Type: Package
Title: Linear Programming Discriminant Analysis
Version: 1.2.1
Description: Classification method obtained through linear programming. It is advantageous with respect to the classical developments when the distribution of the variables involved is unknown or when the number of variables is much greater than the number of individuals. Mathematical details behind the method are published in Nueda, et al. (2022) "LPDA: A new classification method based on linear programming". <doi:10.1371/journal.pone.0270403>.
Depends: R (≥ 3.5.0)
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
LazyData: true
Imports: Rglpk, multiway
Suggests: rmarkdown, knitr, testthat (≥ 3.0.0)
Config/testthat/edition: 3
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2025-07-16 08:48:22 UTC; USUARIO
Author: María José Nueda [aut, cre]
Maintainer: María José Nueda <mj.nueda@ua.es>
Repository: CRAN
Date/Publication: 2025-07-16 09:50:06 UTC

Principal Component Analysis

Description

Computes a Principal Component Analysis when p>n and when p<=n.

Usage

PCA(X)

Arguments

X

Matrix or data.frame with variables in columns and observations in rows.

Value

eigen

A eigen class object with eigenvalues and eigenvectors of the analysis.

var.exp

A matrix containing the explained variance for each component and the cumulative variance.

scores

Scores of the PCA analysis.

loadings

Loadings of the PCA analysis.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

Examples

## Simulate data matrix with 500 variables and 10 observations
datasim = matrix(sample(0:100, 5000, replace = TRUE), nrow = 10)
## PCA
myPCA = PCA(datasim)
## Extracting the variance explained by each principal component
myPCA$var.exp

Simulated RNA-Seq Time Series 3-dimensional dataset example

Description

A simulated RNA-Seq dataset example.

Usage

RNAseq

Format

An array data frame with 20 samples (1st dimension), 600 genes (2nd dimension) and 4 time-points (3rd dimension).

Details

This dataset is a RNA-Seq simulated example. It has been simulated as Negative Binomial distributed and transformed to rpkm (Reads per kilo base per million mapped reads). It contains gene expression from 600 genes measured to 60 samples through 4 time-points. First 10 samples are from first group and the remaining samples from the second one.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

Computing discriminating hyperplane for two groups

Description

This function computes a discriminating hyperplane for two groups with original data (calling lpda.fit) or with principal components (calling lpda.pca)

Usage

lpda(data, group, scale = FALSE, pca = FALSE, PC = 2, Variability = NULL,
                 f1 = NULL, f2 = NULL)
## S3 method for class 'lpda'
print(x, ...)

Arguments

data

Matrix containing data. Individuals in rows and variables in columns

group

Vector with the variable group

scale

Logical indicating if it is required standardize data. When pca=TRUE data is always scaled.

pca

Logical indicating if Principal Components Analysis is required

PC

Number of Principal Components (PC) for PCA. By default it is 2. When the number of PC is not decided, it can be determined choosing the desired proportion of explained variability (Variability parameter).

Variability

Parameter for Principal Components (PC) selection. This is the minimum desired proportion of variability explained for the PC of the variables. The analysis is always done with a minimum of 2 PCs. If it is NULL the PCA will be computed with PC parameter.

f1

Vector with weights for individuals of the first group. If NULL they are equally weighted.

f2

Vector with weights for individuals of the second group. If NULL they are equally weighted.

x

An object of class "lpda", a result of a call to lpda.

...

Other arguments passed.

Value

lpda returns an object of class "lpda".

coef

Hyperplane coefficients

data

Input data matrix

group

Input group vector

scale

Input scale argument

pca

Input pca argument

loadings

Principal Components loadings. Showed when pca = TRUE

scores

Principal Components scores. Showed when pca = TRUE

var.exp

A matrix containing the explained variance for each component and the cumulative variance. Showed when pca = TRUE

PCs

Number of Principal Components in the analysis. Showed when pca = TRUE

The functions predict and plot can be used to obtain the predicted classes and a plot in two dimensions with the distances to the computed hyperplane for the two classes.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

References

Nueda MJ, Gandía C, Molina MD (2022) LPDA: A new classification method based on linear programming. PLoS ONE 17(7): e0270403. <https://doi.org/10.1371/journal.pone.0270403>

See Also

lpda.pca, lpda.fit

Examples


######### palmdates example in lpda package:
data(palmdates)
group = as.factor( c(rep("Spanish",11),rep("Foreign",10)) )

# with concentration data:
model = lpda(data = palmdates$conc, group = group )
summary(model)
predict(model)
plot(model, main = "Palmdates example")

model.pca = lpda(data = palmdates$conc, group = group, pca=TRUE, PC = 2)
plot(model.pca, PCscores = TRUE, main = "Palmdates example")

# with spectra data
model.pca = lpda(data = palmdates$spectra, group = group, pca=TRUE, Variability = 0.9)
model.pca$PCs # 4 PCs to explain 90% of the variability
plot(model.pca, PCscores = TRUE, main = "Spectra palmdates")

Classification with lpda for 3way array data

Description

This function applies lpda methodology to classify individuals in two or more groups with original data (by applying lpda through the third dimension) or by applying lpda to the parafac scores.

