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Digit Recognition with DNN by @akshaybahadur21
import numpy as np
import matplotlib.pyplot as plt
def softmax(z):
cache = z
z -= np.max(z)
sm = (np.exp(z).T / np.sum(np.exp(z), axis=1))
return sm, cache
def relu(z):
"""
:param z:
:return:
"""
s = np.maximum(0, z)
cache = z
return s, cache
def softmax_backward(dA, cache):
"""
:param dA:
:param activation_cache:
:return:
"""
z = cache
z -= np.max(z)
s = (np.exp(z).T / np.sum(np.exp(z), axis=1))
dZ = dA * s * (1 - s)
return dZ
def relu_backward(dA, cache):
"""
:param dA:
:param activation_cache:
:return:
"""
Z = cache
dZ = np.array(dA, copy=True) # just converting dz to a correct object.
dZ[Z <= 0] = 0
return dZ
def initialize_parameters_deep(dims):
"""
:param dims:
:return:
"""
np.random.seed(3)
params = {}
L = len(dims)
for l in range(1, L):
params['W' + str(l)] = np.random.randn(dims[l], dims[l - 1]) * 0.01
params['b' + str(l)] = np.zeros((dims[l], 1))
return params
def linear_forward(A, W, b):
"""
:param A:
:param W:
:param b:
:return:
"""
Z = np.dot(W, A) + b
cache = (A, W, b)
return Z, cache
def linear_activation_forward(A_prev, W, b, activation):
"""
:param A_prev:
:param W:
:param b:
:param activation:
:return:
"""
if activation == "softmax":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = softmax(Z.T)
elif activation == "relu":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
cache = (linear_cache, activation_cache)
return A, cache
def L_model_forward(X, params):
"""
:param X:
:param params:
:return:
"""
caches = []
A = X
L = len(params) // 2 # number of layers in the neural network
# Implement [LINEAR -> RELU]*(L-1). Add "cache" to the "caches" list.
for l in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev,
params["W" + str(l)],
params["b" + str(l)],
activation='relu')
caches.append(cache)
A_last, cache = linear_activation_forward(A,
params["W" + str(L)],
params["b" + str(L)],
activation='softmax')
caches.append(cache)
return A_last, caches
def compute_cost(A_last, Y):
"""
:param A_last:
:param Y:
:return:
"""
m = Y.shape[1]
cost = (-1 / m) * np.sum(Y * np.log(A_last))
cost = np.squeeze(cost) # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).
return cost
def linear_backward(dZ, cache):
"""
:param dZ:
:param cache:
:return:
"""
A_prev, W, b = cache
m = A_prev.shape[1]
dW = (1. / m) * np.dot(dZ, cache[0].T)
db = (1. / m) * np.sum(dZ, axis=1, keepdims=True)
dA_prev = np.dot(cache[1].T, dZ)
return dA_prev, dW, db
def linear_activation_backward(dA, cache, activation):
"""
:param dA:
:param cache:
:param activation:
:return:
"""
linear_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif activation == "softmax":
dZ = softmax_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
def L_model_backward(A_last, Y, caches):
"""
:param A_last:
:param Y:
:param caches:
:return:
"""
grads = {}
L = len(caches) # the number of layers
m = A_last.shape[1]
Y = Y.reshape(A_last.shape) # after this line, Y is the same shape as A_last
dA_last = - (np.divide(Y, A_last) - np.divide(1 - Y, 1 - A_last))
current_cache = caches[-1]
grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dA_last,
current_cache,
activation="softmax")
for l in reversed(range(L - 1)):
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 2)], current_cache,
activation="relu")
grads["dA" + str(l + 1)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
def update_params(params, grads, alpha):
"""
:param params:
:param grads:
:param alpha:
:return:
"""
L = len(params) // 2 # number of layers in the neural network
for l in range(L):
params["W" + str(l + 1)] = params["W" + str(l + 1)] - alpha * grads["dW" + str(l + 1)]
params["b" + str(l + 1)] = params["b" + str(l + 1)] - alpha * grads["db" + str(l + 1)]
return params
def model_DL( X, Y, Y_real, test_x, test_y, layers_dims, alpha, num_iterations, print_cost): # lr was 0.009
"""
Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
Arguments:
X -- data, numpy array of shape (number of examples, num_px * num_px * 3)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
layers_dims -- list containing the input size and each layer size, of length (number of layers + 1).
alpha -- learning rate of the gradient descent update rule
num_iterations -- number of iterations of the optimization loop
print_cost -- if True, it prints the cost every 100 steps
Returns:
params -- params learnt by the model. They can then be used to predict.
"""
np.random.seed(1)
costs = [] # keep track of cost
params = initialize_parameters_deep(layers_dims)
for i in range(0, num_iterations):
A_last, caches = L_model_forward(X, params)
cost = compute_cost(A_last, Y)
grads = L_model_backward(A_last, Y, caches)
if (i > 800 and i<1700):
alpha1 = 0.80 * alpha
params = update_params(params, grads, alpha1)
elif(i>=1700):
alpha1 = 0.50 * alpha
params = update_params(params, grads, alpha1)
else:
params = update_params(params, grads, alpha)
if print_cost and i % 100 == 0:
print("Cost after iteration %i: %f" % (i, cost))
if print_cost and i % 100 == 0:
costs.append(cost)
predictions = predict(params, X)
print("Train accuracy: {} %", sum(predictions == Y_real) / (float(len(Y_real))) * 100)
predictions = predict(params, test_x)
print("Test accuracy: {} %", sum(predictions == test_y) / (float(len(test_y))) * 100)
#plt.plot(np.squeeze(costs))
#plt.ylabel('cost')
#plt.xlabel('iterations (per tens)')
#plt.title("Learning rate =" + str(alpha))
#plt.show()
return params
def predict(parameters, X):
A_last, cache = L_model_forward(X, parameters)
predictions = np.argmax(A_last, axis=0)
return predictions
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