[PYTHON] I implemented Extreme learning machine

What is Extreme Learning Machine (ELM)?

ELM is a special form of feedforward perceptron. It has one hidden layer, but the weight of the hidden layer is randomly determined, and the weight of the output layer is determined using the pseudo inverse matrix. In terms of image, the hidden layer is like making a lot of random feature extractors and selecting features in the output layer.

ELM has the following characteristics.

• Since the solution is just a pseudo inverse matrix, the solution can be found at high speed.
• Convex problem (no local solution)
• Arbitrary function can be approximated (same as ordinary perceptron)
• Any activation can be used (no need to be differentiated)

Implementation

import numpy as np


class ExtremeLearningMachine(object):
    def __init__(self, n_unit, activation=None):
        self._activation = self._sig if activation is None else activation
        self._n_unit = n_unit

    @staticmethod
    def _sig(x):
        return 1. / (1 + np.exp(-x))

    @staticmethod
    def _add_bias(x):
        return np.hstack((x, np.ones((x.shape[0], 1))))

    def fit(self, X, y):
        self.W0 = np.random.random((X.shape[1], self._n_unit))
        z = self._add_bias(self._activation(X.dot(self.W0)))
        self.W1 = np.linalg.lstsq(z, y)[0]

    def transform(self, X):
        if not hasattr(self, 'W0'):
            raise UnboundLocalError('must fit before transform')
        z = self._add_bias(self._activation(X.dot(self.W0)))
        return z.dot(self.W1)

    def fit_transform(self, X, y):
        self.W0 = np.random.random((X.shape[1], self._n_unit))
        z = self._add_bias(self._activation(X.dot(self.W0)))
        self.W1 = np.linalg.lstsq(z, y)[0]
        return z.dot(self.W1)

test

I will try it with iris for the time being.

Method

from sklearn import datasets

iris = datasets.load_iris()
ind = np.random.permutation(len(iris.data))

y = np.zeros((len(iris.target), 3))
y[np.arange(len(y)), iris.target] = 1

acc_train = []
acc_test = []
N = [5, 10, 15, 20, 30, 40, 80, 160]
for n in N:
    elm = ExtremeLearningMachine(n)
    elm.fit(iris.data[ind[:100]], y[ind[:100]])
    acc_train.append(np.average(np.argmax(elm.transform(iris.data[ind[:100]]), axis=1) == iris.target[ind[:100]]))
    acc_test.append(np.average(np.argmax(elm.transform(iris.data[ind[100:]]), axis=1) == iris.target[ind[100:]]))
plt.plot(N, acc_train, c='red', label='train')
plt.plot(N, acc_test, c='blue', label='test')
plt.legend(loc=1)
plt.savefig("result.png ")

result

Conclusion

• Since there are few parameters to tamper with, tuning seems easier than with ordinary neural networks.
• Although it was mentioned in the original paper that the generalization performance is high, it is usually overfitted.
• Both fit and transform are insanely fast, so it seems to have various uses.