# Extreme Learning Machine

05 Jul 2018As 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)
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 : 0.09112573 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 : 22.00705
cat('the rmse error for linear-model is :', rmse(yte, pr_te_lm), '\n')
## the rmse error for linear-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 : 0.03604198 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'))
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 : 0.9337748
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 in combination with the HOG features of the OpenImageR package,

```
# 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
```

The accuracy of the Extreme Learning Machine algorithm is very close to the one of the KernelKnn using HOG features, however it is more than 5 times faster in my operating system in case of a 4-fold cross-validation.

An updated version of the elmNNRcpp package can be found in my Github repository and to report bugs/issues please use the following link, https://github.com/mlampros/elmNNRcpp/issues.