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main.py
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import numpy as np # 导入库
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab
def load_mnist(): # 函数功能： 载入本地.npz类型minst数据
path = 'mnist.npz' # 放置mnist.py的目录、注意斜杠和r
f = np.load(path)
x_train, y_train = f['x_train'], f['y_train']
x_test, y_test = f['x_test'], f['y_test']
f.close()
return (x_train, y_train, x_test, y_test)
def calculate_loss(model, X, y): # 函数功能：计算损失
W1, b1, W2, b2, W3, b3, W4, b4, W5, b5 = model['W1'], model['b1'], model['W2'], model['b2'], model['W3'], model[
'b3'], model['W4'], model['b4'], model['W5'], model['b5']
z1 = X.dot(W1) + b1 # dot点积
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
a2 = np.tanh(z2)
z3 = a2.dot(W3) + b3 # Forward
a3 = np.tanh(z3)
z4 = a3.dot(W4) + b4
a4 = np.tanh(z4)
z5 = a4.dot(W5) + b5
exp_scores = np.exp(z5)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # 标准化
num_examples = X.shape[0]
corect_logprobs = -np.log(probs[range(num_examples), y])
data_loss = np.sum(corect_logprobs)
# data_loss += reg_lambda / 2 * (
# np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3)) + np.sum(np.square(W4)))
return 1. / num_examples * data_loss
def predict(model, x): # Forward
W1, b1, W2, b2, W3, b3, W4, b4, W5, b5 = \
model['W1'], model['b1'], model['W2'], model['b2'], model['W3'], \
model['b3'], model['W4'], model['b4'], model['W5'], model['b5']
z1 = x.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
a2 = np.tanh(z2)
z3 = a2.dot(W3) + b3
a3 = np.tanh(z3)
z4 = a3.dot(W4) + b4
a4 = np.tanh(z4)
z5 = a4.dot(W5) + b5
exp_scores = np.exp(z5)
probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # 标准化
#输出概率最大的点
return np.argmax(probs, axis=1) # argmax返回使得f（x）取得最大值的变量点x的点集合
def build_model(X, y, nn_hdim, epsilon, reg_lambda, num_passes=20000, print_loss=False):
np.random.seed(0) # 随机数生成，seed种子，固定随机数
num_examples = X.shape[0]
nn_input_dim = nn_hdim[0]
print('input dim', nn_input_dim)
hdim1 = nn_hdim[1]
W1 = np.random.randn(nn_input_dim, hdim1) / np.sqrt(hdim1)
b1 = np.zeros((1, hdim1)) # zeros生成零矩阵1Xhdiml1
print('fc: %d -> %d' % (nn_input_dim, hdim1))
hdim2 = nn_hdim[2]
W2 = np.random.randn(hdim1, hdim2) / np.sqrt(hdim2)
b2 = np.zeros((1, hdim2))
print('fc: %d -> %d' % (hdim1, hdim2))
hdim3 = nn_hdim[3]
W3 = np.random.randn(hdim2, hdim3) / np.sqrt(hdim3)
b3 = np.zeros((1, hdim3))
print('fc: %d -> %d' % (hdim2, hdim3))
hdim4 = nn_hdim[4]
W4 = np.random.randn(hdim3, hdim4) / np.sqrt(hdim4)
b4 = np.zeros((1, hdim4))
print('fc: %d -> %d' % (hdim3, hdim4))
hdim5 = nn_hdim[5]
W5 = np.random.randn(hdim4, hdim5) / np.sqrt(hdim5)
b5 = np.zeros((1, hdim5))
print('fc: %d -> %d' % (hdim4, hdim5))
# train：
model = {}
bs = 128 #batchsize
nbs_per_epoch = int(num_examples / bs)
for i in range(0, num_passes):
