

Arguments

Details

For more info about these measures, please check Details in ?vegan::vegdist(). Note that, in the vegan help page, "Ruzicka" corresponds to "quantitative Jaccard". 'BrayCurtis(X)' gives the same result than '1-vegan::vegdist(X,method="bray")', and the same with 'Ruzicka(data)' and '1-vegan::vegdist(data,method="jaccard")'.

Value

Kernel matrix (dimension: NxN).

Examples

data <- soil$abund
Kruz <- Ruzicka(data)
Kbray <- BrayCurtis(data)
Kruz[1:5,1:5]
Kbray[1:5,1:5]

Chi-squared kernel

Description

'Chi2()' computes the basic \chi^2 kernel for bag-of-words (BoW) or bag-of-visual-words data. This kernel computes the similarity between two nonnegative vectors that represent the occurrence counts of words in two different documents.

Usage

Chi2(X, g = NULL)

Arguments

Value

Kernel matrix (dimension: NxN).

References

Zhang, Jianguo, et al. Local features and kernels for classification of texture and object categories: A comprehensive study. International journal of computer vision 73 (2007): 213-238. Link

Examples

## Example dataset: word counts in 4 documents
documents <- matrix( c(0, 1, 3, 2, 1, 0,  1, 1, 6,4,3,1,3,5,6,2), nrow=4,byrow=TRUE)
rownames(documents) <- paste0("doc",1:4)
colnames(documents) <- c("animal","life","tree","ecosystem")
documents
Chi2(documents,g=NULL)

Kernels for categorical variables

Description

From a matrix or data.frame with dimension NxD, where N>1, D>0, 'Dirac()' computes the simplest kernel for categorical data. Samples should be in the rows and features in the columns. When there is a single feature, 'Dirac()' returns 1 if the category (or class, or level) is the same in two given samples, and 0 otherwise. Instead, when D>1, the results for the D features are combined doing a sum, a mean, or a weighted mean.

Usage

Dirac(X, comp = "mean", coeff = NULL, feat_space = FALSE)

Arguments

Value

Kernel matrix (dimension: NxN), or a list with the kernel matrix and the feature space.

References

Belanche, L. A., and Villegas, M. A. (2013). Kernel functions for categorical variables with application to problems in the life sciences. Artificial Intelligence Research and Development (pp. 171-180). IOS Press. Link

Examples

# Categorical data
summary(CO2)
Kdirac <- Dirac(CO2[,1:3])
## Display a subset of the kernel matrix:
Kdirac[c(1,15,50,65),c(1,15,50,65)]

F1 score

Description

'F1()' computes the F1 score between the output of a classification prediction model and the actual values of the target.

Usage

F1(ct, multi.class = "macro")

Arguments

Details

F1 corresponds to the harmonic mean of Precision and Recall.

Value

F1 (a single value).

Examples

y <- c(rep("a",3),rep("b",2))
y_pred <- c(rep("a",2),rep("b",3))
ct <- table(y,y_pred)
F1(ct)

Frobenius kernel

Description

'Frobenius()' computes the Frobenius kernel between numeric matrices.

Usage

Frobenius(DATA, cos.norm = FALSE, feat_space = FALSE)

Arguments

Details

The Frobenius kernel is the same than the Frobenius inner product between matrices.

Value

Kernel matrix (dimension:NxN), or a list with the kernel matrix and the feature space.

Examples

data1 <- matrix(rnorm(250000),ncol=500,nrow=500)
data2 <- matrix(rnorm(250000),ncol=500,nrow=500)
data3 <- matrix(rnorm(250000),ncol=500,nrow=500)

Frobenius(list(data1,data2,data3))

Kernels for sets

Description

'Intersect()' or 'Jaccard()' compute the kernel functions of the same name, which are useful for set data. Their input is a matrix or data.frame with dimension NxD, where N>1, D>0. Samples should be in the rows and features in the columns. When there is a single feature, 'Jaccard()' returns 1 if the elements of the set are exactly the same in two given samples, and 0 if they are completely different (see Details). Instead, in the multivariate case (D>1), the results (for both 'Intersect()' and 'Jaccard()') of the D features are combined with a sum, a mean, or a weighted mean.

