Package of Generalized Network-based Dimensionality Reduction and Analyses

Description

The package of Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona, Zahid Khan

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyan, Z. T., Kurbucz, M. T., & Katona, A. I. (2022). Network-based dimensionality reduction of high-dimensional, low-sample-size datasets. Knowledge-Based Systems, 109180.

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

ndr, ndrlm, plot, biplot, summary, dCor.

Covid'19 case datesets of countries (2020), where the data frame has 138 observations of 18 variables.

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Covid'19 of countries (2020), where the data frame has 138 observations of 18 variables.

Usage

data("COVID19_2020")

Format

A data frame with 138 observations 18 variables.

Source

Kurbucz, M. T. (2020). A joint dataset of official COVID-19 reports and the governance, trade and competitiveness indicators of World Bank group platforms. Data in brief, 31, 105881.

Examples

data(COVID19_2020)

CWTS Leiden's University Ranking 2020 for all scientific fields, within the period of 2016-2019. 1176 observations (i.e., universities), and 42 variables (i.e., indicators).

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

CWTS Leiden's 2020 dataset, where the data frame has 1176 observations of 42 variables.

Usage

data("CWTS_2020")

Format

A data frame with 1176 observations of 42 variables.

Source

CWTS Leiden Ranking 2020: https://www.leidenranking.com/ranking/2020/list

Examples

data(CWTS_2020)

Crimes in USA cities in 1990. Independent variables (X)

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Crimes in USA cities in 1990. Independent variables (X)

Usage

data("CrimesUSA1990.X")

Format

A data frame with 1994 observations 123 variables.

Source

UCI - Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/communities+and+crime

Examples

data(CrimesUSA1990.X)

Crimes in USA cities in 1990. Dependent variable (Y)

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Crimes in USA cities in 1990. Dependent variable (Y)

Usage

data("CrimesUSA1990.Y")

Format

A data frame with 1994 observations 1 variables.

Source

UCI - Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/communities+and+crime

Examples

data(CrimesUSA1990.Y)

Governmental and economic data of countries (2020), where the data frame has 138 observations of 2161 variables.

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Governmental and economic data of countries (2020), where the data frame has 138 observations of 2161 variables.

Usage

data("GOVDB2020")

Format

A data frame with 138 observations of 2161 variables.

Source

Kurbucz, M. T. (2020). A joint dataset of official COVID-19 reports and the governance, trade and competitiveness indicators of World Bank group platforms. Data in brief, 31, 105881.

Examples

data(GOVDB2020)

NUTS2 regional development data (2020) of I4.0 readiness, where the data frame has 414 observations of 101 variables.

Description

Sample datasets for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

NUTS2 regional development data (2020), where the data frame has 414 observations of 101 variables.

Usage

data("COVID19_2020")

Format

A data frame with 414 observations of 101 variables.

Source

Honti, G., Czvetkó, T., & Abonyi, J. (2020). Data describing the regional Industry 4.0 readiness index. Data in Brief, 33, 106464.

Examples

data(I40_2020)

Biplot function for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

Biplot function for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Usage

## S3 method for class 'nda'
biplot(x, main=NULL,...)

Arguments

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

plot, summary, ndr, data_gen.

Examples

# Biplot function without feature selection

# Generate 200 x 50 random block matrix with 3 blocks and lambda=0 parameter

df<-data_gen(200,50,3,0)
p<-ndr(df)
biplot(p)

Calculating distance correlation of two vectors or columns of a matrix

Description

Calculating distance correlation of two vectors or columns of a matrix for Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

The calculation is very slow for large matrices!

Usage

dCor(x,y=NULL)

Arguments

Details

If x is a numeric vector, y must be specified. If x is a numeric matrix or numeric data frame, y will be neglected.

Value

Either a distance correlation coefficient of vectors x and y, or a distance correlation matrix of x if x is a matrix or a dataframe.

Author(s)

Prof. Zsolt T. Kosztyan, Department of Quantitative Methods, Institute of Management, Faculty of Business and Economics, University of Pannonia, Hungary

e-mail: kosztyan.zsolt@gtk.uni-pannon.hu

References

Rizzo M, Szekely G (2021). _energy: E-Statistics: Multivariate Inference via the Energy of Data_. R package version 1.7-8, <URL: https://CRAN.R-project.org/package=energy>.