j = i % nbs_per_epoch
if 0 == j:
ridx = np.asarray(list(range(num_examples)))
np.random.shuffle(ridx)
X = X[ridx, :]
y = y[ridx]
Xb = X[j * bs:(j + 1) * bs, :]
yb = y[j * bs:(j + 1) * bs]
# Forward propagation
z1 = Xb.dot(W1) + b1
a1 = np.tanh(z1)
z2 = a1.dot(W2) + b2
a2 = np.tanh(z2)
z3 = a2.dot(W3) + b3
a3 = np.tanh(z3)
z4 = a3.dot(W4) + b4
a4 = np.tanh(z4)
z5 = a4.dot(W5) + b5
exp_scores = np.exp(z5)
# Backpropagation
delta_loss = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
delta_loss[range(bs), yb] -= 1
dW5 = (a4.T).dot(delta_loss)
db5 = np.sum(delta_loss, axis=0, keepdims=True)
delta5 = delta_loss.dot(W5.T) * (1 - np.power(a4, 2)) # power返回给定数字乘幂
dW4 = (a3.T).dot(delta5)
db4 = np.sum(delta5, axis=0, keepdims=True)
delta4 = delta5.dot(W4.T) * (1 - np.power(a3, 2))
dW3 = (a2.T).dot(delta4)
db3 = np.sum(delta4, axis=0, keepdims=True)
delta3 = delta4.dot(W3.T) * (1 - np.power(a2, 2))
dW2 = a1.T.dot(delta3)
db2 = np.sum(delta3, axis=0, keepdims=True)
delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
dW1 = (Xb.T).dot(delta2)
db1 = np.sum(delta2, axis=0)
# dW5 += reg_lambda * W5
# dW4 += reg_lambda * W4
# dW3 += reg_lambda * W3
# dW2 += reg_lambda * W2
# dW1 += reg_lambda * W1
W1 += -epsilon * dW1
b1 += -epsilon * db1
W2 += -epsilon * dW2
b2 += -epsilon * db2
W3 += -epsilon * dW3
b3 += -epsilon * db3
W4 += -epsilon * dW4
b4 += -epsilon * db4
W5 += -epsilon * dW5
b5 += -epsilon * db5
model = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2,
'W3': W3, 'b3': b3, 'W4': W4, 'b4': b4, 'W5': W5, 'b5': b5}
if print_loss and i % 2000 == 0:
epsilon *= 0.99
y_pred = predict(model, X_test)
accuracy = sum(0 == (y_pred - Y_test)) / Y_test.shape[0]
print("loss after iteration {}: {:.2f}, testing accuracy: {:.2f}%".
format(i, calculate_loss(model, X, y), accuracy * 100))
return model
# load
(train_images, train_labels, test_images, test_labels) = load_mnist() # 调用函数载入数据
n_train, w, h = train_images.shape # shape读取矩阵长度
X_train = train_images.reshape((n_train, w * h)) # reshape将制定矩阵变换为特定维数矩阵
Y_train = train_labels # 标签
n_test, w, h = test_images.shape
X_test = test_images.reshape((n_test, w * h))
Y_test = test_labels
print(X_train.shape, Y_train.shape)
print(X_test.shape, Y_test.shape)
# train
X_train = (X_train.astype(float) - 128.0) / 128.0 # astype实现变量类型的转换
X_test = (X_test.astype(float) - 128.0) / 128.0
num_examples, input_dim = X_train.shape
epsilon = 0.001
reg_lambda = 0.00
model = build_model(X_train, Y_train, [input_dim, 256, 128, 63, 32, 10], epsilon, reg_lambda, 20000, print_loss=True)
# test output
X_test0=X_test[0:3,:]
y_pred0 = predict(model, X_test0)
print(y_pred0)
X_test0=X_test0.reshape(3,w,h)
plt.figure('第一张图预测')
plt.imshow(X_test0[0,:,:])
plt.figure('第二张图预测')
plt.imshow(X_test0[1,:,:])
plt.figure('第三张图预测')
plt.imshow(X_test0[2,:,:])
pylab.show()