Usage

Jaccard(X, elements = LETTERS, comp = "sum", coeff = NULL)

Intersect(
  X,
  elements = LETTERS,
  comp = "sum",
  coeff = NULL,
  feat_space = FALSE
)

Arguments

Details

Let A,B be two sets. Then, the Intersect kernel is defined as:

K_{Intersect}(A,B)=|A \cap B|

And the Jaccard kernel is defined as:

K_{Jaccard}(A,B)=|A \cap B| / |A \cup B|

This specific implementation of the Intersect and Jaccard kernels expects that the set members (elements) are character symbols (length=1). In case the set data is multivariate (D>1 columns, and each one contains a set feature), elements for the D sets should come from the same domain (universe). For instance, a dataset with two variables, so the elements in the first one are colors c("green","black","white","red") and the second are names c("Anna","Elsa","Maria") is not allowed. In that case, set factors should be recoded to colors c("g","b","w","r") and names c("A","E","M") and, if necessary, 'Intersect()' (or 'Jaccard()') should be called twice.

Value

Kernel matrix (dimension: NxN), or a list with the kernel matrix and the feature space.

References

Bouchard, M., Jousselme, A. L., and Doré, P. E. (2013). A proof for the positive definiteness of the Jaccard index matrix. International Journal of Approximate Reasoning, 54(5), 615-626.

Ruiz, F., Angulo, C., and Agell, N. (2008). Intersection and Signed-Intersection Kernels for Intervals. Frontiers in Artificial Intelligence and Applications. 184. 262-270. doi: 10.3233/978-1-58603-925-7-262.

Examples

# Sets data
## Generating a dataset with sets containing uppercase letters
random_set <- function(x)paste(sort(sample(LETTERS,x,FALSE)),sep="",collapse = "")
max_setsize <- 4
setsdata <- matrix(replicate(20,random_set(sample(2:max_setsize,1))),nrow=4,ncol=5)

## Computing the Intersect kernel:
Intersect(setsdata,elements=LETTERS,comp="sum")

## Computing the Jaccard kernel weighting the variables:
coeffs <- c(0.1,0.15,0.15,0.4,0.20)
Jaccard(setsdata,elements=LETTERS,comp="weighted",coeff=coeffs)

Kernel-target alignment

Description

'KTA()' computes the alignment between a kernel matrix and a target variable.

Usage

KTA(K, y)

Arguments

Value

Alignment value.

Examples

K1 <- RBF(iris[1:100,1:4],g=0.1)
y <- factor(iris[1:100,5])
KTA(K1,y)

Kendall's tau kernel

Description

‘Kendall()' computes the Kendall’s tau, which happens to be a kernel function for ordinal variables, ranks or permutations.

Usage

Kendall(X, NA.as.0 = TRUE, samples.in.rows = FALSE, comp = "mean")

Arguments

Value

Kernel matrix (dimension: NxN).

References

Jiao, Y. and Vert, J.P. The Kendall and Mallows kernels for permutations. International Conference on Machine Learning. PMLR, 2015. Link

Examples

# 3 people are given a list of 10 colors. They rank them from most (1) to least
# (10) favorite
color_list <-  c("black","blue","green","grey","lightblue","orange","purple",
"red","white","yellow")
survey1 <- 1:10
survey2 <- 10:1
survey3 <- sample(10)
color <- cbind(survey1,survey2,survey3) # Samples in columns
rownames(color) <- color_list
Kendall(color)

# The same 3 people are asked the number of times they ate 5 different kinds of
# food during the last month:
food <- matrix(c(10, 1,18, 25,30, 7, 5,20, 5, 12, 7,20, 20, 3,22),ncol=5,nrow=3)
rownames(food) <- colnames(color)
colnames(food) <- c("spinach", "chicken", "beef" , "salad","lentils")
# (we can observe that, for person 2, vegetables << meat, while for person 3
# is the other way around)
Kendall(food,samples.in.rows=TRUE)

# We can combine this results:
dataset <- list(color=color,food=t(food)) #All samples in columns
Kendall(dataset)

Laplacian kernel

Description

'Laplace()' computes the laplacian kernel between all possible pairs of rows of a matrix or data.frame with dimension NxD.

Usage

Laplace(X, g = NULL)

Arguments

Details

Let x_i,x_j be two real vectors. Then, the laplacian kernel is defined as:

K_{Lapl}(x_i,x_j)=\exp(-\gamma \|x_i - x_j \|_1)

Value

Kernel matrix (dimension: NxN).