Examples

# Specification of distance correlation value of vectors x and y.
x<-rnorm(36)
y<-rnorm(36)
dCor(x,y)
# Specification of distance correlaction matrix.
x<-matrix(rnorm(36),nrow=6)
dCor(x)

Calculating distance covariance of two vectors or columns of a matrix

Description

Calculating distance covariance of two vectors or columns of a matrix for Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

The calculation is very slow for large matrices!

Usage

dCov(x,y=NULL)

Arguments

Details

If x is a numeric vector, y must be specified. If x is a numeric matrix or numeric data frame, y will be neglected.

Value

Either a distance covariance value of vectors x and y, or a distance covariance matrix of x if x is a matrix or a dataframe.

Author(s)

Prof. Zsolt T. Kosztyan, Department of Quantitative Methods, Institute of Management, Faculty of Business and Economics, University of Pannonia, Hungary

e-mail: kosztyan.zsolt@gtk.uni-pannon.hu

References

Rizzo M, Szekely G (2021). _energy: E-Statistics: Multivariate Inference via the Energy of Data_. R package version 1.7-8, <URL: https://CRAN.R-project.org/package=energy>.

Examples

# Specification of distance covariance value of vectors x and y.
x<-rnorm(36)
y<-rnorm(36)
dCov(x,y)
# Specification of distance covariance matrix.
x<-matrix(rnorm(36),nrow=6)
dCov(x)

Generate random block matrix for GNDA

Description

Generate random block matrix for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Usage

data_gen(n,m,nfactors=2,lambda=1)

Arguments

Details

n, m, nfactors must beintegers, and they are not less than 1; lambda should be a positive real number.

Value

Author(s)

Prof. Zsolt T. Kosztyan, Department of Quantitative Methods, Institute of Management, Faculty of Business and Economics, University of Pannonia, Hungary

e-mail: kzst@gtk.uni-pannon.hu

Examples

# Specification 30 by 10 random block matrices with 2 blocks/factors
df<-data_gen(30,10)
library(psych)
scree(df)
biplot(ndr(df))
# Specification 40 by 20 random block matrices with 3 blocks/factors
df<-data_gen(40,20,3)
library(psych)
scree(df)
biplot(ndr(df))
plot(ndr(df))

# Specification 50 by 20 random block matrices with 4 blocks/factors
# lambda=0.1
df<-data_gen(50,15,4,0.1)
scree(df)
biplot(ndr(df))
plot(ndr(df))

Calculation of fitted values of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Description

Calculation of fitted values of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Usage

## S3 method for class 'ndrlm'
fitted(object, ...)

Arguments

Value

Fitted values (data frame)

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

plot, print, ndrlm.

Examples

# Example of fitted function of NDRLM without optimization of fittings

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)

fitted(NDRLM)

Feature selection for KMO

Description

Drop variables if their MSA_i valus is lower than a threshold, in order to increase the overall KMO (MSA) value.

Usage

fs.KMO(data,min_MSA=0.5,cor.mtx=FALSE)

Arguments

Details

Low Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy does not suggest using principal component or factor analysis. Therefore, this function drop variables with low KMO/MSA values.

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Abonyi, J., Czvetkó, T., Kosztyán, Z. T., & Héberger, K. (2022). Factor analysis, sparse PCA, and Sum of Ranking Differences-based improvements of the Promethee-GAIA multicriteria decision support technique. Plos one, 17(2), e0264277. doi:10.1371/journal.pone.0264277

See Also

summary.

Examples

library(psych)
data(I40_2020)
data<-I40_2020
KMO(fs.KMO(data,min_MSA=0.7,cor.mtx=FALSE))

Feature selection for PCA, FA, and (G)NDA

Description

This function drops variables that have low communality values and/or are common indicators (i.e., correlates more than one latent variables).

Usage

fs.dimred(fn,DF,min_comm=0.25,com_comm=0.25)

Arguments

Details

This function only works with principal, and fa, and ndr functions.

This function drops each variable that has a low communality value (under min_comm value). In other words, that variable does not fit enough of any latent variable.

This function also drops so-called common indicators, which correlate highly with more than one latent variable. And the difference in the correlation is either lower than the com_comm value or the greatest absolute factor loading value is not twice greater than the second greatest factor loading.

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Abonyi, J., Czvetkó, T., Kosztyán, Z. T., & Héberger, K. (2022). Factor analysis, sparse PCA, and Sum of Ranking Differences-based improvements of the Promethee-GAIA multicriteria decision support technique. Plos one, 17(2), e0264277. doi:10.1371/journal.pone.0264277

See Also

psych::principal, psych::fa, ndr.

