Binary Classification via GMDH-Type Neural Network Algorithms

Description

Performs binary classification via Group Method of Data Handling (GMDH) - type neural network algorithms. There exist two main algorithms available in GMDH() and dceGMDH() functions. GMDH() performs classification via GMDH algorithm for a binary response and returns important variables. dceGMDH() performs classification via diverse classifiers ensemble based on GMDH (dce-GMDH) algorithm. Also, the package produces a well-formatted table of descriptives for a binary response. Moreover, it produces confusion matrix, its related statistics and scatter plot (2D and 3D) with classification labels of binary classes to assess the prediction performance. All 'GMDH2' functions are designed for a binary response (Dag et al., 2019, <https://download.atlantis-press.com/article/125911202.pdf>).

Details

Feature Selection and Classification via GMDH-Type Neural Network Algorithm for a Binary Response

Description

GMDH makes feature selection and classification via GMDH-type neural network algorithm.

Usage

GMDH(x.train, y.train, x.valid, y.valid, alpha = 0.6, maxlayers = 10, maxneurons = 15, 
  exCriterion = "MSE", verbose = TRUE, ...)

Arguments

Value

A list with class "GMDH" and "GMDHplot" containing the following components:

Author(s)

Osman Dag, Erdem Karabulut, Reha Alpar

References

Dag, O., Karabulut, E., Alpar, R. (2019). GMDH2: Binary Classification via GMDH-Type Neural Network Algorithms - R Package and Web-Based Tool. International Journal of Computational Intelligence Systems, 12:2, 649-660.

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via GMDH algorithm
model <- GMDH(x.train, y.train, x.valid, y.valid)
predict(model, x.test)

Table for Simple Descriptive Statistics

Description

Table produces a table for simple descriptive statistics for a binary response.

Usage

Table(x, y, option = "min-max", percentages = "column", ndigits = c(2,1), 
  output = "R")

Arguments

Author(s)

Osman Dag

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data[,2:10]
y <- data[,11]

Table(x, y)
Table(x, y, output = "LaTeX")

Confusion Matrix

Description

confMat constructs a 2\times2 confusion matrix and returns some statistics related to confusion matrix.

Usage

confMat(data, ...)

## Default S3 method:
confMat(data, reference, positive = NULL, verbose = TRUE, ...)

## S3 method for class 'table'
confMat(data, positive = NULL, verbose = TRUE, ...)

Arguments

Details

The confMat function requires that the factors have exactly the same levels. The function constructs 2\times2 confusion matrix and calculates accuracy, no information rate (NIR), unweighted Kappa statistic, Matthews correlation coefficient, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), prevalence, balanced accuracy, youden index, detection rate, detection prevalence, precision, recall and F1 measure.

Suppose a 2\times2 table with notation

TP is the number of true positives, FP is the number of false positives, FN is the number of false negatives and TN is the number of true negatives.

Accuracy = \frac{TP + TN}{TP + FP + FN + TN}

NIR = max(Prevalence, 1 - Prevalence)

Kappa = \frac{Accuracy - \frac{(TP + FP)(TP + FN)+(FN + TN)(FP + TN)}{(TP + FP + FN + TN)^2}}{1 - \frac{(TP + FP)(TP + FN)+(FN + TN)(FP + TN)}{(TP + FP + FN + TN)^2}}

MCC = \frac{TP \times TN - FP \times FN}{\sqrt{(TP+FP) \times (FN+TN) \times (TP+FN) \times (FP+TN)}}

Sensitivity = \frac{TP}{TP+FN}

Specificity = \frac{TN}{TN+FP}

PPV = \frac{TP}{TP+FP}

NPV = \frac{TN}{TN+FN}

Prevalence = \frac{TP + FN}{TP + FP + FN + TN}

Balanced\ accuracy = \frac{Sensitivity + Specificity}{2}

Youden\ index = Sensitivity + Specificity -1

Detection\ rate = \frac{TP}{TP + FP + FN + TN}

Detection\ prevalence = \frac{TP+FP}{TP + FP + FN + TN}

Precision = \frac{TP}{TP + FP}

Recall = \frac{TP}{TP+FN}

F1 = \frac{2}{\frac{1}{Recall}+\frac{1}{Precision}}

Value

Returns a list containing following elements:

Note

If the factors, reference and data, have the same levels, but in the incorrect order, the confMat will reorder data with the order of reference.

Author(s)

Osman Dag

See Also

confusionMatrix

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]


set.seed(seed)
# to construct model via dce-GMDH algorithm
model <- dceGMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
y.test_pred <- predict(model, x.test, type = "class")

# to obtain confusion matrix and some statistics for test set
confMat(y.test_pred, y.test, positive = "malignant")

# to obtain statistics from table
result <- table(y.test_pred, y.test)
confMat(result, positive = "malignant")

2D Scatter Plot with Classification Labels

Description

cplot2d produces two dimensional scatter plot with classification labels of binary classes.

Usage

cplot2d(x1, x2, ypred, yobs, colors = c("red", "blue"), symbols = c("circle", "o"), 
  size = 10, xlab = NULL, ylab = NULL, title = NULL)

Arguments

Details

Symbols indicate the observed classes of binary response. Colors show TRUE or FALSE classification of the observations.

Value

An object with class "plotly" and "htmlwidget".

