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backpropagation.py
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backpropagation.py
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import numpy as np
import matplotlib.pylab as plt
def xavier_initializer(ni, nh): # Xavier normal
np.random.seed(1)
nin = ni
nout = nh
ih_weights = np.zeros((ni, nh))
sd = np.sqrt(2.0 / (nin + nout))
for i in range(ni):
for j in range(nh):
x = np.float64(np.random.normal(0.0, sd))
ih_weights[i, j] = x
return ih_weights
def initialize_parameters(layers, L):
np.random.seed(1)
parameters = dict()
for l in range(1, L + 1):
# parameters[f'W{str(l)}'] = np.random.randn(layers[l], layers[l - 1]) / np.sqrt(layers[l - 1])
parameters[f'W{str(l)}'] = xavier_initializer(layers[l], layers[l - 1])
parameters[f'b{str(l)}'] = np.zeros((layers[l], 1))
return parameters
def sigmoid(Z):
A = 1 / (1 + np.exp(-Z))
return A
def d_sigmoid(Z):
sig = sigmoid(Z)
return sig * (1 - sig)
def relu(Z):
A = np.maximum(0, Z)
return A
def d_relu(Z):
Z[Z <= 0] = 0
Z[Z > 0] = 1
return Z
def tanh(Z):
return np.tanh(Z)
def d_tanh(Z):
return 1.0 - np.tanh(Z) ** 2
def linear(Z):
return Z
def d_linear(Z):
return np.ones(Z.shape)
# def softmax(Z):
# # exps = np.exp(Z - np.max(Z))
# # return exps / np.sum(exps)
# Z -= np.max(Z)
# sm = (np.exp(Z) / np.sum(np.exp(Z), axis=0))
# return sm
def softmax(Z):
expZ = np.exp(Z - np.max(Z))
return expZ / expZ.sum(axis=0, keepdims=True)
def categorical_crossentropy(A, Y):
return -np.mean(Y * np.log(A.T))
def plot_cost(costs):
plt.figure()
plt.plot(np.arange(len(costs)), costs)
plt.xlabel("epochs")
plt.ylabel("cost")
plt.show()
def forward_prop(X, parameters, L, af, af_choices):
store = dict()
A = X.T
for l in range(L - 1):
Z = parameters[f'W{str(l + 1)}'].dot(A) + parameters[f'b{str(l + 1)}']
A = af_choices[af[l]][0](Z)
store[f'A{str(l + 1)}'] = A
store[f'W{str(l + 1)}'] = parameters[f'W{str(l + 1)}']
store[f'Z{str(l + 1)}'] = Z
Z = parameters[f'W{str(L)}'].dot(A) + parameters[f'b{str(L)}']
A = af_choices[af[-1]][0](Z)
store[f"A{str(L)}"] = A
store[f"W{str(L)}"] = parameters[f"W{str(L)}"]
store[f"Z{str(L)}"] = Z
return A, store
def backward_prop(X, Y, store, m, L, af, af_choices):
derivatives = dict()
store['A0'] = X.T
A = store[f'A{str(L)}']
dZ = A - Y.T
dW = (1. / m) * dZ.dot(store[f'A{str(L - 1)}'].T)
db = (1. / m) * np.sum(dZ, axis=1, keepdims=True)
dA_prev = store[f'W{str(L)}'].T.dot(dZ)
derivatives[f'dW{str(L)}'] = dW
derivatives[f'db{str(L)}'] = db
for l in range(L - 1, 0, -1):
dZ = dA_prev * af_choices[af[l - 1]][1](store[f'Z{str(l)}'])
dW = (1. / m) * dZ.dot(store[f'A{str(l - 1)}'].T)
db = (1. / m) * np.sum(dZ, axis=1, keepdims=True)
if l > 1:
dA_prev = store[f'W{str(l)}'].T.dot(dZ)
derivatives[f'dW{str(l)}'] = dW
derivatives[f'db{str(l)}'] = db
return derivatives
def pred(X, Y, parameters, L, af, af_choices):
A, store = forward_prop(X, parameters, L, af, af_choices)
Y_hat = np.argmax(A, axis=0)
Y = np.argmax(Y, axis=1)
accuracy = (Y_hat == Y).mean()
return accuracy * 100