Examples

data<-I40_2020

library(psych)

# Principal Component Analysis (PCA)

pca<-principal(data,nfactors=2,covar=TRUE)
pca

# Feature selection with default values

PCA<-fs.dimred(pca,data)
PCA

# List of dropped, low communality value indicators
print(colnames(PCA$dropped_low))

# List of dropped, common communality value indicators
print(colnames(PCA$dropped_com))

# List of retained indicators
print(colnames(PCA$retained_DF))

## Not run: 
# Principal Component Analysis (PCA) of correlation matrix

pca<-principal(cor(data,method="spearman"),nfactors=2,covar=TRUE)
pca

# Feature selection
min_comm<-0.25 # Minimal communality value
com_comm<-0.20 # Minimal common communality value

PCA<-fs.dimred(pca,cor(data,method="spearman"),min_comm,com_comm)
PCA

## End(Not run)

Genearlized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

The main function of Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

Usage

ndr(r,covar=FALSE,cor_method=1,cor_type=1,min_R=0,min_comm=2,Gamma=1,null_model_type=4,
mod_mode=6,min_evalue=0,min_communality=0,com_communalities=0,use_rotation=FALSE,
rotation="oblimin",weight=NULL,seed=NULL)

Arguments

Details

NDA both works on low and high simple size datasets. If min_evalue=min_communality=com_communalities=0 than there is no feature selection.

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyan, Z. T., Kurbucz, M. T., & Katona, A. I. (2022). Network-based dimensionality reduction of high-dimensional, low-sample-size datasets. Knowledge-Based Systems, 109180. doi:10.1016/j.knosys.2022.109180

See Also

plot, biplot, summary.

Examples

# Dimension reduction without using any hyperparameters

data(swiss)
df<-swiss
p<-ndr(df)
summary(p)
plot(p)
biplot(p)

# Dimension reduction with using hyperparameters
# min_R=0.1 # The mininal square correlation must be grater than 0.1

p<-ndr(df,min_R = 0.1)
summary(p)
plot(p)

# min_evalue=0.1 # Minimal evector centalities must be greater than 0.1

p<-ndr(df,min_evalue = 0.1)
summary(p)
plot(p)

# minimal and common communality value must be greater than 0.25

p<-ndr(df,min_communality = 0.25,
 com_communalities = 0.25)

# Print factor matrix
cor(p$scores)
plot(p)

# Use factor rotation

p<-ndr(df,min_communality = 0.25,
 com_communalities = 0.25,use_rotation=TRUE)

# Print factor matrix
cor(p$scores)
biplot(p)

# Data reduction - clustering
# Distance is Euclidean's distance
# covar=TRUE means only the distance matrix is considered.

q<-ndr(1-normalize(as.matrix(dist(df))),covar=TRUE)
summary(q)
plot(q)

Genearlized Network-based Dimensionality Reduction and Regression (GNDR)

Description

The main function of Generalized Network-based Dimensionality Reduction and Regression (GNDR) for supervised learning.

Usage

ndrlm(Y,X,latents="in",dircon=FALSE,optimize=TRUE,
                target="adj.r.square",rel_weight=FALSE,
                cor_method=1,
                cor_type=1,min_comm=2,Gamma=1,
                null_model_type=4,mod_mode=1,use_rotation=FALSE,
                rotation="oblimin",pareto=FALSE,fit_weights=NULL,
                lower.bounds.x = c(rep(-100,ncol(X))),
                upper.bounds.x = c(rep(100,ncol(X))),
                lower.bounds.latentx = c(0,0,0,0),
                upper.bounds.latentx = c(0.6,0.6,0.6,0.3),
                lower.bounds.y = c(rep(-100,ncol(Y))),
                upper.bounds.y = c(rep(100,ncol(Y))),
                lower.bounds.latenty = c(0,0,0,0),
                upper.bounds.latenty = c(0.6,0.6,0.6,0.3),
                popsize = 20, generations = 30, cprob = 0.7, cdist = 5,
                mprob = 0.2, mdist=10, seed=NULL)

Arguments

Details

NDRLM is a variable fitting with feature selection based on the tunes of GNDA method with NSGA-II algorithm for parameter fittings.