Usage

lpda.3D(data, group, scale = FALSE,  pfac = FALSE, nfac = 2,
                     nstart = 10, seed=2, f1 = NULL, f2 = NULL)
## S3 method for class 'lpda.3D'
print(x, ...)

Arguments

data

Array containing data. Individuals in the first mode, variables in the second mode and third mode with time or similar.

group

Vector with the variable group.

scale

Logical indicating if it is required standardize data.

pfac

Logical indicating if Parafac Analysis is required

nfac

Number of factors for Parafac Analysis.

nstart

Number of random starts for multiway analysis.

seed

A single value to reproduce same results in multiway methods.

f1

Vector with weights for individuals of the first group. If NULL they are equally weighted.

f2

Vector with weights for individuals of the second group. If NULL they are equally weighted.

x

An object of class "lpda.3D", a result of a call to lpda.3D.

...

Other arguments passed.

Value

lpda.3D returns an object of class "lpda.3D".

MOD

When pfac=FALSE, MOD is a list of lpda objects obtained from the application of lpda to each slide matrix of the third node. When pfac=TRUE, MOD is a list of two elements: (1) mod.pfac the parafac model obtained with Multiway package and (2) the lpda object, obtained from the application of lpda to the parafac scores.

data

Input array data

group

Input group vector

pfac

Input pfac argument

The functions predict and plot can be used to obtain the predicted classes and a plot in two dimensions with the distances to the computed hyperplane for the two classes.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

References

Nueda MJ, Gandía C, Molina MD (2022) LPDA: A new classification method based on linear programming. PLoS ONE 17(7): e0270403. <https://doi.org/10.1371/journal.pone.0270403>

See Also

lpda, parafac

Examples


### RNAseq is a 3-dimensional array
  data(RNAseq)
  group = as.factor(rep(c("G1","G2"), each = 10))

## Strategy 1
  model3D = lpda.3D(RNAseq, group)
  summary(model3D)
  predict(model3D)
  plot(model3D, mfrow=c(2,2))

## Strategy 2: with parafac
  model3Ds2 = lpda.3D(RNAseq, group, pfac=TRUE, nfac=2)
  model3Ds2$MOD$mod.pfac$Rsq
  predict(model3Ds2)
  summary(model3Ds2)
  plot(model3Ds2, pfacscores=FALSE, main="Parafac Model", mfrow=c(1,1))
  plot(model3Ds2, pfacscores=TRUE, cex=1.5, main="Parafac components")
  legend("bottomright", levels(group), col=c(2,3), pch=20)

lpda.fit computes the discriminating hyperplane for two groups

Description

lpda.fit computes the discriminating hyperplane for two groups, giving as a result the coefficients of the hyperplane.

Usage

lpda.fit(data, group, f1 = NULL, f2 = NULL)

Arguments

data

Matrix containing data. Individuals in rows and variables in columns

group

Vector with the variable group

f1

Vector with weights for individuals of the first group

f2

Vector with weights for individuals of the second group

Value

coef

Hyperplane coefficients

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

References

Nueda MJ, Gandía C, Molina MD (2022) LPDA: A new classification method based on linear programming. PLoS ONE 17(7): e0270403. <https://doi.org/10.1371/journal.pone.0270403>

See Also

lpda

lpda.pca computes a PCA to the original data and selects the desired PCs when Variability is supplied

Description

lpda.pca computes the discriminating hyperplane for two groups with Principal Components (PC)

Usage

lpda.pca(data, group, PC = 2, Variability = NULL)

Arguments

data

Matrix containing data. Individuals in rows and variables in columns

group

Vector with the variable group

PC

Number of Principal Components (PC) for PCA. By default it is 2. When the number of PC is not decided, it can be determined choosing the desired proportion of explained variability (Variability parameter).

Variability

Parameter for Principal Components (PC) selection. This is the minimum desired proportion of variability explained for the PC of the variables. The analysis is always done with a minimum of 2 PCs. If it is NULL the PCA will be computed with PC parameter.

Value

loadings

Principal Components loadings.

scores

Principal Components scores.

var.exp

A matrix containing the explained variance for each component and the cumulative variance.

