In this repository, we provide a tensorflow implementation of Online Sequential Extreme Learning Machine (OS-ELM) introduced by Liang et al. in this paper. You can execute our OS-ELM module either on CPUs or GPUs.
OS-ELM is able to learn faster and training will always converge to the global optimal solution, while ordinary backpropagation-based neural networks have to deal with the local minima problem.
We tested our codes by using the following libraries.
- Python==3.6.0
- Numpy==1.14.1
- Tensorflow==1.6.0
- Keras==2.1.5
- scikit-learn==0.17.1
We used Keras only for downloading the MNIST dataset.
You don't have to use exactly the same version of the each library, but we can not guarantee the codes work well in the case.
All the above libraries can be installed in the following command.
$ pip install -U numpy Keras scikit-learn tensorflow
If you want to run our OS-ELM module on GPUs, please install tensorflow-gpu
in addition to the above command.
Here, we show how to train a OS-ELM module and predict on it. For the sake of simplicity, we assume to train the model on MNIST, a hand-written digits dataset.
from keras.datasets import mnist
from keras.utils import to_categorical
from os_elm import OS_ELM
import numpy as np
import tensorflow as tf
import tqdm
def softmax(a):
c = np.max(a, axis=-1).reshape(-1, 1)
exp_a = np.exp(a - c)
sum_exp_a = np.sum(exp_a, axis=-1).reshape(-1, 1)
return exp_a / sum_exp_a
def main():
# ===========================================
# Instantiate os-elm
# ===========================================
n_input_nodes = 784
n_hidden_nodes = 1024
n_output_nodes = 10
os_elm = OS_ELM(
# the number of input nodes.
n_input_nodes=n_input_nodes,
# the number of hidden nodes.
n_hidden_nodes=n_hidden_nodes,
# the number of output nodes.
n_output_nodes=n_output_nodes,
# loss function.
# the default value is 'mean_squared_error'.
# for the other functions, we support
# 'mean_absolute_error', 'categorical_crossentropy', and 'binary_crossentropy'.
loss='mean_squared_error',
# activation function applied to the hidden nodes.
# the default value is 'sigmoid'.
# for the other functions, we support 'linear' and 'tanh'.
# NOTE: OS-ELM can apply an activation function only to the hidden nodes.
activation='sigmoid',
)
# ===========================================
# Prepare dataset
# ===========================================
n_classes = n_output_nodes
# load MNIST
(x_train, t_train), (x_test, t_test) = mnist.load_data()
# normalize images' values within [0, 1]
x_train = x_train.reshape(-1, n_input_nodes) / 255.
x_test = x_test.reshape(-1, n_input_nodes) / 255.
x_train = x_train.astype(np.float32)
x_test = x_test.astype(np.float32)
# convert label data into one-hot-vector format data.
t_train = to_categorical(t_train, num_classes=n_classes)
t_test = to_categorical(t_test, num_classes=n_classes)
t_train = t_train.astype(np.float32)
t_test = t_test.astype(np.float32)
# divide the training dataset into two datasets:
# (1) for the initial training phase
# (2) for the sequential training phase
# NOTE: the number of training samples for the initial training phase
# must be much greater than the number of the model's hidden nodes.
# here, we assign int(1.5 * n_hidden_nodes) training samples
# for the initial training phase.
border = int(1.5 * n_hidden_nodes)
x_train_init = x_train[:border]
x_train_seq = x_train[border:]
t_train_init = t_train[:border]
t_train_seq = t_train[border:]
# ===========================================
# Training
# ===========================================
# the initial training phase
pbar = tqdm.tqdm(total=len(x_train), desc='initial training phase')
os_elm.init_train(x_train_init, t_train_init)
pbar.update(n=len(x_train_init))
# the sequential training phase
pbar.set_description('sequential training phase')
batch_size = 64
for i in range(0, len(x_train_seq), batch_size):
x_batch = x_train_seq[i:i+batch_size]
t_batch = t_train_seq[i:i+batch_size]
os_elm.seq_train(x_batch, t_batch)
pbar.update(n=len(x_batch))
pbar.close()
# ===========================================
# Prediction
# ===========================================
# sample 10 validation samples from x_test
n = 10
x = x_test[:n]
t = t_test[:n]
# 'predict' method returns raw values of output nodes.
y = os_elm.predict(x)
# apply softmax function to the output values.
y = softmax(y)
# check the answers.
for i in range(n):
max_ind = np.argmax(y[i])
print('========== sample index %d ==========' % i)
print('estimated answer: class %d' % max_ind)
print('estimated probability: %.3f' % y[i,max_ind])
print('true answer: class %d' % np.argmax(t[i]))
# ===========================================
# Evaluation
# ===========================================
# we currently support 'loss' and 'accuracy' for 'metrics'.
# NOTE: 'accuracy' is valid only if the model assumes
# to deal with a classification problem, while 'loss' is always valid.
# loss = os_elm.evaluate(x_test, t_test, metrics=['loss']
[loss, accuracy] = os_elm.evaluate(x_test, t_test, metrics=['loss', 'accuracy'])
print('val_loss: %f, val_accuracy: %f' % (loss, accuracy))
# ===========================================
# Save model
# ===========================================
print('saving model parameters...')
os_elm.save('./checkpoint/model.ckpt')
# initialize weights of os_elm
os_elm.initialize_variables()
# ===========================================
# Load model
# ===========================================
# If you want to load weights to a model,
# the architecture of the model must be exactly the same
# as the one when the weights were saved.
print('restoring model parameters...')
os_elm.restore('./checkpoint/model.ckpt')
# ===========================================
# ReEvaluation
# ===========================================
# loss = os_elm.evaluate(x_test, t_test, metrics=['loss']
[loss, accuracy] = os_elm.evaluate(x_test, t_test, metrics=['loss', 'accuracy'])
print('val_loss: %f, val_accuracy: %f' % (loss, accuracy))
if __name__ == '__main__':
main()The following figure shows OS-ELM training formula.
- important: Since matrix inversion in OS-ELM update formula has a lot of conditional operations, even if it is executed on GPUs, the training is not necessarily accelerated.
- In OS-ELM, you can apply an activation function only to the hidden nodes.
- OS-ELM always finds the global optimal solution for the weight matrices at every training.
- If you feed all the training samples to OS-ELM in the initial training phase, the computational procedures will be exactly the same as ELM. So, we can consider ELM is a special case of OS-ELM.
- OS-ELM does not need to train iteratively on the same data samples, while backpropagation-based models usually need to do that.
- OS-ELM does not update 'alpha', the weight matrix connecting the input nodes and the hidden nodes. It makes OS-ELM train faster.
- OS-ELM does not need to compute gradients. The weight matrices are trained by computing some matrix products and a matrix inversion.
- The computational complexity for the matrix inversion is about O(batch_size^3), so take care for the cost when you increase batch_size.
You can execute the above sample code with the following command.
$ python train_mnist.py
- support more activation functions
- support more loss functions
- provide benchmark results