Extreme Learning Machine

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Lampros Mouselimis

2022-01-27

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 : 0.07127595 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 : 0.03828526 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

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