用Python进行神经网络逻辑回归
学习内容：
使用神经网络进行逻辑回归，学习算法的总体框架，包括初始化参数、计算成本函数和梯度、使用优化算法（梯度下降）
使用到的包：
numpy, matplotlib.pyplot, h5py, scipy, PIL.Image, scipy.ndimage, (lr_utils.load_dataset)
读取图片：
plt.imshow(train_set_x_orig[index]
了解训练集和测试集的维度：
train_set_x_orig 是shape为 (m_train, num_px, num_px, 3) 的array
可以通过train_set_x_orig[0]来取得m_train
为方便计算，一般要将图片的形状由(num_px, num_px, 3)转化为(num_px * num_px * 3, 1)，使每一列的数组代表一张平铺的图片。
X_flatten = X.reshape(X.shape[0], -1).T
对每个像素进行归一化预处理
train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.
需要定义的函数:
def sigmoid(z):
s = 1 / (1 + np.exp(-z))
return s
这里z = np.dot(w.T, x) + b
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def initialize_with_zeros(dim):
w = np.zeros((dim, 1))
b = 0
return w, b
这里dim = num_px * num_px * 3
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def propagate(w, b, X, Y):m = X.shape[1] # number of examples
A = sigmoid(np.dot(w.T, X) + b) # forward
cost = - np.sum(Y * np.log(A) + (1 - Y) * np.log(1 - A)) / m
dw = np.dot(X, (A - Y).T) / m # backward
db = np.sum((A - Y)) / m
cost = np.squeeze(cost)
grads = {'dw': dw, 'db': db}
return grads, cost
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def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost=False):
costs = []
for i in range(num_iterations):
grads, cost = propagate(w, b, X, Y)
dw = grads['dw']
db = grads['db']
w = w - learning_rate * dw
b = b - learning_rate * db
if i % 100 ==0:
costs.append(cost)
if print_cost and i % 100 == 0:
print ('Cost after interation %i: %f' %(i, cost))
params = {'w': w, 'b': b}
grads = {'dw': dw, 'db': db}
return params, grads, costs
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def predict(w, b, X):
m = X.shape[1]
Y_prediction = np.zeros((1, m))
w = w.reshape(X.shape[0], 1)
A = sigmoid(np.dot(w.T, X) + b
for i in range(A.shape[1]):
if A[0, i] <= 0.5:
Y_prediction[0, i] = 0
else:
Y_prediction[0, i] =1
return Y_prediction
模型：
def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
w, b = initialize_with_zeros(X_train.shape[0])
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_interations, learning_rate, print_cost)
w = parameters['w']
b = parameters['b']
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)
print('train accuracy: {} %'.format(100 - np.mean(np.abs(Y_prediction_train)) * 100))
print('test accuracy: {} %'.format(100 - np.mean(np.abs(Y_prediction_test)) * 100))
d = {'cost': cost, 'Y_prediction_test': Y_prediction_test, 'Y_prediction_train': Y_prediction_train, 'w': w, 'b': b, 'learning_rate': learning_rate, 'num_iterations': num_iterations}
return d
读取图片：
index =
plt.imshow(test_set_x[:, index].reshape((num_px, num_px, 3)))
print('y = ' + str(test_set_y[0, index]) + ', you predicted that it is a \ ' ' + classes[d['Y_prediction_test'][0, index]].decode('utf-8') + '\' picture.')
图形化成本函数：
costs = np.squeeze(d['costs'])
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title('Learning rate =' + str(d['learning_rate']))
plt.show()
进一步探索：
learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
print('learning rate is : ' + str(i))
models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_interations = 1500, learning_rate = i, print_cost = False)
print('\n' + '---------------------------------')
for i in learning_rates:
plt.plot(np.squeeze(models[str(i)]['costs']), label = str(models[str(i)]['learning_rate']))
plt.ylabel('cost')
plt.xlabel('iterations')
legend = plt.legend(loc='upper center', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()
测试新图片：
my_image = ' '
fname = 'images/' + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(num_px, num_px)).reshape((1, num_px * num_px * 3)).T
my_predicted_image = predict(d['w'], d['b'], my_image)
plt.imshow(image)
print('y= ' + str(np.squeeze(my_predicted_image)) + ', your algorithm predicts a \' ' + classes[int(np.squeeze(my_predicted_image)), ].decode('utf-8') + '\ 'picture.')