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.

- 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 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) |

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) 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') cat('the rmse error for liner-model is :', rmse(yte, pr_te_lm), '\n')

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) 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') cat('the accuracy for glm is :', mean(yte_class == pr_glm), '\n')

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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