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
Laplace(dat,g=0.1)

Linear kernel

Description

'Linear()' computes the inner product between all possible pairs of rows of a matrix or data.frame with dimension NxD.

Usage

Linear(X, cos.norm = FALSE, coeff = NULL)

Arguments

Value

Kernel matrix (dimension: NxN).

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
Linear(dat)

Multiple Kernel (Matrices) Combination

Description

Combination of kernel matrices coming from different datasets / feature types into a single kernel matrix.

Usage

MKC(K, coeff = NULL)

Arguments

Value

A kernel matrix.

Examples

# For illustrating a possible use of this function, we work with a dataset
# that contains numeric and categorical features.

summary(mtcars)
cat_feat_idx <- which(colnames(mtcars) %in% c("vs", "am"))

# vs and am are categorical variables. We make a list, with the numeric features
# in the first element and the categorical features in the second:
DATA <- list(num=mtcars[,-cat_feat_idx], cat=mtcars[,cat_feat_idx])
# Our N, D and M dimensions are:
N <- nrow(mtcars); D <- ncol(mtcars); M <- length(DATA)

# Now we prepare a kernel matrix:
K <- array(dim=c(N,N,M))
K[,,1] <- Linear(DATA[[1]],cos.norm = TRUE) ## Kernel for numeric data
K[,,2] <- Dirac(DATA[[2]]) ## Kernel for categorical data

# Here, K1 has the same weight than K2 when computing the final kernel, although
# K1 has 9 variables and K2 has only 2.
Kconsensus <- MKC(K)
Kconsensus[1:5,1:5]

# If we want to weight equally each one of the 11 variables in the final
# kernel, K1 will weight 9/11 and K2 2/11.
coeff <- sapply(DATA,ncol)
coeff
Kweighted <- MKC(K,coeff=coeff)
Kweighted[1:5,1:5]

Confidence Interval using Normal Approximation

Description

'Normal_CI()' computes the Confidence Interval (CI) of a performance measure (for instance, accuracy) using normal approximation. Thus, it is advisable that the test has a size of, at least, 30 instances.

Usage

Normal_CI(value, ntest, confidence = 95)

Arguments

Value

A vector containing the CI.

Examples

# Computing accuracy
y <- c(rep("a",30),rep("b",20))
y_pred <- c(rep("a",20),rep("b",30))
ct <- table(y,y_pred)
accuracy <- Acc(ct)
# Computing 95%CI
Normal_CI(accuracy, ntest=length(y), confidence=95)

Precision or PPV

Description

'Prec()' computes the Precision of PPV (Positive Predictive Value) between the output of a classification model and the actual values of the target. The precision of each class can be aggregated. Macro-precision is the average of the precision of each classes. Micro-precision is the weighted average.

Usage

Prec(ct, multi.class = "macro")

Arguments

Value

PPV (a single value).

Examples

y <- c(rep("a",3),rep("b",2))
y_pred <- c(rep("a",2),rep("b",3))
ct <- table(y,y_pred)
Prec(ct)

Procrustes Analysis

Description

Procrustes Analysis compares two PCA/PCoA/MDS/other ordination methods' projections after "removing" the translation, scaling and rotation effects. Thus, they are compared in their configuration of "maximum similarity". Samples in the two projections should be related. The similarity of the projections X1 and X2 is quantified using a correlation-like statistic derived from the symmetric Procrustes sum of squared differences between X1 and X2.

Usage

Procrustes(X1, X2, plot = NULL, labels = NULL)

Arguments

Details

'Procrustes()' performs a Procrustes Analysis equivalent to 'vegan::procrustes(X,Y,scale=FALSE,symmetric=TRUE)'.

Value

A list containing:

* X1 (zero-centered and scaled).

* X2 superimposed over X1 (after translating, scaling and rotating X2).

* Procrustes correlation between X1 and X2.

* (optional) A 'ggplot2' plot.