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyan, Z. T., Kurbucz, M. T., & Katona, A. I. (2022). Network-based dimensionality reduction of high-dimensional, low-sample-size datasets. Knowledge-Based Systems, 109180. doi:10.1016/j.knosys.2022.109180

See Also

ndr, plot, summary, mco::nsga2.

Examples

# Using NDRLM without fitting optimization
X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)
summary(NDRLM)
plot(NDRLM)

## Not run: 
# Using NDRLM with optimized fitting

NDRLM<-ndrlm(Y,X)
summary(NDRLM)

# Using Leiden's modularity for grouping variables

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,mod_mode=6)
plot(NDRLM)

# Using relative weights

NDRLM<-ndrlm(Y,X,mod_mode=6,rel_weight=TRUE)
plot(NDRLM)

# Using Spearman's correlation

NDRLM<-ndrlm(Y,X,cor_method=2)
summary(NDRLM)

# Using greater population and generations

NDRLM<-ndrlm(Y,X,popsize=52,generations=40)
summary(NDRLM)

# No latent variables
NDRLM<-ndrlm(Y,X,latents="none")
plot(NDRLM)

# In-out model
library(lavaan)
df<-PoliticalDemocracy # Data of Political Democracy

dem<-PoliticalDemocracy[,c(1:8)]
ind60<-PoliticalDemocracy[,-c(1:8)]

NBSEM<-ndrlm(dem,ind60,latents = "both",seed = 2)
plot(NBSEM)

## End(Not run)

Min-max normalization

Description

Min-max normalization for data matrices and data frames

Usage

normalize(x,type="all")

Arguments

Value

Returns a normalized data.frame/matrix.

Author(s)

Zsolt T. Kosztyan, University of Pannonia

e-mail: kosztyan.zsolt@gtk.uni-pannon.hu

Examples

  mtx<-matrix(rnorm(20),5,4)
  n_mtx<-normalize(mtx) # Fully normalized matrix
  r_mtx<-normalize(mtx,type="row") # Normalize row by row
  c_mtx<-normalize(mtx,type="col") # Normalize col by col
  print(n_mtx) # Print fully normalized matrix

Calculating partial distance correlation of columns of a matrix

Description

Calculating partial distance correlation of two columns of a matrix for Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

The calculation is very slow for large matrices!

Usage

pdCor(x)

Arguments

Value

Partial distance correlation matrix of x.

Author(s)

Prof. Zsolt T. Kosztyan, Department of Quantitative Methods, Institute of Management, Faculty of Business and Economics, University of Pannonia, Hungary

e-mail: kosztyan.zsolt@gtk.uni-pannon.hu

References

Rizzo M, Szekely G (2021). _energy: E-Statistics: Multivariate Inference via the Energy of Data_. R package version 1.7-8, <URL: https://CRAN.R-project.org/package=energy>.

Examples

# Specification of partial distance correlaction matrix.
x<-matrix(rnorm(36),nrow=6)
pdCor(x)

Plot function for Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

Plot variable network graph

Usage

## S3 method for class 'nda'
plot(x, cuts=0.3, interactive=TRUE,edgescale=1.0,labeldist=-1.5,show_weights=FALSE,...)

Arguments

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

biplot, summary, ndr.

Examples

# Plot function with feature selection

data("CrimesUSA1990.X")
df<-CrimesUSA1990.X
p<-ndr(df)
biplot(p,main="Biplot of CrimesUSA1990 without feature selection")

# Plot function with feature selection
# minimal eigen values (min_evalue) is 0.0065
# minimal communality value (min_communality) is 0.1
# minimal common communality value (com_communalities) is 0.1

p<-ndr(df,min_evalue = 0.0065,min_communality = 0.1,com_communalities = 0.1)

# Plot with default (cuts=0.3)
plot(p)

# Plot with higher cuts
plot(p,cuts=0.6)

# GNDA is used for clustering, where the similarity function is the 1-Euclidean distance
# Data is the swiss data

SIM<-1-normalize(as.matrix(dist(swiss)))
q<-ndr(SIM,covar = TRUE)
plot(q,interactive = FALSE)

Plot function for Generalized Network-based Dimensionality Reduction and Regression (GNDR)

Description

Plot the structural equation model, based on the GNDR

Usage

## S3 method for class 'ndrlm'
plot(x, sig=0.05, interactive=FALSE,...)

Arguments

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

summary, ndr,ndrlm.

