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bpnn.py
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# Standard library
import random
# Third-party libraries
import numpy as np
class Network(object):
def __init__(self,sizes): #the list sizes contains the number of neurons in the respective layers.
self.num_layers = len(sizes) #the number of the layers in Network
self.sizes = sizes
self.biases = [np.random.randn(y,1) for y in sizes[1:]]
self.weights = [np.random.randn(y,x)
for x,y in zip(sizes[:-1],sizes[1:])]
# print(len(self.biases))
# print(len(self.weights))
# print(self.biases[-1].shape)
# print(self.weights[-1].shape)
# print(self.weights[0].shape)
# print(self.weights[1].shape)
def feedforward(self,a):
"""Return the output of the network if "a" is input"""
a = a.reshape((len(a),1))
# print('a shape', a.shape)
for b,w in zip(self.biases,self.weights):
# print(w.shape)
# print(a.shape)
# print(b.shape)
a = sigmoid(np.dot(w,a) + b)
# print("a shape", a.shape)
return a
def SGD(self, training_data, training_labels, epochs, mini_batch_size,eta,
test_data = None, test_labels=None):
"""
Train the neural network using mini-batch stochastic gradient descent.
The "training_data" is a list of tuples "(x,y)" representing the training inputs
and the desired output. The other non-optional parameters are self-explanatory.
If "test_data" is provided then the network will be evaluated against the test
data after each epoch, and partial progress printed out. This is useful for tracking
process, but slows things down substantially.
"""
tr_data = []
for i in range(0,training_data.shape[1]):
label = np.zeros((2,1))
label[int(training_labels[i])] = 1
tr_data.append((training_data[:,i].reshape((training_data.shape[0],1)), label))
training_data = tr_data
ts_data = []
for i in range(0,test_data.shape[1]):
ts_data.append((test_data[:,i], test_labels[i]))
test_data = ts_data
if test_data:
n_test = len(test_data)
n = len(training_data)
for j in range(epochs):
random.shuffle(training_data) #rearrange the training_data randomly
mini_batches = [ training_data[k:k + mini_batch_size]
for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch,eta)
if test_data:
eva = self.evaluate(test_data)
pred = self.predict(test_data)
print("Epoch {0}: {1} / {2} = {3}".format(j,eva,n_test,eva/n_test))
return (self.confusion_matrix(test_data), pred)
else:
print("Epoch {0} complete".format(j))
def SGD_prob(self, training_data, training_labels, epochs, mini_batch_size,eta,
test_data = None, test_labels=None):
"""
Train the neural network using mini-batch stochastic gradient descent.
The "training_data" is a list of tuples "(x,y)" representing the training inputs
and the desired output. The other non-optional parameters are self-explanatory.
If "test_data" is provided then the network will be evaluated against the test
data after each epoch, and partial progress printed out. This is useful for tracking
process, but slows things down substantially.
"""
probs = np.zeros((test_data.shape[1],2), dtype=np.float64)
tr_data = []
for i in range(0,training_data.shape[1]):
label = np.zeros((2,1))
label[int(training_labels[i])] = 1
tr_data.append((training_data[:,i].reshape((training_data.shape[0],1)), label))
training_data = tr_data
ts_data = []
for i in range(0,test_data.shape[1]):
ts_data.append((test_data[:,i], test_labels[i]))
test_data = ts_data
num_iter = 20
if test_data:
for i in range(0,num_iter):
n_test = len(test_data)
n = len(training_data)
for j in range(epochs):
random.shuffle(training_data) #rearrange the training_data randomly
mini_batches = [ training_data[k:k + mini_batch_size]
for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch,eta)
if test_data:
eva = self.evaluate_verbose(test_data)
for j in range(0,n_test):
if eva[j][0] == 0:
probs[j,0] += 1
else:
probs[j,1] += 1
probs[:,0] = probs[:,0]/num_iter
probs[:,1] = probs[:,1]/num_iter
return probs
def update_mini_batch(self,mini_batch,eta):
"""
Update the network's weights and biases by applying gradient descent using backpropagation
to a single mini batch. The "mini_batch" is a list of tuples "(x,y)" and "eta" is the learning
rate.
"""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def predict(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
# print('test_data shape', test_data[0][0].shape)
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return test_results
def evaluate(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
# print('test_data shape', test_data[0][0].shape)
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
num_samples = len(test_results)
fp = 0
fn = 0
tp = 0
tn = 0
for i in range(0, num_samples):
if test_results[i][0] == 0:
if test_results[i][0] == test_results[i][1]:
tn += 1
else:
fn += 1
else:
if test_results[i][0] == test_results[i][1]:
tp += 1
else:
fp += 1
print('TP:',tp,'TN:',tn,'FP:',fp,'FN:',fn)
# print("Evaluate")
# print(self.feedforward(test_data[0][0]))
# print(np.argmax(self.feedforward(test_data[0][0])))
# print(test_results[0:10])
return sum(int(x == y) for (x, y) in test_results)
def confusion_matrix(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
# print('test_data shape', test_data[0][0].shape)
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
num_samples = len(test_results)
fp = 0
fn = 0
tp = 0
tn = 0
for i in range(0, num_samples):
if test_results[i][0] == 0:
if test_results[i][0] == test_results[i][1]:
tn += 1
else:
fn += 1
else:
if test_results[i][0] == test_results[i][1]:
tp += 1
else:
fp += 1
conf_mat = np.zeros((2,2))
conf_mat[0,0] = tp
conf_mat[0,1] = fp
conf_mat[1,0] = fn
conf_mat[1,1] = tn
return conf_mat
def evaluate_verbose(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return test_results
def cost_derivative(self, output_activations, y):
"""Return the vector of partial derivatives \partial C_x /
\partial a for the output activations."""
return (output_activations-y)
#### Miscellaneous functions
def sigmoid(z):
# print(z.shape)
"""The sigmoid function."""
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z):
"""Derivative of the sigmoid function."""
return sigmoid(z)*(1-sigmoid(z))