Examples

data1 <- matrix(rnorm(900),ncol=30,nrow=30)
data2 <- matrix(rnorm(900),ncol=30,nrow=30)
pca1 <- kPCA(Linear(data1),center=TRUE)
pca2 <- kPCA(Linear(data2),center=TRUE)
procr <- Procrustes(pca1,pca2)
# Procrustean correlation between pca1 and pca2:
procr$pro.cor
# With plot (first two axes):
procr <- Procrustes(pca1,pca2,plot=1:2,labels=1:30)
procr$plot

Gaussian RBF (Radial Basis Function) kernel

Description

'RBF()' computes the RBF kernel between all possible pairs of rows of a matrix or data.frame with dimension NxD.

Usage

RBF(X, g = NULL)

Arguments

Details

Let x_i,x_j be two real vectors. Then, the RBF kernel is defined as:

K_{RBF}(x_i,x_j)=\exp(-\gamma \|x_i - x_j \|^2)

Sometimes the RBF kernel is given a hyperparameter called sigma. In that case: \gamma = 1/\sigma^2.

Value

Kernel matrix (dimension: NxN).

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
RBF(dat,g=0.1)

Recall or Sensitivity or TPR

Description

'Rec()' computes the Recall, also known as Sensitivity or TPR (True Positive Rate), between the output of a classification model and the actual values of the target.

Usage

Rec(ct, multi.class = "macro")

Arguments

Value

TPR (a single value).

Examples

y <- c(rep("a",3),rep("b",2))
y_pred <- c(rep("a",2),rep("b",3))
ct <- table(y,y_pred)
Rec(ct)

Specificity or TNR

Description

'Spe()' computes the Specificity or TNR (True Negative Rate) between the output of a classification prediction model and the actual values of the target.

Usage

Spe(ct, multi.class = "macro")

Arguments

Value

TNR (a single value).

Examples

y <- c(rep("a",3),rep("b",2))
y_pred <- c(rep("a",2),rep("b",3))
ct <- table(y,y_pred)
Spe(ct)

Spectrum kernel

Description

'Spectrum()' computes the basic Spectrum kernel between strings. This kernel computes the similarity of two strings by counting how many matching substrings of length l are present in each one.

Usage

Spectrum(
  x,
  alphabet,
  l = 1,
  group.ids = NULL,
  weights = NULL,
  feat_space = FALSE,
  cos.norm = FALSE
)

Arguments

Details

In large datasets this function may be slow. In that case, you may use the 'stringdot()' function of the 'kernlab' package, or the 'spectrumKernel()' function of the 'kebabs' package.

Value

Kernel matrix (dimension: NxN), or a list with the kernel matrix and the feature space.

References

Leslie, C., Eskin, E., and Noble, W.S. The spectrum kernel: a string kernel for SVM protein classification. Pac Symp Biocomput. 2002:564-75. PMID: 11928508. Link

Examples

## Examples of alphabets. _ stands for a blank space, a gap, or the
## start or the end of sequence)
NT <- c("A","C","G","T","_") # DNA nucleotides
AA <- c("A","C","D","E","F","G","H","I","K","L","M","N","P","Q","R","S","T",
"V","W","Y","_") ##canonical aminoacids
letters_ <- c(letters,"_")
## Example of data
strings <- c("hello_world","hello_word","hola_mon","kaixo_mundua",
"saluton_mondo","ola_mundo", "bonjour_le_monde")
names(strings) <- c("english1","english_typo","catalan","basque",
"esperanto","galician","french")
## Computing the kernel:
Spectrum(strings,alphabet=letters_,l=2)

Total Sum Scaling

Description

This function transforms a dataset from absolute to relative frequencies (by row or column).

Usage

TSS(X, rows = TRUE)

Arguments

Value

A relative frequency matrix or data.frame with the same dimension than X.

Examples

dat <- matrix(rnorm(50),ncol=5,nrow=10)
TSS(dat) #It can be checked that, after scaling, the sum of each row is equal to 1.

Aggregate importances

Description

'aggregate_imp()' sums the importances present in a matrix or data.frame according to some user-specified grouping criterion.

Usage

aggregate_imp(X, lev = NULL, samples = "rows")

Arguments

Value

X, a matrix or data.frame containing the aggregated importances.

