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Extreme Learning Machine implementation in Python

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**---> ARCHIVED March 2021 <---**

It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: 1) the slow gradient- based learning algorithms are extensively used to train neural networks, and 2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Unlike these traditional implementations, this paper proposes a new learning algorithm called extreme learning machine (ELM) for single- hidden layer feedforward neural networks (SLFNs) which ran- domly chooses the input weights and analytically determines the output weights of SLFNs. In theory, this algorithm tends to provide the best generalization performance at extremely fast learning speed. The experimental results based on real- world benchmarking function approximation and classification problems including large complex applications show that the new algorithm can produce best generalization performance in some cases and can learn much faster than traditional popular learning algorithms for feedforward neural networks.

It's a work in progress, so things can/might/will change.

**David C. Lambert**

**dcl [at] panix [dot] com**

**Copyright © 2013**

**License: Simple BSD**

Contains the **RandomLayer**, **MLPRandomLayer**, **RBFRandomLayer** and **GRBFRandomLayer** classes.

RandomLayer is a transformer that creates a feature mapping of the inputs that corresponds to a layer of hidden units with randomly generated components.

The transformed values are a specified function of input activations that are a weighted combination of dot product (multilayer perceptron) and distance (rbf) activations:

input_activation = alpha * mlp_activation + (1-alpha) * rbf_activationmlp_activation(x) = dot(x, weights) + bias rbf_activation(x) = rbf_width * ||x - center||/radius

*mlp*activation_ is multi-layer perceptron input activation

*rbf*activation_ is radial basis function input activation

*alpha* and *rbf*width_ are specified by the user

*weights* and *biases* are taken from normal distribution of
mean 0 and sd of 1

*centers* are taken uniformly from the bounding hyperrectangle
of the inputs, and

radius = max(||x-c||)/sqrt(n_centers*2)

(All random components can be supplied by the user by providing entries in the dictionary given as the *user*components_ parameter.)

The input activation is transformed by a transfer function that defaults
to numpy.tanh if not specified, but can be any callable that returns an
array of the same shape as its argument (the input activation array, of
shape [n*samples, n*hidden]).

Transfer functions provided are:

- sine
- tanh
- tribas
- inv_tribas
- sigmoid
- hardlim
- softlim
- gaussian
- multiquadric
- inv_multiquadric

MLPRandomLayer and RBFRandomLayer classes are just wrappers around the RandomLayer class, with the *alpha* mixing parameter set to 1.0 and 0.0 respectively (for 100% MLP input activation, or 100% RBF input activation)

The RandomLayer, MLPRandomLayer, RBFRandomLayer classes can take a callable user provided transfer function. See the docstrings and the example ipython notebook for details.

The GRBFRandomLayer implements the Generalized Radial Basis Function from [3]

Contains the **ELMRegressor**, **ELMClassifier**, **GenELMRegressor**, and **GenELMClassifier** classes.

GenELMRegressor and GenELMClassifier both take *RandomLayer instances as part of their contructors, and an optional regressor (conforming to the sklearn API)for performing the fit (instead of the default linear fit using the pseudo inverse from scipy.pinv2). GenELMClassifier is little more than a wrapper around GenELMRegressor that binarizes the target array before performing a regression, then unbinarizes the prediction of the regressor to make its own predictions.

The ELMRegressor class is a wrapper around GenELMRegressor that uses a RandomLayer instance by default and exposes the RandomLayer parameters in the constructor. ELMClassifier is similar for classification.

A small demo (based on scikit-learn's plot*classifier*comparison) that shows the decision functions of a couple of different instantiations of the GenELMClassifier on three different datasets.

An IPython notebook, illustrating several ways to use the ***ELM*** and ***RandomLayer** classes.

Written using Python 2.7.3, numpy 1.6.1, scipy 0.10.1, scikit-learn 0.13.1 and ipython 0.12.1

[1] http://www.extreme-learning-machines.org[2] G.-B. Huang, Q.-Y. Zhu and C.-K. Siew, "Extreme Learning Machine: Theory and Applications", Neurocomputing, vol. 70, pp. 489-501, 2006.

[3] Fernandez-Navarro, et al, "MELM-GRBF: a modified version of the

extreme learning machine for generalized radial basis function

neural networks", Neurocomputing 74 (2011), 2502-2510