PCs

Number of Principal Components in the analysis.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

References

Nueda MJ, Gandía C, Molina MD (2022) LPDA: A new classification method based on linear programming. PLoS ONE 17(7): e0270403. <https://doi.org/10.1371/journal.pone.0270403>

See Also

lpda

Crossvalidation procedure for lpda evaluation

Description

lpdaCV evaluates the error rate classification with a crossvalidation procedure

Usage

lpdaCV(data, group, scale = FALSE, pca = FALSE, PC = 2, Variability = NULL,
                   CV = "ktest", ntest = 10, R = 10, f1 = NULL, f2 = NULL)
                   
## S3 method for class 'lpdaCV'
print(x, ...)

Arguments

data

Matrix containing data. Individuals in rows and variables in columns

group

Vector with the variable group

scale

Logical indicating if it is required standardize data.

pca

Logical indicating if a reduction of dimension is required

PC

Number of Principal Components (PC) for PCA. By default it is 2. When the number of PC is not decided, it can be determined choosing the desired proportion of explained variability (Variability parameter) or choosing the maximum number of errors allowed in the training set (Error.max).

Variability

Parameter for Principal Components (PC) selection. This is the desired proportion of variability explained for the PC of the variables.

CV

Crossvalidation mode: loo "leave one out" or ktest: that leaves k in the test set.

ntest

Number of samples to evaluate in the test-set.

R

Number of times that the error is evaluated.

f1

Vector with weights for individuals of the first group. If NULL they are equally weighted.

f2

Vector with weights for individuals of the second group. If NULL they are equally weighted.

x

An object of class "lpdaCV", a result of a call to lpdaCV or lpdaCV.3D.

...

Other arguments passed.

Value

lpdaCV returns the prediction error rate classification.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda

Examples


### RNAseq is a 3-dimensional array
  data(RNAseq)
  data = RNAseq[,,3]
  group = as.factor(rep(c("G1","G2"), each = 10))
  lpdaCV(data, group, pca = TRUE, CV = "ktest", ntest = 2)

Crossvalidation procedure for lpda3D evaluation

Description

lpdaCV.3D evaluates the error rate classification with a crossvalidation procedure

Usage


lpdaCV.3D(data, group, scale = FALSE, pfac = FALSE, nfac = 2, nstart = 10, seed=2,
                       CV = "ktest", ntest = 10, R = 10, f1 = NULL, f2 = NULL)

Arguments

data

Array containing data. Individuals in the first mode, variables in the second mode and third mode with time or similar.

group

Vector with the variable group.

scale

Logical indicating if it is required standardize data.

pfac

Logical indicating if Parafac Analysis is required

nfac

Number of factors for Parafac Analysis. By default it is 2.

nstart

Number of random starts for multiway analysis.

seed

A single value to reproduce same results in multiway methods. If NULL the start will be random.

CV

Crossvalidation mode: loo "leave one out" or ktest: that leaves k in the test set.

ntest

Number of samples to evaluate in the test-set.

R

Number of times that the error is evaluated.

f1

Vector with weights for individuals of the first group. If NULL they are equally weighted.

f2

Vector with weights for individuals of the second group. If NULL they are equally weighted.

Value

lpda.3D returns the prediction error rate classification.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda.3D, lpdaCV

Examples


### RNAseq is a 3-dimensional array
  
  data(RNAseq)
  group = as.factor(rep(c("G1","G2"), each = 10))
  lpdaCV.3D(RNAseq, group , CV = "ktest", R=5, ntest=5, pfac=TRUE, nfac=c(2,10))

Spectrometry and composition chemical of Spanish and Arabian palm dates

Description

A data set with scores of 21 dates on spectrometry and concentration measurements of the substances that better define the quality of the dates: fibre, sorbitol, fructose, glucose and myo-inositol. The first 11 dates are Spanish (from Elche, Alicante) and the last 10 are from other countries, mainly Arabian.

Usage

palmdates

Format

A data frame with 2 elements:

conc

a data frame with 5 columns: fibre, sorbitol, fructose, glucose and myo-inositol.

spectra

a data frame with 2050 columns.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

References

Abdrabo, S.S., Gras, L., Grindlay, G. and Mora, J. (2021) Evaluation of Fourier Transform-Raman Spectroscopy for palm dates characterization. Journal of food composition and analysis. Submitted.

Plot method for lpda classification

Description

plot.lpda is applied to an lpda class object. It shows a plot in two dimensions with the distances to the computed hyperplane of each individual coloring each case with the real class.

Usage

## S3 method for class 'lpda'
plot(x, PCscores = FALSE, main = NULL, xlab = NULL, ylab = NULL,
                    col= NULL, pch = NULL, lty = NULL,
                    legend.pos = "topright",...)