Examples

importances <- matrix(rnorm(90),nrow=3,ncol=30)
rownames(importances) <- c("sample1","sample2","sample3")
colnames(importances) <- paste0("Feat",
rep(1:5,times=2*(1:5)), "_", unlist(lapply(2*(1:5),function(x)LETTERS[1:x])))

## The grouping criterion is:
groups <- paste0("Feat",1:5)
aggregate_imp(X=importances,samples="rows",lev=groups)
## We can also use the colnames:
colnames(importances)
aggregate_imp(X=importances,samples="rows")

Compositional kernels

Description

'cLinear()' is the compositional-linear kernel, which is useful for compositional data (relative frequencies or proportions). 'Aitchison()' is akin to the RBF kernel for this type of data. Thus, the expected input for both kernels is a matrix or data.frame containing strictly non-negative or (even better) positive numbers. This input has dimension NxD, with N>1 samples and D>1 compositional features.

Usage

cLinear(X, cos.norm = FALSE, feat_space = FALSE, zeros = "none")

Aitchison(X, g = NULL, zeros = "none")

Arguments

Details

In compositional data, samples (rows) sum to an arbitrary or irrelevant number. This is most clear when working with relative frequencies, as all samples add to 1 (or 100, or other uninformative value). Zeroes are a typical challenge when using compositional approaches. They introduce ambiguity because they can have multiple causes; a zero may signal a true absence, or a value so small that it is below the detection threshold of an instrument. A simple approach to deal with zeroes is replacing them by a pseudocount. More sophisticated approaches are reviewed elsewhere; see for instance the R package 'zCompositions'.

Value

Kernel matrix (dimension: NxN).

References

Ramon, E., Belanche-Muñoz, L. et al (2021). kernInt: A kernel framework for integrating supervised and unsupervised analyses in spatio-temporal metagenomic datasets. Frontiers in microbiology 12 (2021): 609048. doi: 10.3389/fmicb.2021.609048

Examples

data <- soil$abund

## This data is sparse and contains a lot of zeroes. We can replace them by pseudocounts:
Kclin <- cLinear(data,zeros="pseudo")
Kclin[1:5,1:5]

## With the feature space:
Kclin <- cLinear(data,zeros="pseudo",feat_space=TRUE)

## With cosine normalization:
Kcos <- cLinear(data,zeros="pseudo",cos.norm=TRUE)
Kcos[1:5,1:5]

## Aitchison kernel:
Kait <- Aitchison(data,g=0.0001,zeros="pseudo")
Kait[1:5,1:5]

Centering a kernel matrix

Description

It is equivalent to compute 'K' over centered data (i.e. the mean of each column is subtracted) in Feature Space.

Usage

centerK(K)

Arguments

Value

Centered 'K' (class "matrix").

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
K <- Linear(dat)
centerK(K)

Centering a squared matrix by row or column

Description

It centers a numeric matrix with dimension N x N by row (rows=TRUE) or column (rows=FALSE).

Usage

centerX(X, rows = TRUE)

Arguments

Value

Centered X (class "matrix").

Examples

dat <- matrix(rnorm(25),ncol=5,nrow=5)
centerX(dat)

Cosine normalization of a kernel matrix

Description

It is equivalent to compute K using the normalization 'X/sqrt(sum(X^2))' in Feature Space.

Usage

cosNorm(K)

Arguments

Value

Cosine-normalized K (class "matrix").

References

Ah-Pine, J. (2010). Normalized kernels as similarity indices. In Advances in Knowledge Discovery and Data Mining: 14th Pacific-Asia Conference, PAKDD 2010, Hyderabad, India, June 21-24, 2010. Proceedings. Part II 14 (pp. 362-373). Springer Berlin Heidelberg. Link

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
K <- Linear(dat)
cosNorm(K)

Cosine normalization of a matrix

Description

Normalizes a numeric matrix dividing each row (if rows=TRUE) or column (if rows=FALSE) by their L2 norm. Thus, each row (or column) has unit norm.

Usage

cosnormX(X, rows = TRUE)

Arguments

Value

Cosine-normalized X.

Examples

dat <- matrix(rnorm(50),ncol=5,nrow=10)
cosnormX(dat)

This function deletes those columns and/or rows in a matrix/data.frame that only contain 0s.

Description

This function deletes those columns and/or rows in a matrix/data.frame that only contain 0s.

Usage

desparsify(X, dim = 2)

Arguments

Value

X with less rows or columns. (Class: the same than X).

Examples

dat <- matrix(rnorm(150),ncol=50,nrow=30)
dat[c(2,6,12),] <- 0
dat[,c(30,40,50)] <- 0
dim(desparsify(dat))
dim(desparsify(dat,dim=c(1,2)))

Convert categorical data to dummies.

Description

Given a matrix or data.frame containing character/factors, this function performs one-hot-encoding.

Usage

dummy_data(X, lev = NULL)

Arguments

Value

X (class: "matrix") after performing one-hot-encoding.

Examples

summary(CO2)
CO2_dummy <- dummy_data(CO2[,1:3],lev=dummy_var(CO2[,1:3]))
CO2_dummy[1:10,1:5]

Levels per factor variable

Description

This function gives the categories ("levels") per categorical variable ("factor").

Usage

dummy_var(X)

Arguments

Value

A list with the levels.

Examples

summary(showdata)
dummy_var(showdata)

Gamma hyperparameter estimation (RBF kernel)

Description

This function returns an estimation of the optimum value for the gamma hyperparameter (required by the RBF kernel function) using different heuristics:

D criterion

It returns the inverse of the number of features in X.

Scale criterion

It returns the inverse of the number of features, normalized by the total variance of X.

Quantiles criterion

A range of values, computed with the function 'kernlab::sigest()'.

Usage

estimate_gamma(X)

Arguments

Value

A list with the gamma value estimation according to different criteria.

Examples

data <- matrix(rnorm(150),ncol=50,nrow=30)
gamma <- estimate_gamma(data)
gamma
K <- RBF(data, g = gamma$scale_criterion)
K[1:5,1:5]

Frobenius normalization

Description

This function computes the Frobenius normalization of a matrix.

Usage

frobNorm(X)

Arguments

Value

Frobenius-normalized X (class: "matrix").

Examples

dat <- matrix(rnorm(50),ncol=5,nrow=10)
frobNorm(dat)

Kernel matrix heatmap

Description

'heatK()' plots the heatmap of a kernel matrix.

Usage

heatK(
  K,
  cos.norm = FALSE,
  title = NULL,
  color = c("red", "yellow"),
  name_leg = NULL,
  raster = FALSE
)

Arguments

Value

A 'ggplot2' heatmap.

Examples

data <- matrix(rnorm(150),ncol=50,nrow=30)
K <- Linear(data)
heatK(K)

Kernel matrix histogram

Description

'histK()' plots the histogram of a kernel matrix.

Usage

histK(K, main = "Histogram of K", vn = FALSE, ...)

Arguments

Details

Information about the von Neumann entropy can be found at '?vonNeumann()'.

Value

An object of class "histogram".

Examples

data <- matrix(rnorm(150),ncol=50,nrow=30)
K <- RBF(data,g=0.01)
histK(K)

Kernel PCA

Description

'kPCA()' computes the kernel PCA from a kernel matrix and, if desired, produces a plot. The contribution of the original variables to the Principal Components (PCs), sometimes referred as "loadings", is NOT returned (to do so, go to 'kPCA_imp()').

Usage

kPCA(
  K,
  center = TRUE,
  Ktest = NULL,
  plot = NULL,
  y = NULL,
  colors = "black",
  na_col = "grey70",
  title = "Kernel PCA",
  pos_leg = "right",
  name_leg = "",
  labels = NULL,
  ellipse = NULL
)

Arguments

Details

As the ordinary PCA, kernel PCA can be used to summarize, visualize and/or create new features of a dataset. Data can be projected in a linear or nonlinear way, depending on the kernel used. When the kernel is 'Linear()', kernel PCA is equivalent to ordinary PCA.

Value

A list with two objects:

* The PCA projection (class "matrix"). Please note that if K was computed from a NxD table with N > D, only the first N-D PCs may be useful.

* (optional) A 'ggplot2' plot of the selected PCs.

Examples

dat <- matrix(rnorm(150),ncol=50,nrow=30)
K <- Linear(dat)

## Projection's coordinates only:
pca <- kPCA(K)

## Coordinates + plot of the two first principal components (PC1 and PC2):
pca <- kPCA(K,plot=1:2, colors = "coral2")
pca$plot

Plot the original variables' contribution to a PCA plot

Description

'kPCA_arrows()' draws arrows on a (kernel) PCA plot to represent the contribution of the original variables to the two displayed Principal Components (PCs).

