对y进行独立热编码处理（one-hot处理）

def one_hot_encoder(raw_y):result=[]for i in raw_y:#1-10y_temp=np.zeros(10)#1行10列0向量y_temp[i-1]=1result.append(y_temp)#一行一行写入，每一行都仅有一个1，循环写入5000次return np.array(result)结果[[0. 0. 0. ... 0. 0. 1.][0. 0. 0. ... 0. 0. 1.][0. 0. 0. ... 0. 0. 1.]...[0. 0. 0. ... 0. 1. 0.][0. 0. 0. ... 0. 1. 0.][0. 0. 0. ... 0. 1. 0.]]

序列化权重参数

"""
序列化权重参数函数
"""
def seriallize(a,b):return np.append(a.flatten(),b.flatten())

"""
解序列化
"""
def deserialize(theta_serialize):theta1=theta_serialize[:25*401].reshape(25,401)theta2=theta_serialize[25*401].reshape(10,26)return theta1,theta2

theta_serialize=seriallize(theta1,theta2)#序列化
theta1,theta2=deserialize(theta_serialize)#解序列化

前向传播

"""
前向传播函数
"""
def sigmoid(z):return 1/(1+np.exp(-z))
def feed_forward(theta_serialize,x):theta1,theta2=deserialize(theta_serialize)a1 = xz2 = x @ theta1.Ta2 = sigmoid(z2)a2 = np.insert(a2, 0, 1, axis=1)z3 = a2 @ theta2.Th = sigmoid(z3)return a1,z2,a2,z3,h

代价函数

"""
代价函数（不带正则化）"""
def cost(theta_serialize,x,y):a1, z2, a2, z3, h=feed_forward(theta_serialize,x)J=-np.sum(y*np.log(h)+(1-y)*np.log(1-h))/len(x)return J
"""
代价函数（正则化）
"""
def reg_cost(theta_serialize,x,y,lamda):sum1=np.sum(np.power(theta1[:,1:],2))sum2 = np.sum(np.power(theta2[:, 1:], 2))reg=(sum1+sum2)*lamda /(2*len(x))return reg+cost(theta_serialize,x,y)

反向传播

"""
反向传播
无正则化"""
def sigmoid_gradient(z):return sigmoid(z)*(1-sigmoid(z))def gridient(theta_serialize,x,y):theta1,theta2=deserialize(theta_serialize)a1, z2, a2, z3, h=feed_forward(theta_serialize,x)d3=h-yd2=d3@theta2[:,1:]*sigmoid_gradient(z2)D2=(d3.T@a2)/len(x)D1=(d2.T@a1)/len(x)return seriallize(D1,D2)
"""
反向传播
带正正则化"""
def reg_gradient(theta_serialize,x,y,lamda):D=gridient(theta_serialize,x,y)D1,D2=deserialize(D)theta1, theta2 = deserialize(theta_serialize)D1[:,1:]=D1[:,1:]+theta1[:,1:]*lamda/len(x)return seriallize(D1,D2)

神经网络优化

"""
神经网络优化
"""def nn_training(x,y):init_theta = np.random.uniform(-0.5,0.5,10285)res = minimize(fun =reg_cost,x0=init_theta,args= (x,y,lamda),method='TNC',jac = reg_gradient,options = {'maxiter':300})return reslamda=10# print(cost(theta_serialize,x,y))
# print(reg_cost(theta_serialize,x,y,lamda))
#
res = nn_training(x,y)
raw_y = data['y'].reshape(5000,)
_,_,_,_,h = feed_forward(res.x,x)
y_pred = np.argmax(h,axis=1)+1
acc = np.mean(y_pred == raw_y)
print(acc)

可视化隐藏层

"""
可视化隐藏层
"""
def plot_hidden_layer(theta):theta1,_=deserialize(theta)hidden_layer=theta1[:,1:]fig, ax = plt.subplots(figsize=(8, 8), nrows=5, ncols=5, sharey=True, sharex=True)plt.xticks([])plt.yticks([])for r in range(5):for c in range(5):ax[r, c].imshow(hidden_layer[5 * r + c].reshape(20, 20).T, cmap="gray_r")plt.show()