Extreme Learning Machine

Lampros Mouselimis

2023-05-27

Source: vignettes/extreme_learning_machine.Rmd

As of 2018-06-17 the elmNN package was archived and due to the fact that it was one of the machine learning functions that I used when I started learning R (it returns the output results pretty fast too) plus that I had to utilize the package last week for a personal task I decided to reimplement the R code in Rcpp. It didn’t take long because the R package was written, initially by the author, in a clear way. In the next lines I’ll explain the differences and the functionality just for reference.


Differences between the elmNN (R package) and the elmNNRcpp (Rcpp Package)

  • The reimplementation assumes that both the predictors ( x ) and the response variable ( y ) are in the form of a matrix. This means that character, factor or boolean columns have to be transformed (onehot encoded would be an option) before using either the elm_train or the elm_predict function.
  • The output predictions are in the form of a matrix. In case of regression the matrix has one column whereas in case of classification the number of columns equals the number of unique labels
  • In case of classification the unique labels should begin from 0 and the difference between the unique labels should not be greater than 1. For instance, unique_labels = c(0, 1, 2, 3) are acceptable whereas the following case will raise an error : unique_labels = c(0, 2, 3, 4)
  • I renamed the poslin activation to relu as it’s easier to remember ( both share the same properties ). Moreover I added the leaky_relu_alpha parameter so that if the value is greater than 0.0 a leaky-relu-activation for the single-hidden-layer can be used.
  • The initilization weights in the elmNN were set by default to uniform in the range [-1,1] ( ‘uniform_negative’ ) . I added two more options : ‘normal_gaussian’ ( in the range [0,1] ) and ‘uniform_positive’ ( in the range [0,1] ) too
  • The user has the option to include or exclude bias of the one-layer feed-forward neural network


The elmNNRcpp functions

The functions included in the elmNNRcpp package are the following and details for each parameter can be found in the package documentation,


elmNNRcpp
elm_train(x, y, nhid, actfun, init_weights = “normal_gaussian”, bias = FALSE, …)
elm_predict(elm_train_object, newdata, normalize = FALSE)
onehot_encode(y)


elmNNRcpp in case of Regression

The following code chunk gives some details on how to use the elm_train in case of regression and compares the results with the lm ( linear model ) base function,


# load the data and split it in two parts
#----------------------------------------

data(Boston, package = 'KernelKnn')

library(elmNNRcpp)
## Loading required package: KernelKnn
Boston = as.matrix(Boston)
dimnames(Boston) = NULL

X = Boston[, -dim(Boston)[2]]
xtr = X[1:350, ]
xte = X[351:nrow(X), ]


# prepare / convert the train-data-response to a one-column matrix
#-----------------------------------------------------------------

ytr = matrix(Boston[1:350, dim(Boston)[2]], nrow = length(Boston[1:350, dim(Boston)[2]]),
             
             ncol = 1)


# perform a fit and predict [ elmNNRcpp ]
#----------------------------------------

fit_elm = elm_train(xtr, ytr, nhid = 1000, actfun = 'purelin',
                    
                    init_weights = "uniform_negative", bias = TRUE, verbose = T)
## Input weights will be initialized ...
## Dot product of input weights and data starts ...
## Bias will be added to the dot product ...
## 'purelin' activation function will be utilized ...
## The computation of the Moore-Pseudo-inverse starts ...
## The computation is finished!
## 
## Time to complete : 0.44121 secs
pr_te_elm = elm_predict(fit_elm, xte)



# perform a fit and predict [ lm ]
#----------------------------------------

data(Boston, package = 'KernelKnn')

fit_lm = lm(medv~., data = Boston[1:350, ])

pr_te_lm = predict(fit_lm, newdata = Boston[351:nrow(X), ])



# evaluation metric
#------------------

rmse = function (y_true, y_pred) {
  
  out = sqrt(mean((y_true - y_pred)^2))
  
  out
}


# test data response variable
#----------------------------

yte = Boston[351:nrow(X), dim(Boston)[2]]


# mean-squared-error for 'elm' and 'lm'
#--------------------------------------

cat('the rmse error for extreme-learning-machine is :', rmse(yte, pr_te_elm[, 1]), '\n')
## the rmse error for extreme-learning-machine is : 23.36543
cat('the rmse error for liner-model is :', rmse(yte, pr_te_lm), '\n')
## the rmse error for liner-model is : 23.36543


elmNNRcpp in case of Classification

The following code script illustrates how elm_train can be used in classification and compares the results with the glm ( Generalized Linear Models ) base function,


# load the data
#--------------

data(ionosphere, package = 'KernelKnn')

y_class = ionosphere[, ncol(ionosphere)]

x_class = ionosphere[, -c(2, ncol(ionosphere))]     # second column has 1 unique value

x_class = scale(x_class[, -ncol(x_class)])

x_class = as.matrix(x_class)                        # convert to matrix
dimnames(x_class) = NULL 