Usage

kPCA_arrows(plot, contributions, colour = "steelblue", size = 4, ...)

Arguments

Details

It is important to note that the arrows are scaled to match the samples' projection plot. Thus, arrows' directions are correct, but do not expect that their magnitudes match the output of 'kPCA_imp()' or other functions('prcomp', 'princomp...'). (Nevertheless, they should at least be proportional to the real magnitudes.)

Value

The PCA plot with the arrows ('ggplot2' object).

Examples

dat <- matrix(rnorm(500),ncol=10,nrow=50)
K <- Linear(dat)

## Computing the kernel PCA. The plot represents PC1 and PC2:
kpca <- kPCA(K,plot=1:2)

## Computing the contributions to all the PCS:
pcs <- kPCA_imp(dat,secure=FALSE)

## We will draw the arrows for PC1 and PC2.
contributions <- t(pcs$loadings[1:2,])
rownames(contributions) <- 1:10
kPCA_arrows(plot=kpca$plot,contributions=contributions)

Contributions of the variables to the Principal Components ("loadings")

Description

'kPCA_imp()' performs a PCA and a kernel PCA simultaneously and returns the contributions of the variables to the Principal Components (sometimes, these contributions are called "loadings") in Feature Space. Optionally, it can also return the samples' projection (cropped to the relevant PCs) and the values used to centering the variables in Feature Space. It does not return any plot, nor it projects test data. To do so, please use 'kPCA()'.

Usage

kPCA_imp(DATA, center = TRUE, projected = NULL, secure = FALSE)

Arguments

Details

This function may be not valid for all kernels. Do not use it with the RBF, Laplacian, Bray-Curtis, Jaccard/Ruzicka, or Kendall's tau kernels unless you know exactly what you are doing.

Value

A list with three objects:

* The PCA projection (class "matrix") using only the relevant Principal Components.

* The loadings.

* The values used to center each variable in Feature Space.

Examples

dat <- matrix(rnorm(150),ncol=30,nrow=50)
contributions <- kPCA_imp(dat)
contributions$loadings[c("PC1","PC2"),1:5]

Minmax normalization

Description

Minmax normalization. Custom min/max values may be passed to the function.

Usage

minmax(X, rows = FALSE, values = NULL)

Arguments

Value

Minmax-normalized X.

Examples

dat <- matrix(rnorm(100),ncol=10,nrow=10)
dat_minmax <- minmax(dat)
apply(dat_minmax,2,min) ## Min values = 0
apply(dat_minmax,2,max) ## Max values = 1
# We can also explicitly state the max and min values:
values <- list(min=apply(dat,2,min),max=apply(dat,2,max))
dat_minmax <- minmax(dat,values=values)

NMSE (Normalized Mean Squared Error)

Description

'nmse()' computes the Normalized Mean Squared Error between the output of a regression model and the actual values of the target.

Usage

nmse(target, pred)

Arguments

Details

The Normalized Mean Squared error is defined as:

NMSE=MSE/((N-1)*var(target))

where MSE is the Mean Squared Error.

Value

The normalized mean squared error (a single value).

Examples

y <- 1:10
y_pred <- y+rnorm(10)
nmse(y,y_pred)

Importance barplot

Description

'plotImp()' displays the barplot of a numeric vector, which is assumed to contain the features importance (from a prediction model) or the contribution of each original variable to a Principal Component (PCA). In the barplot, features/PCs are sorted by decreasing importance.

Usage

plotImp(
  x,
  y = NULL,
  relative = TRUE,
  absolute = TRUE,
  nfeat = NULL,
  names = NULL,
  main = NULL,
  xlim = NULL,
  color = "grey",
  leftmargin = NULL,
  ylegend = NULL,
  leg_pos = "right",
  ...
)

Arguments

Value

A list containing:

* The vector of importances in decreasing order. When 'nfeat' is not NULL, only the top 'nfeat' are returned.

* The cumulative sum of (absolute) importances.

* A numeric vector giving the coordinates of all the drawn bars' midpoints.

