(一)####
1.numpy.random.seed()
seed( ) 用于指定随机数生成时所用算法开始的整数值，如果使用相同的seed( )值，则每次生成的随机数都相同，如果不设置这个值，则系统根据时间来自己选择这个值，此时每次生成的随机数因时间差异而不同。
seed( ) 用于指定随机数生成时所用算法开始的整数值。
1.如果使用相同的seed( )值，则每次生成的随即数都相同；
2.如果不设置这个值，则系统根据时间来自己选择这个值，此时每次生成的随机数因时间差异而不同。
3.设置的seed()值仅一次有效
2.plt.rcParams()
plt.rcParams['image.interpolation'] = 'nearest' # 最近邻差值:
像素为正方形 #Interpolation/resampling即插值，是一种图像处理方法，它可以为数码图像增加或减少象素的数目。
(二)构建L-layer层神经网络的主要步骤：
1.初始化参数
其中，用到的random函数，np.random.randn(x,y)表示返回的是一个标准正态分布的x*y的矩阵。
个人想法：randn表示的是random+normal呀！
np.zeros(shape, dtype=float, order='C')
注意要标明此0矩阵的维度问题，默认为float类型，但要注意当写该方法时需要将默认的写为np.zeros((3,4)),注意要有两个括号喔！
dtype类型：t ,位域,如t4代表4位
b,布尔值，true or false
i,整数,如i8(64位）
u,无符号整数，u8(64位）
f,浮点数，f8（64位）
c,浮点负数，
o,对象，
s,a，字符串，s24
u,unicode,u24
def initialize_parameters_deep(layer_dims):
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layer_dims[l],layer_dims[l-1])*0.01
parameters['b' + str(l)] = np.zeros((layer_dims[l],1))
return parameters
三行代码完成整个参数的初始化
2.前馈神经网络
①线性计算
def linear_forward(A, W, b):
Z = np.dot(W,A)+b
assert(Z.shape == (W.shape[0], A.shape[1]))
cache = (A, W, b)
return Z, cache
②求激活函数
def linear_activation_forward(A_prev, W, b, activation):
if activation == "sigmoid":
Z, linear_cache =linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
assert (A.shape == (W.shape[0], A_prev.shape[1]))
cache = (linear_cache, activation_cache)
return A, cache
③L-Layer Model
def L_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for l in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev , parameters["W" + str(l)], parameters["b" + str(l)], "relu")
caches.append(cache)
AL, cache = linear_activation_forward(A,parameters['W' + str(L)], parameters['b' + str(L)], "sigmoid")
caches.append(cache)
assert(AL.shape == (1,X.shape[1]))
return AL, caches
其中的caches表示的是运算过程中的A,W,b,z
3.计算代价函数
def compute_cost(AL, Y):
m = Y.shape[1]
cost = (-1/m)*np.sum(Y*np.log(AL)+(1-Y)*np.log(1-AL))
cost = np.squeeze(cost) # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).
assert(cost.shape == ())
return cost
4.后馈神经网络
①计算梯度
def linear_backward(dZ, cache):
A_prev, W, b = cache
m = A_prev.shape[1]
dW =1/m*np.dot(dZ,A_prev.T)
db = np.sum(dZ,axis=1,keepdims=True)/m
dA_prev = np.dot(W.T,dZ)
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
②计算激活函数对A的倒数
def linear_activation_backward(dA, cache, activation):
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 == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ,linear_cache)
return dA_prev, dW, db
③L-Model Backward
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches) # the number of layers
m = AL.shape[1]
Y = Y.reshape(AL.shape)
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
current_cache = caches[L-1]
grads["dA" + str(L-1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL,current_cache, "sigmoid")
for l in reversed(range(L-1)):
current_cache = caches[L-2]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l+1)], current_cache, "relu")
grads["dA" + str(l)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
问题：感觉对caches的维度表示怀疑，，
其中包含A，W，b，Z
5.更新参数
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2
for l in range(L):
parameters["W" + str(l+1)] = parameters["W" + str(l+1)]-learning_rate*grads["dW" + str(l+1)]
parameters["b" + str(l+1)] = parameters["b" + str(l+1)]-learning_rate*grads["db" + str(l+1)]
return parameters
(三)用深度学习实现图片的分类
1.导入包
2.导入数据集
3.定义两层的神经网络函数，可调用之前使用过的函数
def initialize_parameters(n_x, n_h, n_y):
...
return parameters
def linear_activation_forward(A_prev, W, b, activation):
...
return A, cache
def compute_cost(AL, Y):
...
return cost
def linear_activation_backward(dA, cache, activation):
...
return dA_prev, dW, db
def update_parameters(parameters, grads, learning_rate):
...
return parametersdef two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
np.random.seed(1)
grads = {}
costs = [] # to keep track of the cost
m = X.shape[1] # number of examples
(n_x, n_h, n_y) = layers_dims
# Initialize parameters dictionary, by calling one of the functions you'd previously implemented
parameters = initialize_parameters(n_x, n_h, n_y)
# Get W1, b1, W2 and b2 from the dictionary parameters.
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1, W2, b2". Output: "A1, cache1, A2, cache2".
A1, cache1 = linear_activation_forward(X, W1, b1, "relu")
A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid")
# Compute cost
cost = compute_cost(A2, Y)
# Initializing backward propagation
dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
# Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1".
dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid")
dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu")
# Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2
grads['dW1'] = dW1
grads['db1'] = db1
grads['dW2'] = dW2
grads['db2'] = db2
# Update parameters.
parameters = update_parameters(parameters, grads, learning_rate)
# Retrieve W1, b1, W2, b2 from parameters
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Print the cost every 100 training example
if print_cost and i % 100 == 0:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if print_cost and i % 100 == 0:
costs.append(cost)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
4.定义多层的神经网络，可调用之前的函数
def initialize_parameters_deep(layers_dims):
...
return parameters
def L_model_forward(X, parameters):
...
return AL, caches
def compute_cost(AL, Y):
...
return cost
def L_model_backward(AL, Y, caches):
...
return grads
def update_parameters(parameters, grads, learning_rate):
...
return parameterslayers_dims = [12288, 20, 7, 5, 1]
def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
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).
learning_rate -- 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:
parameters -- parameters learnt by the model. They can then be used to predict.
np.random.seed(1)
costs = [] # keep track of cost
# Parameters initialization. (≈ 1 line of code)
parameters =initialize_parameters_deep(layers_dims)
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
AL, caches = L_model_forward(X, parameters)
# Compute cost.
cost = compute_cost(AL, Y)
# Backward propagation.
grads = L_model_backward(AL, Y, caches)
# Update parameters.
parameters = update_parameters(parameters, grads, learning_rate)
# Print the cost every 100 training example
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)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters