吴恩达机器学习作业3.2神经网络

# neural network（神经网络）
import matplotlib.pyplot as plt
import numpy as np
import scipy.io as sio
import matplotlib
import scipy.optimize as opt
from sklearn.metrics import classification_report#这个包是评价报告

def load_data(path, transpose=True):data = sio.loadmat(path)y = data.get('y')  # (5000,1)y = y.reshape(y.shape[0])  # make it back to column vectorX = data.get('X')  # (5000,400)if transpose:# for this dataset, you need a transpose to get the orientation rightX = np.array([im.reshape((20, 20)).T for im in X])# and I flat the image again to preserve the vector presentationX = np.array([im.reshape(400) for im in X])
return X, y

X, y = load_data('ex3data1.mat')
print(X.shape)
print(y.shape)

def plot_an_image(image):
#     """
#     image : (400,)
#     """fig, ax = plt.subplots(figsize=(1, 1))ax.matshow(image.reshape((20, 20)), cmap=matplotlib.cm.binary)plt.xticks(np.array([]))  # just get rid of ticksplt.yticks(np.array([]))

#绘图函数
pick_one = np.random.randint(0, 5000)
plot_an_image(X[pick_one, :])
plt.show()
print('this should be {}'.format(y[pick_one]))

def plot_100_image(X):""" sample 100 image and show themassume the image is squareX : (5000, 400)"""size = int(np.sqrt(X.shape[1]))# sample 100 image, reshape, reorg itsample_idx = np.random.choice(np.arange(X.shape[0]), 100)  # 100*400sample_images = X[sample_idx, :]fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))for r in range(10):for c in range(10):ax_array[r, c].matshow(sample_images[10 * r + c].reshape((size, size)),cmap=matplotlib.cm.binary)plt.xticks(np.array([]))plt.yticks(np.array([]))  #绘图函数，画100张图片
plot_100_image(X)
plt.show()

raw_X, raw_y = load_data('ex3data1.mat')
print(raw_X.shape)
print(raw_y.shape)

# 准备数据
# add intercept=1 for x0
X = np.insert(raw_X, 0, values=np.ones(raw_X.shape[0]), axis=1)#插入了第一列（全部为1）
X.shape

# y have 10 categories here. 1..10, they represent digit 0 as category 10 because matlab index start at 1
# I'll ditit 0, index 0 again
y_matrix = []
for k in range(1, 11):y_matrix.append((raw_y == k).astype(int))    # 见配图 "向量化标签.png"
# last one is k==10, it's digit 0, bring it to the first position，最后一列k=10，都是0，把最后一列放到第一列
y_matrix = [y_matrix[-1]] + y_matrix[:-1]
y = np.array(y_matrix)
y.shape
# 扩展 5000*1 到 5000*10
#     比如 y=10 -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]: ndarray
#     """y

# train 1 model（训练一维模型）
def cost(theta, X, y):''' cost fn is -l(theta) for you to minimize'''return np.mean(-y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)))

def regularized_cost(theta, X, y, l=1):'''you don't penalize theta_0'''theta_j1_to_n = theta[1:]regularized_term = (l / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()return cost(theta, X, y) + regularized_term

def regularized_gradient(theta, X, y, l=1):'''still, leave theta_0 alone'''theta_j1_to_n = theta[1:]regularized_theta = (l / len(X)) * theta_j1_to_n# by doing this, no offset is on theta_0regularized_term = np.concatenate([np.array([0]), regularized_theta])return gradient(theta, X, y) + regularized_term

def sigmoid(z):return 1 / (1 + np.exp(-z))
def gradient(theta, X, y):'''just 1 batch gradient'''return (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)
def logistic_regression(X, y, l=1):"""generalized logistic regressionargs:X: feature matrix, (m, n+1) # with incercept x0=1y: target vector, (m, )l: lambda constant for regularizationreturn: trained parameters"""# init thetatheta = np.zeros(X.shape[1])# train itres = opt.minimize(fun=regularized_cost,x0=theta,args=(X, y, l),method='TNC',jac=regularized_gradient,options={'disp': True})# get trained parametersfinal_theta = res.xreturn final_theta

def predict(x, theta):prob = sigmoid(x @ theta)return (prob >= 0.5).astype(int)
t0 = logistic_regression(X, y[0])
print(t0.shape)
y_pred = predict(X, t0)
print('Accuracy={}'.format(np.mean(y[0] == y_pred)))

# train k model（训练k维模型）
k_theta = np.array([logistic_regression(X, y[k]) for k in range(10)])
print(k_theta.shape)
'''# 进行预测
* think about the shape of k_theta, now you are making $X\times\theta^T$
> $(5000, 401) \times (10, 401).T = (5000, 10)$
* after that, you run sigmoid to get probabilities and for each row, you find the highest prob as the answer
'''

prob_matrix = sigmoid(X @ k_theta.T)
np.set_printoptions(suppress=True)
prob_matrix

y_pred = np.argmax(prob_matrix, axis=1)#返回沿轴axis最大值的索引，axis=1代表行
y_pred

y_answer = raw_y.copy()
y_answer[y_answer==10] = 0
print(classification_report(y_answer, y_pred))

# 神经网络模型图示
'''<img style="float: left;" src="../img/nn_model.png">
'''

def load_weight(path):data = sio.loadmat(path)return data['Theta1'], data['Theta2']
theta1, theta2 = load_weight('ex3weights.mat')
theta1.shape, theta2.shape

#因此在数据加载函数中，原始数据做了转置，然而，转置的数据与给定的参数不兼容，因为这些参数是由原始数据训练的。 所以为了应用给定的参数，我需要使用原始数据（不转置）
X, y = load_data('ex3data1.mat',transpose=False)
X = np.insert(X, 0, values=np.ones(X.shape[0]), axis=1)  # intercept
X.shape, y.shape

# feed forward prediction（前馈预测）
a1 = X
z2 = a1 @ theta1.T # (5000, 401) @ (25,401).T = (5000, 25)
z2.shape

z2 = np.insert(z2, 0, values=np.ones(z2.shape[0]), axis=1)
a2 = sigmoid(z2)
a2.shape
z3 = a2 @ theta2.T
z3.shape

a3 = sigmoid(z3)
a3

y_pred = np.argmax(a3, axis=1) + 1  # numpy is 0 base index, +1 for matlab convention，返回沿轴axis最大值的索引，axis=1代表行
y_pred.shape

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