目錄
1、總體流程
2、代碼實現(xiàn)
下載數(shù)據(jù)集
確定激活函數(shù)、損失函數(shù)、計算梯度函數(shù)等
神經(jīng)網(wǎng)絡(luò)的搭建
模型的訓(xùn)練與驗證?
測試模型的泛化能力
1、總體流程
step1：下載數(shù)據(jù)集、讀取數(shù)據(jù)
step2：搭建神經(jīng)網(wǎng)絡(luò)（確定輸出層、隱藏層（層數(shù)）、輸出層的結(jié)構(gòu)）
step3：初始化偏置和權(quán)重
step4：設(shè)置損失函數(shù)、激活函數(shù)
step5：設(shè)置超參數(shù)
step6：神經(jīng)網(wǎng)絡(luò)訓(xùn)練數(shù)據(jù)（通過誤差反向傳播求導(dǎo)、學(xué)習）
step7：測試驗證數(shù)據(jù)集（確定Loss、精確度）
step8：測試模型的泛化能力（輸入自己手寫的數(shù)字進行判斷）
2、代碼實現(xiàn)
下載數(shù)據(jù)集
# coding: utf-8
try:
import urllib.request
except ImportError:
raise ImportError('You should use Python 3.x')
import os.path
import gzip
import pickle
import os
import numpy as np
url_base = 'http://yann.lecun.com/exdb/mnist/'
key_file = {
'train_img':'train-images-idx3-ubyte.gz',
'train_label':'train-labels-idx1-ubyte.gz',
'test_img':'t10k-images-idx3-ubyte.gz',
'test_label':'t10k-labels-idx1-ubyte.gz'
}
dataset_dir = os.path.abspath('.')
save_file = dataset_dir + "/mnist.pkl"
train_num = 60000
test_num = 10000
img_dim = (1, 28, 28)
img_size = 784
def _download(file_name):
file_path = dataset_dir + "/" + file_name
if os.path.exists(file_path):
return
print("Downloading " + file_name + " ... ")
urllib.request.urlretrieve(url_base + file_name, file_path)
print("Done")
def download_mnist():
for v in key_file.values():
_download(v)
def _load_label(file_name):
file_path = dataset_dir + "/" + file_name
print("Converting " + file_name + " to NumPy Array ...")
with gzip.open(file_path, 'rb') as f:
labels = np.frombuffer(f.read(), np.uint8, offset=8)
print("Done")
return labels
def _load_img(file_name):
file_path = dataset_dir + "/" + file_name
print("Converting " + file_name + " to NumPy Array ...")
with gzip.open(file_path, 'rb') as f:
data = np.frombuffer(f.read(), np.uint8, offset=16)
data = data.reshape(-1, img_size)
print("Done")
return data
def _convert_numpy():
dataset = {}
dataset['train_img'] = _load_img(key_file['train_img'])
dataset['train_label'] = _load_label(key_file['train_label'])
dataset['test_img'] = _load_img(key_file['test_img'])
dataset['test_label'] = _load_label(key_file['test_label'])
return dataset
def init_mnist():
download_mnist()
dataset = _convert_numpy()
print("Creating pickle file ...")
with open(save_file, 'wb') as f:
pickle.dump(dataset, f, -1)
print("Done!")
def _change_one_hot_label(X):
T = np.zeros((X.size, 10))
for idx, row in enumerate(T):
row[X[idx]] = 1
return T
def load_mnist(normalize=False, flatten=True, one_hot_label=False):
"""讀入MNIST數(shù)據(jù)集
Parameters
----------
normalize : 將圖像的像素值正規(guī)化為0.0~1.0
one_hot_label :
one_hot_label為True的情況下，標簽作為one-hot數(shù)組返回
one-hot數(shù)組是指[0,0,1,0,0,0,0,0,0,0]這樣的數(shù)組
flatten : 是否將圖像展開為一維數(shù)組
Returns
-------
(訓(xùn)練圖像, 訓(xùn)練標簽), (測試圖像, 測試標簽)
"""
if not os.path.exists(save_file):
init_mnist()
with open(save_file, 'rb') as f:
dataset = pickle.load(f)
if normalize:
for key in ('train_img', 'test_img'):
dataset[key] = dataset[key].astype(np.float32)
dataset[key] /= 255.0
if one_hot_label:
dataset['train_label'] = _change_one_hot_label(dataset['train_label'])
dataset['test_label'] = _change_one_hot_label(dataset['test_label'])
if not flatten:
for key in ('train_img', 'test_img'):
dataset[key] = dataset[key].reshape(-1, 1, 28, 28)
return (dataset['train_img'], dataset['train_label']), (dataset['test_img'], dataset['test_label'])
if __name__ == '__main__':
init_mnist()
確定激活函數(shù)、損失函數(shù)、計算梯度函數(shù)等
##激活函數(shù)
def sigmoid(x):
return 1/(1+np.exp(-x))
def softmax(x):
if x.ndim == 2:
x = x.T
x = x - np.max(x, axis=0)
y = np.exp(x) / np.sum(np.exp(x), axis=0)
return y.T
x = x - np.max(x) # 溢出對策
return np.exp(x) / np.sum(np.exp(x))
def cross_entropy_error(y, t):
if y.ndim == 1:
t = t.reshape(1, t.size)
y = y.reshape(1, y.size)
# 監(jiān)督數(shù)據(jù)是one-hot-vector的情況下，轉(zhuǎn)換為正確解標簽的索引
if t.size == y.size:
t = t.argmax(axis=1)
batch_size = y.shape[0]
return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size
# 計算梯度
def numerical_gradient(f, x):
h = 1e-4 # 0.0001
grad = np.zeros_like(x)
it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
while not it.finished:
idx = it.multi_index
tmp_val = x[idx]
x[idx] = float(tmp_val) + h
fxh1 = f(x) # f(x+h)
x[idx] = tmp_val - h