Arguments

x

Object of class inheriting from "lpda"

PCscores

Logical to show the first 2 PCscores. Only possible when PCA is applied.

main

An optional title for the plot.

xlab

An optional title for x-axis.

ylab

An optional title for y-axis.

col

An optional vector with colours for the groups.

pch

An integer specifying the symbol to be used in plotting points. When NULL, pch=20.

lty

The line type. If it is not specified, lty = 2 for the distances to the hiperplane and lty = 1 for PCs plot

legend.pos

The position for the legend. By default it is topright. NULL when no legend is required.

...

Other arguments passed.

Value

Two dimensional plot representing the distances to the computed hyperplane of each individual colored with the real class.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda

Plot method for lpda classification

Description

plot.lpda.3D is applied to an lpda.3D class object. It shows a plot in two dimensions with the distances to the computed hyperplane of each individual coloring each case with the real class.

Usage

## S3 method for class 'lpda.3D'
plot(x, pfacscores = FALSE, main = NULL,
legend.pos = "topright", ...)

Arguments

x

Object of class inheriting from "lpda"

pfacscores

Logical to show the first 2 parafac scores. Only possible when parafac is applied.

main

An optional title for the plot.

legend.pos

The position for the legend. By default it is topright. NULL when no legend is required.

...

Other arguments passed.

Value

Two dimensional plot representing the distances to the computed hyperplane of each individual colored with the real class.

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda.3D, plot.lpda

Predict method for lpda classification

Description

Predict method for lpda classification

Usage

## S3 method for class 'lpda'
predict(object, datatest = object$data,...)

## S3 method for class 'predict.lpda'
print(x, ...)

Arguments

object

Object of class inheriting from "lpda"

datatest

An optional data to predict their class. If omitted, the original data is used.

x

An object of class "predict.lpda", a result of a call to predict.lpda.

...

Other arguments passed.

Value

fitted

Predicted class

eval

Evaluation of each individual in the fitted model

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda

Predict method for lpda.3D classification

Description

Predict method for lpda.3D classification

Usage

## S3 method for class 'lpda.3D'
predict(object, datatest = NULL,...)

## S3 method for class 'predict.lpda.3D'
print(x, ...)

Arguments

object

Object of class inheriting from "lpda.3D"

datatest

An optional data to predict their class. If omitted, the original data is used.

x

An object of class "predict.lpda.3D", a result of a call to predict.lpda.3D.

...

Other arguments passed.

Value

fitted

Predicted class

eval

Evaluation of each individual in all the fitted models

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda

stand center and scale a data matrix

Description

stand center and scale a data matrix

Usage

stand(X)

Arguments

X

a data matrix with individuals in rows and variables in columns

Value

Scaled data matrix

stand2 center and scale a data matrix with the parameters of another one

Description

stand2 center and scale a data matrix with the parameters of another one

Usage

stand2(X, X2)

Arguments

X

the data matrix from which mean and standard deviation is computed

X2

the data matrix to center and scale

Value

Scaled X2 data matrix

Summarizing lpda classification

Description

summary method for class "lpda"

Usage

## S3 method for class 'lpda'
summary(object, datatest = object$data, grouptest=object$group,...)

## S3 method for class 'summary.lpda'
print(x, ...)

Arguments

object

Object of class inheriting from "lpda"

datatest

An optional data to predict their class and compare with real in the confusion matrix. If omitted, the original data is used.

grouptest

When datatest is specified, grouptest must also be specified and viceversa.

x

An object of class "summary.lpda", a result of a call to summary.lpda.

...

Other arguments passed.

Value

Confusion.Matrix

Table of confusion. Predicted classes in rows and real classes in columns, giving the hit (in the diagonal) and misclassification counts (out of the diagonal)

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda

Summarizing lpda.3D classification

Description

summary method for class "lpda.3D"

Usage

## S3 method for class 'lpda.3D'
summary(object, datatest = NULL, grouptest=NULL,...)

## S3 method for class 'summary.lpda.3D'
print(x, ...)

Arguments

object

Object of class inheriting from "lpda.3D"

datatest

An optional data to predict their class and compare with real in the confusion matrix. If omitted, the original data is used.

grouptest

When datatest is specified, grouptest must also be specified and viceversa.

x

An object of class "summary.lpda.3D", a result of a call to summary.lpda.3D.

...

Other arguments passed.

Value

Confusion.Matrix

Table of confusion. Predicted classes in rows and real classes in columns, giving the hit (in the diagonal) and misclassification counts (out of the diagonal)

Author(s)

Maria Jose Nueda, mj.nueda@ua.es

See Also

lpda.3D