Examples

# Plot function for non-optimized SEM

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)
plot(NDRLM)

Calculation of predicted values of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

Calculation of predicted values of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Usage

## S3 method for class 'nda'
predict(object, newdata, ...)

Arguments

Value

Residual values (data frame)

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

plot, print, ndr.

Examples

# Example of prediction function of GNDA
set.seed(1) # Fix the random seed
data(swiss) # Use Swiss dataset
resdata<-swiss
sample <- sample(c(TRUE, FALSE), nrow(resdata), replace=TRUE, prob=c(0.9,0.1))
train <- resdata[sample, ] # Split the dataset to train and test
test <- resdata[!sample, ]
p<-ndr(train) # Use GNDA only on the train dataset
P<-ndr(swiss) # USE GNDA on the entire dataset
res<-predict(p,test) # Calculate the prediction to the test dataset
real<-P$scores[!sample, ]
cor(real,res) # The correlation between original and predicted values

Calculation of predicted values of Generalized Network-based Dimensionality Reduction and Regression with Linear Models (NDRLM)

Description

Calculation of predicted values of Generalized Network-based Dimensionality Reduction and Regression with Linear Models (NDRLM)

Usage

## S3 method for class 'ndrlm'
predict(object, newdata,
         se.fit = FALSE, scale = NULL, df = Inf,
        interval = c("none", "confidence", "prediction"),
        level = 0.95, type = c("response", "terms"),
        terms = NULL, na.action = stats::na.pass,
        pred.var = 1/weights, weights = 1, ...)

Arguments

Details

predict.ndrlm produces predicted values, obtained by evaluating the multiple regression function and model reduction by GNDA in the frame newdata (which defaults to model.frame(object)). If the logical se.fit is TRUE, standard errors of the predictions are calculated. If the numeric argument scale is set (with optional df), it is used as the residual standard deviation in the computation of the standard errors, otherwise this is extracted from the model fit. Setting intervals specifies computation of confidence or prediction (tolerance) intervals at the specified level, sometimes referred to as narrow vs. wide intervals.

If the fit is rank-deficient, some of the columns of the design matrix will have been dropped. Prediction from such a fit only makes sense if newdata is contained in the same subspace as the original data. That cannot be checked accurately, so a warning is issued.

If newdata is omitted the predictions are based on the data used for the fit. In that case how cases with missing values in the original fit are handled is determined by the na.action argument of that fit. If na.action = na.omit omitted cases will not appear in the predictions, whereas if na.action = na.exclude they will appear (in predictions, standard errors or interval limits), with value NA. See also napredict.

The prediction intervals are for a single observation at each case in newdata (or by default, the data used for the fit) with error variance(s) pred.var. This can be a multiple of res.var, the estimated value of standard deviation: the default is to assume that future observations have the same error variance as those used for fitting. If weights is supplied, the inverse of this is used as a scale factor. For a weighted fit, if the prediction is for the original data frame, weights defaults to the weights used for the model fit, with a warning since it might not be the intended result. If the fit was weighted and newdata is given, the default is to assume constant prediction variance, with a warning.

Value

predict.ndrlm produces list of a vector of predictions or a matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. For type = "terms" this is a matrix with a column per term and may have an attribute "constant".

The 'prediction' list contains the following element:

Note

Variables are first looked for in newdata and then searched for in the usual way (which will include the environment of the formula used in the fit). A warning will be given if the variables found are not of the same length as those in newdata if it was supplied.

Notice that prediction variances and prediction intervals always refer to future observations, possibly corresponding to the same predictors as used for the fit. The variance of the residuals will be smaller.

Strictly speaking, the formula used for prediction limits assumes that the degrees of freedom for the fit are the same as those for the residual variance. This may not be the case if res.var is not obtained from the fit.

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

plot, print, ndr.

Examples

# Example of prediction function of NDRLM without optimization of fittings

set.seed(1)
X<-as.data.frame(freeny.x)
Y<-as.data.frame(freeny.y)
sample <- sample(c(TRUE, FALSE), nrow(X), replace=TRUE, prob=c(0.9,0.1))
train.X <- X[sample, ] # Split the dataset X to train and test
test.X <- X[!sample, ]
train.Y <- as.data.frame(Y[sample,]) # Split the dataset Y to train and test
colnames(train.Y)<-colnames(Y)
test.Y <- as.data.frame(Y[!sample,])
colnames(test.Y)<-colnames(Y)
train<-cbind(train.Y,train.X)
test<-cbind(test.Y,test.X)
res<-predict(lm(x~.,train),test)
cor(test.Y,res) # The correlation between original and predicted values

# Use NDRLM without optimization
NDRLM<-ndrlm(train.Y,train.X,optimize=FALSE)

# Calculate the prediction to the test dataset
res<-predict(NDRLM,test)
cor(test.Y,res[[1]]) # The correlation between original and predicted values

Print function of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

Print summary of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Usage

## S3 method for class 'nda'
print(x, digits = getOption("digits"), ...)

Arguments

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kzst@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

biplot, plot, summary, ndr.

