前言：

文章以Andrew Ng 的 deeplearning.ai 视频课程为主线，记录Programming Assignments 的实现过程。相对于斯坦福的CS231n课程，Andrew的视频课程更加简单易懂，适合深度学习的入门者系统学习！

这一部分的作业主要涉及到Logistic Regression，Logistic Regression 用于Binary Classification二分类的问题（0,1），基于多分类的Softmax也是在Logistic Regression的基础上改进而来，这次Assignment的数据集为data.h5，包含train_data和test_data，label分别为cat和non_cat,，首先我们看一下数据集，对数据集有一个直观的认识：

1 Overview of the Problem set

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

index = 25

plt.imshow(train_set_x_orig[index])

print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") +  "' picture.")

程序输出：y = [1], it's a 'cat' picture.

我们需要对图片进行预处理，从而转化为我们需要的shape类型，并且需要normalization从而加速收敛

m_train = train_set_x_orig.shape[0]

m_test = test_set_x_orig.shape[0]

num_px = train_set_x_orig.shape[1]

train_set_x_flatten =train_set_x_orig.reshape([train_set_x_orig.shape[0],-1]).T

test_set_x_flatten = test_set_x_orig.reshape([test_set_x_orig.shape[0],-1]).T

print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape))

print ("train_set_y shape: " + str(train_set_y.shape))

print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape))

print ("test_set_y shape: " + str(test_set_y.shape))

print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))

train_set_x = train_set_x_flatten/255.

test_set_x = test_set_x_flatten/255.

2 General Architecture of the learning algorithm

The following figure explains the architecture of the learning algorithm,this algorithm can distinguish cat images from non-cat images:

3 Building the parts of our algorithm

def sigmoid(z):

s = 1./(1+np.exp(-z))

return s

def initialize_with_zeros(dim):

w =np.zeros((dim,1))

b = 0

return w, b

def propagate(w, b, X, Y):

A = sigmoid(np.dot(w.T,X)+b)                                 

cost =-1/m*(np.sum(Y*np.log(A)+(1-Y)*np.log(1-A)))                               

dw =1/m*np.dot(X,(A-Y).T)

db = 1/m*np.sum(A-Y)

cost = np.squeeze(cost)

grads = {"dw": dw,

"db": db}

return grads, cost

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 iteration %i: %f" %(i, cost))

params = {"w": w,

"b": b}

grads = {"dw": dw,

"db": db}

return params, grads, costs

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]=1

else:

Y_prediction[0][i]=0

return Y_prediction

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_iterations,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 - Y_train)) * 100))

print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

d = {"costs": costs,

"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

现在我们可以用model函数来进行训练：

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)

训练结果如图所示：

index = 1

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.")

我们可以看一下随着迭代次数的增加，cost的变化情况

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()

对于不同的learning_rate，cost曲线变化明显：

4 Test with your own image

我们可以用模型训练出来的参数对图片进行预测，判断是否为猫的图片

my_image = "my_image.jpg"

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.")

预测结果为：

y = 0.0, your algorithm predicts a "non-cat" picture.

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