Examples

importances <- rnorm(30)
names_imp <- paste0("Feat",1:length(importances))

plot1 <- plotImp(x=importances,names=names_imp,main="Barplot")
plot2 <- plotImp(x=importances,names=names_imp,relative=FALSE,
main="Barplot",nfeat=10)
plot3 <- plotImp(x=importances,names=names_imp,absolute=FALSE,
main="Barplot",color="coral2")

Showdata

Description

A toy dataset that contains the results of a (fictional) survey commissioned from a well-known streaming platform. The platform invited 100 people to watch footage of their new show before the premiere. After that, the participants were asked to pick their favorite color, actress, actors and shows from a list. Finally, they were asked to disclose if they liked the new show.

Usage

showdata

Format

A data.frame with 100 rows and 5 factor variables:

Favorite.color

Favorite color

Favorite.actress

Favorite actress

Favorite.actor

Favorite actor

Favorite.show

Favorite show

Liked.new.show

Do you like the new show?

Source

Own

Kernel matrix similarity

Description

'simK()' computes the similarity between kernel matrices.

Usage

simK(Klist)

Arguments

Details

It is a wrapper of 'Frobenius()'.

Value

Kernel matrix (dimension: MxM).

Examples

K1 <- Linear(matrix(rnorm(7500),ncol=150,nrow=50))
K2 <- Linear(matrix(rnorm(7500),ncol=150,nrow=50))
K3 <- Linear(matrix(rnorm(7500),ncol=150,nrow=50))

simK(list(K1,K2,K3))

Soil microbiota (raw counts)

Description

Bacterial abundances in 89 soils from across North and South America.

Usage

soil

Format

A list containing the following elements:

abund

Bacterial abundances of 7396 taxa in 88 sites.

metadata

Samples' metadata

taxonomy

Taxonomic information

References

Lauber CL, Hamady M, Knight R, Fierer N. Pyrosequencing-based assessment of soil pH as a predictor of soil bacterial community structure at the continental scale. Appl Environ Microbiol. 2009 Aug;75(15):5111-20. doi: 10.1128/AEM.00335-09.

SVM feature importance

Description

Recovering the features importances from a SVM model.

Usage

svm_imp(
  X,
  svindx,
  coeff,
  result = "absolute",
  cos.norm = FALSE,
  center = FALSE,
  scale = FALSE
)

Arguments

Details

This function may be not valid for all kernels. Do not use it with the RBF, Laplacian, Bray-Curtis, Jaccard/Ruzicka, or Kendall's tau kernels unless you know exactly what you are doing.

Usually the sign of the importances is irrelevant, thus justifying working with the absolute or squared values; see for instance Guyon et al. (2002). Some classification tasks are an exception to this, when it can be demonstrated that the feature space is strictly nonnegative. In that case, a positive importance implies that a feature contributes to the "positive" class, and the same with a negative importance and the "negative" class.

Value

The importance of each feature (a vector).

References

Guyon, I., Weston, J., Barnhill, S., and Vapnik, V. (2002) Gene selection for cancer classification using support vector machines. Machine learning, 46, 389-422. Link

Examples

data1 <- iris[1:100,]
sv_index <- c( 24, 42, 58, 99)
coefficients <- c(-0.2670988, -0.3582848,  0.2129282,  0.4124554)
# This SV and coefficients were obtained from a model generated with kernlab:
# model <- kernlab::ksvm(Species ~ .,data=data1, kernel="vanilladot",scaled = TRUE)
# sv_index <- unlist(kernlab::alphaindex(model))
# coefficients <- kernlab::unlist(coef(model))
# Now we compute the importances:
svm_imp(X=data1[,-5],svindx=sv_index,coeff=coefficients,center=TRUE,scale=TRUE)

Von Neumann entropy

Description

'vonNeumann()' computes the von Neumann entropy of a kernel matrix. Entropy values close to 0 indicate that all its elements are very similar, which may result in underfitting when training a prediction model. Instead, values close to 1 indicate a high variability which may produce overfitting.

Usage

vonNeumann(K)

Arguments

Value

Von Neumann entropy (a single value).

References

Belanche-Muñoz, L.A. and Wiejacha, M. (2023) Analysis of Kernel Matrices via the von Neumann Entropy and Its Relation to RVM Performances. Entropy, 25, 154. doi:10.3390/e25010154. Link

Examples

data <- matrix(rnorm(150),ncol=50,nrow=30)
K <- Linear(data)
vonNeumann(K)