Examples

# Example of summary function of NDA without feature selection

data("CrimesUSA1990.X")
df<-CrimesUSA1990.X
p<-ndr(df)
summary(p)

# Example of summary function of NDA with feature selection
# minimal eigen values (min_evalue) is 0.0065
# minimal communality value (min_communality) is 0.1
# minimal common communality value (com_communalities) is 0.1

p<-ndr(df,min_evalue = 0.0065,min_communality = 0.1,com_communalities = 0.1)
print(p)

Print summary of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Description

Print summary of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Usage

## S3 method for class 'ndrlm'
print(x, digits = getOption("digits"), ...)

Arguments

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kzst@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

biplot, plot, summary, ndrlm.

Examples

# Example of print function of NDRLM without optimization of fittings

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)
print(NDRLM)

Calculation of residual values of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Description

Calculation of residual values of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Usage

## S3 method for class 'ndrlm'
residuals(object, ...)

Arguments

Value

Residual values (data frame)

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

plot, print, ndrlm.

Examples

# Example of residual function of NDRLM without optimization of fittings

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)

# Normality test for residuals
shapiro.test(residuals(NDRLM))

Calculating semi-partial distance correlation of columns of a matrix

Description

Calculating semi-partial distance correlation of two columns of a matrix for Generalized Network-based Dimensionality Reduction and Analysis (GNDA).

The calculation is very slow for large matrices!

Usage

spdCor(x)

Arguments

Value

Semi-partial distance correlation matrix of x.

Author(s)

Prof. Zsolt T. Kosztyan, Department of Quantitative Methods, Institute of Management, Faculty of Business and Economics, University of Pannonia, Hungary

e-mail: kosztyan.zsolt@gtk.uni-pannon.hu

References

Rizzo M, Szekely G (2021). _energy: E-Statistics: Multivariate Inference via the Energy of Data_. R package version 1.7-8, <URL: https://CRAN.R-project.org/package=energy>.

Examples

# Specification of semi-partial distance correlaction matrix.
x<-matrix(rnorm(36),nrow=6)
spdCor(x)

Summary function of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Description

Print summary of Generalized Network-based Dimensionality Reduction and Analysis (GNDA)

Usage

## S3 method for class 'nda'
summary(object, digits = getOption("digits"), ...)

Arguments

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

biplot, plot, print, ndr.

Examples

# Example of summary function of NDA without feature selection

data("CrimesUSA1990.X")
df<-CrimesUSA1990.X
p<-ndr(df)
summary(p)

# Example of summary function of NDA with feature selection
# minimal eigen values (min_evalue) is 0.0065
# minimal communality value (min_communality) is 0.1
# minimal common communality value (com_communalities) is 0.1

p<-ndr(df,min_evalue = 0.0065,min_communality = 0.1,com_communalities = 0.1)
summary(p)

Summary function of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Description

Print summary of Generalized Network-based Dimensionality Reduction and Linear Regression Model (NDRLM)

Usage

## S3 method for class 'ndrlm'
summary(object, digits = getOption("digits"), ...)

Arguments

Value

Author(s)

Zsolt T. Kosztyan*, Marcell T. Kurbucz, Attila I. Katona

e-mail*: kosztyan.zsolt@gtk.uni-pannon.hu

References

Kosztyán, Z. T., Katona, A. I., Kurbucz, M. T., & Lantos, Z. (2024). Generalized network-based dimensionality analysis. Expert Systems with Applications, 238, 121779. <URL: https://doi.org/10.1016/j.eswa.2023.121779>.

See Also

biplot, plot, print, ndrlm.

Examples

# Example of summary function of NDRLM without optimization of fittings

X<-freeny.x
Y<-freeny.y
NDRLM<-ndrlm(Y,X,optimize=FALSE)
summary(NDRLM)