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neural_network.py
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neural_network.py
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import numpy as np
from tqdm.auto import trange
import os
import pickle
DIR = os.getcwd()
class NeuralNetwork:
def __init__(self, sizes, train=False):
"""
:param sizes: list
A list of integers used to determine the sizes of the input, hidden, and output layers.
ex: [784, 128, 10] : Will initialize a 128x784 matrix of weights and a 128x1 matrix of biases.
Also, it will initialize a 10x128 matrix of weights and a 10x1 matrix of biases.
:param train: boolean, optional
When this flag is true it will randomize the biases and weights even if it can load model from disk
"""
self.sizes = sizes
self.learning_rate = 0.01
self.nodes = {}
self.error_nodes = {}
self.trained = False
# set biases and weights to random number if not able to load model from disk
if train or self.load() is False:
self.biases = self.initialize_bias()
self.weights = self.initialize_weights()
else:
self.trained = True
@staticmethod
def sigmoid(x):
return 1 / (1 + np.exp(-x))
@staticmethod
def squared_error_cost(prediction, target, derivative=False):
if derivative:
return 2 * (prediction - target)
return (prediction - target) ** 2
def activation(self, inputs, weights, bias):
"""
Calculates the next layer by using the dot product, it multiplies the weights matrix by the inputs matrix
connecting them to the neurons in the next layer. Next it adds the bias vector using matrix addition. Lastly,
it applies the sigmoid function to the layer.
:param inputs: numpy.ndarray
:param weights: numpy.ndarray
:param bias: numpy.ndarray
:return: numpy.ndarray
"""
return self.sigmoid(np.dot(weights, inputs) + bias)
def sigmoid_derivative(self, x):
"""
return self.sigmoid(x) * (1 - self.sigmoid(x)) - actual sigmoid derivative
since sigmoid is already applied to x in forward_pass() we do not apply sigmoid to x again
:param x: numpy.ndarray
:return: numpy.ndarray
"""
return x * (1 - x)
def initialize_weights(self):
"""
Initializes random matrices that will be used as weights. Each weight matrix is added to dictionary with the
corresponding index as its key.
:return: dict
"""
weights = {}
for i in range(1, len(self.sizes)):
weights[i-1] = np.random.randn(self.sizes[i], self.sizes[i-1]) * np.sqrt(1. / self.sizes[i])
return weights
def initialize_bias(self):
"""
Initializes random matrices that will be used as biases. Each bias matrix is added to dictionary with the
corresponding index as its key.
:return: dict
"""
bias = {}
for i in range(1, len(self.sizes)):
bias[i-1] = np.random.randn(self.sizes[i], 1) * np.sqrt(1. / self.sizes[i])
return bias
def save(self):
"""
save weights and biases to disk in '/model' folder
"""
try:
with open(DIR + '/model/weights.pickle', 'wb') as handle:
pickle.dump(self.weights, handle)
with open(DIR + '/model/bias.pickle', 'wb') as handle:
pickle.dump(self.biases, handle)
except FileNotFoundError as e:
print('ERROR: Could not save files successfully: ' + e)
def load(self):
"""
Loads weights and biases from disk
:return: Boolean
"""
try:
with open(DIR + '/model/weights.pickle', 'rb') as handle:
self.weights = pickle.load(handle)
with open(DIR + '/model/bias.pickle', 'rb') as handle:
self.biases = pickle.load(handle)
except IOError:
return False
return True
def forward_pass(self, image):
"""
Calculates every layer and stores it in self.nodes dictionary
:param image: numpy.ndarray
:return: numpy.ndarray
This is the output layer
"""
self.nodes[0] = layer = image.reshape((28, 28)).reshape(28 ** 2, 1) # convert image to 784x1 matrix
for i in range(len(self.weights)):
layer = self.activation(layer, self.weights[i], self.biases[i])
self.nodes[i+1] = layer
return layer
def predict_image(self, image):
"""
Predicts the handwritten digit that's in the image
:param image: numpy.ndarray
:return: numpy.int64
"""
return np.argmax(self.forward_pass(image), axis=0)[0]
def update_parameters_iter(self, target):
"""
Updates weights and biases like update_parameters() but for n amount of hidden layers
todo: correctly update weights and biases!
:param target: numpy.ndarray
"""
index = len(self.weights) - 1
self.weights[index] += self.learning_rate * (target - self.nodes[index+1]).dot(self.nodes[index].T)
self.biases[index] += self.learning_rate * (target - self.nodes[index + 1]).sum()
for i in range(len(self.weights)-2, -1, -1):
gradient = self.weights[i+1].T.dot(2*(self.error_nodes[i+2] - self.nodes[i+2])) * self.sigmoid_derivative(self.nodes[i+1])
self.weights[i] += self.learning_rate * gradient.dot(self.nodes[i].T)
self.biases[i] += self.learning_rate * gradient
def update_parameters(self, target):
"""
Updates weights and biases
:param target: numpy.ndarray
"""
self.weights[2] += self.learning_rate * (target - self.nodes[3]).dot(self.nodes[2].T)
self.biases[2] += self.learning_rate * (target - self.nodes[3]).sum()
gradient = self.weights[2].T.dot(target - self.nodes[3]) * self.sigmoid_derivative(self.nodes[2])
self.weights[1] += self.learning_rate * gradient.dot(self.nodes[1].T)
self.biases[1] += self.learning_rate * gradient
gradient = self.weights[1].T.dot(self.error_nodes[2]) * self.sigmoid_derivative(self.nodes[1])
self.weights[0] += self.learning_rate * gradient.dot(self.nodes[0].T)
self.biases[0] += self.learning_rate * gradient
def backpropagation(self, prediction, target):
"""
This is the backpropagation algorithm, for calculating the updates
of the neural network's parameters.
:param prediction: numpy.ndarray
:param target: numpy.ndarray
"""
self.error_nodes[len(self.weights)] = layer = self.squared_error_cost(prediction, target)
for i in range(len(self.weights)-1, -1, -1):
layer = np.dot(self.weights[i].T, layer)
self.error_nodes[i] = layer
self.update_parameters(target)
def train(self, data, labels, epochs=5):
"""
Trains model by using the corresponding data and label. The method expects Label[i] to be the label of data[i]
:param data: numpy.ndarray
:param labels: numpy.ndarray
:param epochs: int, optional
"""
for epoch in range(epochs):
for i in trange(len(data), desc=str(epoch) + '/' + str(epochs)):
prediction = self.forward_pass(data[i])
# initialize a 10 by 1 matrix of the desired output
target = np.zeros([10, 1], dtype=int)
target[labels[i]] = 1
self.backpropagation(prediction, target)