Author(s)

Osman Dag

See Also

plot_ly

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via dce-GMDH algorithm
model <- dceGMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
y.test_pred <- predict(model, x.test, type = "class")

# to obtain confusion matrix and some statistics for test set
confMat(y.test_pred, y.test, positive = "malignant")

# to produce 2D scatter plot with classification labels for test set
cplot2d(x.test[,1], x.test[,6], y.test_pred, y.test, symbols = c("x", "o"))
cplot2d(x.test[,1], x.test[,6], y.test_pred, y.test, colors = c("red", "black"))

3D Scatter Plot with Classification Labels

Description

cplot3d produces three dimensional scatter plot with classification labels of binary classes.

Usage

cplot3d(x1, x2, x3, ypred, yobs, colors = c("red", "blue"), 
  symbols = c("circle", "o"), size = 10, xlab = NULL, ylab = NULL, zlab = NULL, 
  title = NULL)

Arguments

Details

Symbols indicate the observed classes of binary response. Colors show TRUE or FALSE classification of the observations.

Value

An object with class "plotly" and "htmlwidget".

Author(s)

Osman Dag

See Also

plot_ly

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]


set.seed(seed)
# to construct model via dce-GMDH algorithm
model <- dceGMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
y.test_pred <- predict(model, x.test, type = "class")

# to obtain confusion matrix and some statistics for test set
confMat(y.test_pred, y.test, positive = "malignant")

# to produce 3D scatter plot with classification labels for test set
cplot3d(x.test[,1], x.test[,6], x.test[,3], y.test_pred, y.test,
colors = c("red", "black"))

Diverse Classifiers Ensemble Based on GMDH-Type Neural Network Algorithm for Binary Classification

Description

dceGMDH makes a binary classification via diverse classifiers ensemble Based on GMDH-Type Neural Network (dce-GMDH) Algorithm.

Usage

dceGMDH(x.train, y.train, x.valid, y.valid, alpha = 0.6, maxlayers = 10, 
  maxneurons = 15, exCriterion = "MSE", verbose = TRUE, svm_options, 
   randomForest_options, naiveBayes_options, cv.glmnet_options, nnet_options, ...)

Arguments

Value

A list with class "dceGMDH" and "GMDHplot" containing the following components:

Author(s)

Osman Dag, Erdem Karabulut, Reha Alpar

References

Dag, O., Karabulut, E., Alpar, R. (2019). GMDH2: Binary Classification via GMDH-Type Neural Network Algorithms - R Package and Web-Based Tool. International Journal of Computational Intelligence Systems, 12:2, 649-660.

Dag, O., Kasikci, M., Karabulut, E., Alpar, R. (2022). Diverse Classifiers Ensemble Based on GMDH-Type Neural Network Algorithm for Binary Classification. Communications in Statistics - Simulation and Computation, 51:5, 2440-2456.

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via dce-GMDH algorithm
model <- dceGMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
predict(model, x.test)

Plotting Using GMDH and dce-GMDH Algorithms for Binary Classification

Description

This function plots minimum specified external criterion across layers based upon a model trained by GMDH or dceGMDH. This is plotted for validation set.

Usage

## S3 method for class 'GMDHplot'
plot(x, ...)

Arguments

Author(s)

Osman Dag

See Also

GMDH, dceGMDH

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets
indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via GMDH algorithm
model <- GMDH(x.train, y.train, x.valid, y.valid)
plot(model)

# to construct model via dce-GMDH algorithm
model2 <- dceGMDH(x.train, y.train, x.valid, y.valid)
plot(model2)

Predicting Using GMDH Algorithm for Binary Classification

Description

This function predicts values based upon a model trained by GMDH.

Usage

## S3 method for class 'GMDH'
predict(object, x, type = "class", ...)

Arguments

Value

A vector of predicted values of corresponding classes depending on type specified.

Author(s)

Osman Dag, Erdem Karabulut, Reha Alpar

See Also

GMDH

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via GMDH algorithm
model <- GMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
predict(model, x.test, type = "class")
# to obtain predicted probabilities for test set
predict(model, x.test, type = "probability")

Predicting Using dce-GMDH Algorithm for Binary Classification

Description

This function predicts values based upon a model trained by dceGMDH.

Usage

## S3 method for class 'dceGMDH'
predict(object, x, type = "class", ...)

Arguments

Value

A vector of predicted values of corresponding classes depending on type specified.

Author(s)

Osman Dag, Erdem Karabulut, Reha Alpar

See Also

dceGMDH

Examples

library(GMDH2)

library(mlbench)
data(BreastCancer)

data <- BreastCancer

# to obtain complete observations
completeObs <- complete.cases(data)
data <- data[completeObs,]

x <- data.matrix(data[,2:10])
y <- data[,11]

seed <- 12345
set.seed(seed)
nobs <- length(y)

# to split train, validation and test sets

indices <- sample(1:nobs)

ntrain <- round(nobs*0.6,0)
nvalid <- round(nobs*0.2,0)
ntest <- nobs-(ntrain+nvalid)

train.indices <- sort(indices[1:ntrain])
valid.indices <- sort(indices[(ntrain+1):(ntrain+nvalid)])
test.indices <- sort(indices[(ntrain+nvalid+1):nobs])


x.train <- x[train.indices,]
y.train <- y[train.indices]

x.valid <- x[valid.indices,]
y.valid <- y[valid.indices]

x.test <- x[test.indices,]
y.test <- y[test.indices]

set.seed(seed)
# to construct model via dce-GMDH algorithm
model <- dceGMDH(x.train, y.train, x.valid, y.valid)

# to obtain predicted classes for test set
predict(model, x.test, type = "class")
# to obtain predicted probabilities for test set
predict(model, x.test, type = "probability")