# split data in train-test
#-------------------------

xtr_class = x_class[1:200, ]                    
xte_class = x_class[201:nrow(ionosphere), ]

ytr_class = as.numeric(y_class[1:200])
yte_class = as.numeric(y_class[201:nrow(ionosphere)])

ytr_class = onehot_encode(ytr_class - 1)                                     # class labels should begin from 0 (subtract 1)


# perform a fit and predict [ elmNNRcpp ]
#----------------------------------------

fit_elm_class = elm_train(xtr_class, ytr_class, nhid = 1000, actfun = 'relu',
                          
                          init_weights = "uniform_negative", bias = TRUE, verbose = TRUE)
## Input weights will be initialized ...
## Dot product of input weights and data starts ...
## Bias will be added to the dot product ...
## 'relu' activation function will be utilized ...
## The computation of the Moore-Pseudo-inverse starts ...
## The computation is finished!
## 
## Time to complete : 0.1766419 secs
pr_elm_class = elm_predict(fit_elm_class, xte_class, normalize = FALSE)

pr_elm_class = max.col(pr_elm_class, ties.method = "random")



# perform a fit and predict [ glm ]
#----------------------------------------

data(ionosphere, package = 'KernelKnn')

fit_glm = glm(class~., data = ionosphere[1:200, -2], family = binomial(link = 'logit'))
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
pr_glm = predict(fit_glm, newdata = ionosphere[201:nrow(ionosphere), -2], type = 'response')

pr_glm = as.vector(ifelse(pr_glm < 0.5, 1, 2))


# accuracy for 'elm' and 'glm'
#-----------------------------

cat('the accuracy for extreme-learning-machine is :', mean(yte_class == pr_elm_class), '\n')
## the accuracy for extreme-learning-machine is : 0.9006623
cat('the accuracy for glm is :', mean(yte_class == pr_glm), '\n')
## the accuracy for glm is : 0.8940397


Classify MNIST digits using elmNNRcpp

I found an interesting Python implementation / Code on the web and I thought I give it a try to reproduce the results. I downloaded the MNIST data from my Github repository and I used the following parameter setting,

# using system('wget..') on a linux OS 
#-------------------------------------

system("wget https://raw.githubusercontent.com/mlampros/DataSets/master/mnist.zip")             

mnist <- read.table(unz("mnist.zip", "mnist.csv"), nrows = 70000, header = T, 
                    
                    quote = "\"", sep = ",")

x = mnist[, -ncol(mnist)]

y = mnist[, ncol(mnist)]

# using system('wget..') on a linux OS 
#-------------------------------------

system("wget https://raw.githubusercontent.com/mlampros/DataSets/master/mnist.zip")             

mnist <- read.table(unz("mnist.zip", "mnist.csv"), nrows = 70000, header = T, 
                    
                    quote = "\"", sep = ",")

x = mnist[, -ncol(mnist)]

y = mnist[, ncol(mnist)] + 1


# use the hog-features as input data
#-----------------------------------

hog = OpenImageR::HOG_apply(x, cells = 6, orientations = 9, rows = 28, columns = 28, threads = 6)

y_expand = elmNNRcpp::onehot_encode(y - 1)


# 4-fold cross-validation
#------------------------

folds = KernelKnn:::class_folds(folds = 4, as.factor(y))
str(folds)

START = Sys.time()


fit = lapply(1:length(folds), function(x) {
  
  cat('\n'); cat('fold', x, 'starts ....', '\n')
  
  tmp_fit = elmNNRcpp::elm_train(as.matrix(hog[unlist(folds[-x]), ]), y_expand[unlist(folds[-x]), ], 
  
                                 nhid = 2500, actfun = 'relu', init_weights = 'uniform_negative',
                                 
                                 bias = TRUE, verbose = TRUE)
  
  cat('******************************************', '\n')
  
  tmp_fit
})

END = Sys.time()

END - START

# Time difference of 5.698552 mins


str(fit)


# predictions for 4-fold cross validation
#----------------------------------------

test_acc = unlist(lapply(1:length(fit), function(x) {
  
  pr_te = elmNNRcpp::elm_predict(fit[[x]], newdata = as.matrix(hog[folds[[x]], ]))
  
  pr_max_col = max.col(pr_te, ties.method = "random")
  
  y_true = max.col(y_expand[folds[[x]], ])
  
  mean(pr_max_col == y_true)
}))
  
  

test_acc

# [1] 0.9825143 0.9848571 0.9824571 0.9822857


cat('Accuracy ( Mnist data ) :', round(mean(test_acc) * 100, 2), '\n')

# Accuracy ( Mnist data ) : 98.3