fxh2 = f(x) # f(x-h)
grad[idx] = (fxh1 - fxh2) / (2*h)
x[idx] = tmp_val # 還原值
it.iternext()
return grad
def sigmoid_grad(x):
return (1.0 - sigmoid(x)) * sigmoid(x)神經(jīng)網(wǎng)絡(luò)的搭建
class TwoLayerNet:
def __init__(self, input_size, hidden_size, output_size, weight_init_std=0.01):
# 初始化權(quán)重
self.params = {}
self.params['W1'] = weight_init_std * np.random.randn(input_size, hidden_size)
self.params['b1'] = np.zeros(hidden_size)
self.params['W2'] = weight_init_std * np.random.randn(hidden_size, output_size)
self.params['b2'] = np.zeros(output_size)
def predict(self, x):
W1, W2 = self.params['W1'], self.params['W2']
b1, b2 = self.params['b1'], self.params['b2']
a1 = np.dot(x, W1) + b1
z1 = sigmoid(a1)
a2 = np.dot(z1, W2) + b2
y = softmax(a2)
return y
# x:輸入數(shù)據(jù), t:監(jiān)督數(shù)據(jù)
def loss(self, x, t):
y = self.predict(x)
return cross_entropy_error(y, t)
def accuracy(self, x, t):
y = self.predict(x)
y = np.argmax(y, axis=1)
t = np.argmax(t, axis=1)
accuracy = np.sum(y == t) / float(x.shape[0])
return accuracy
# x:輸入數(shù)據(jù), t:監(jiān)督數(shù)據(jù)
def numerical_gradient(self, x, t):
loss_W = lambda W: self.loss(x, t)
grads = {}
grads['W1'] = numerical_gradient(loss_W, self.params['W1'])
grads['b1'] = numerical_gradient(loss_W, self.params['b1'])
grads['W2'] = numerical_gradient(loss_W, self.params['W2'])
grads['b2'] = numerical_gradient(loss_W, self.params['b2'])
return grads
def gradient(self, x, t):
W1, W2 = self.params['W1'], self.params['W2']
b1, b2 = self.params['b1'], self.params['b2']
grads = {}
batch_num = x.shape[0]
# forward
a1 = np.dot(x, W1) + b1
z1 = sigmoid(a1)
a2 = np.dot(z1, W2) + b2
y = softmax(a2)
# backward
dy = (y - t) / batch_num
grads['W2'] = np.dot(z1.T, dy)
grads['b2'] = np.sum(dy, axis=0)
da1 = np.dot(dy, W2.T)
dz1 = sigmoid_grad(a1) * da1
grads['W1'] = np.dot(x.T, dz1)
grads['b1'] = np.sum(dz1, axis=0)
return grads模型的訓(xùn)練與驗證?
# 讀入數(shù)據(jù)
(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True,normalize=True, one_hot_label=True)
network = TwoLayerNet(input_size=784, hidden_size=50, output_size=10)
iters_num = 10000
train_size = x_train.shape[0]
batch_size = 100
learning_rate = 0.1
train_loss_list = []
train_acc_list = []
test_acc_list = []
iter_per_epoch = max(train_size / batch_size, 1)
for i in range(iters_num):
batch_mask = np.random.choice(train_size, batch_size)
x_batch = x_train[batch_mask]
t_batch = t_train[batch_mask]
# 梯度
#grad = network.numerical_gradient(x_batch, t_batch)
grad = network.gradient(x_batch, t_batch)
# 更新
for key in ('W1', 'b1', 'W2', 'b2'):
network.params[key] -= learning_rate * grad[key]
loss = network.loss(x_batch, t_batch)
train_loss_list.append(loss)
if i % iter_per_epoch == 0:
train_acc = network.accuracy(x_train, t_train)
test_acc = network.accuracy(x_test, t_test)
train_acc_list.append(train_acc)
test_acc_list.append(test_acc)
print(train_acc, test_acc)
## 驗證
import matplotlib.pyplot as plt
plt.subplot(1,2,1)
plt.plot(np.arange(0,10000),train_loss_list)
plt.title('Loss')
plt.subplot(1,2,2)
plt.plot(np.arange(0,np.size(train_acc_list)),train_acc_list,np.arange(0,np.size(test_acc_list)),test_acc_list)
plt.title('accuracy')
plt.show()?訓(xùn)練過程中的誤差和精確度變化：
?
測試模型的泛化能力
import cv2
def img_show(name,img):
cv2.imshow(name,img)
cv2.waitKey(0)
cv2.destroyAllWindows()
def predict_img_num(filename, img_width, img_height, threshold, kernel_size):
img_original = cv2.imread(filename)
img = cv2.resize(img_original,(img_width,img_width),fx=1,fy=1)
img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, thresh2 = cv2.threshold(img_gray, threshold, 255, cv2.THRESH_BINARY)
kernel = np.ones(kernel_size,np.uint8)
thresh2 = cv2.erode(thresh2,kernel,iterations = 1)
ret, thresh2 = cv2.threshold(thresh2, threshold, 255, cv2.THRESH_BINARY_INV)
print(thresh2.shape)
img_show('test',thresh2)
thresh2 = thresh2.reshape(1,img_width*img_width)
a = network.predict(thresh2)
label = np.argmax(np.array(a))
return label
predict_img_num('8.jpg',28,28,127,(3,3))
輸入手寫圖片8：
輸出結(jié)果：
文章來源：http://www.zghlxwxcb.cn/news/detail-471791.html
?同樣你也可以輸入一些你自己手寫的數(shù)字，來測試模型的泛化能力文章來源地址http://www.zghlxwxcb.cn/news/detail-471791.html
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