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本篇內(nèi)容介紹了“純numpy數(shù)值微分法如何實現(xiàn)手寫數(shù)字識別”的有關(guān)知識,在實際案例的操作過程中,不少人都會遇到這樣的困境,接下來就讓小編帶領(lǐng)大家學(xué)習(xí)一下如何處理這些情況吧!希望大家仔細(xì)閱讀,能夠?qū)W有所成!
程序分為兩部分,首先是手寫數(shù)字?jǐn)?shù)據(jù)的準(zhǔn)備,直接使用如下mnist.py文件中的方法load_minist即可。文件代碼如下:
# 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.dirname(os.path.abspath(__file__)) 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=True, 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(biāo)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(biāo)簽), (測試圖像, 測試標(biāo)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()
使用上述文件中的函數(shù)就可以直接得到手寫數(shù)字的訓(xùn)練數(shù)據(jù)、訓(xùn)練標(biāo)簽,測試樣本以及測試標(biāo)簽。
接下里使用如下代碼就可以進(jìn)行手寫數(shù)字的訓(xùn)練,代碼如下:
import numpy as np from numpy.lib.function_base import select from dataset.mnist import load_mnist import matplotlib.pylab as plt def sigmoid(x): return 1 / (1 + np.exp(-x)) def sigmoid_grad(x): return (1.0 - sigmoid(x)) * sigmoid(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(biāo)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 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 fxh2 = f(x) # f(x+h) x[idx] = tmp_val - h fxh3 = f(x) # f(x-h) grad[idx] = (fxh2 - fxh3) / (2*h) x[idx] = tmp_val # 還原值 it.iternext() return grad #(x_train,t_train),(x_test,t_test)=load_mnist(normalize=True,one_hot_label=True) #兩層神經(jīng)網(wǎng)絡(luò)的類 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 #損失函數(shù) def loss(self,x,t): y=self.predict(x) return cross_entropy_error(y,t) #數(shù)值微分法 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 #誤差反向傳播法 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 #準(zhǔn)確率 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 if __name__=='__main__': (x_train,t_train),(x_test,t_test)=load_mnist(normalize=True,one_hot_label=True) net=TwoLayerNet(input_size=784,hidden_size=50,output_size=10) train_loss_list=[] #超參數(shù) iter_nums=10000 train_size=x_train.shape[0] batch_size=100 learning_rate=0.1 #記錄準(zhǔn)確率 train_acc_list=[] test_acc_list=[] #平均每個epoch的重復(fù)次數(shù) iter_per_epoch=max(train_size/batch_size,1) for i in range(iter_nums): #小批量數(shù)據(jù) batch_mask=np.random.choice(train_size,batch_size) x_batch=x_train[batch_mask] t_batch=t_train[batch_mask] #計算梯度 #數(shù)值微分 計算很慢 #grad=net.numerical_gradient(x_batch,t_batch) #誤差反向傳播法 計算很快 grad=net.gradient(x_batch,t_batch) #更新參數(shù) 權(quán)重W和偏重b for key in ['W1','b1','W2','b2']: net.params[key]-=learning_rate*grad[key] #記錄學(xué)習(xí)過程 loss=net.loss(x_batch,t_batch) print('訓(xùn)練次數(shù):'+str(i)+' loss:'+str(loss)) train_loss_list.append(loss) #計算每個epoch的識別精度 if i%iter_per_epoch==0: #測試在所有訓(xùn)練數(shù)據(jù)和測試數(shù)據(jù)上的準(zhǔn)確率 train_acc=net.accuracy(x_train,t_train) test_acc=net.accuracy(x_test,t_test) train_acc_list.append(train_acc) test_acc_list.append(test_acc) print('train acc:'+str(train_acc)+' test acc:'+str(test_acc)) print(train_acc_list) print(test_acc_list) # 繪制圖形 markers = {'train': 'o', 'test': 's'} x = np.arange(len(train_acc_list)) plt.plot(x, train_acc_list, label='train acc') plt.plot(x, test_acc_list, label='test acc', linestyle='--') plt.xlabel("epochs") plt.ylabel("accuracy") plt.ylim(0, 1.0) plt.legend(loc='lower right') plt.show()
訓(xùn)練完成后,查看繪制準(zhǔn)確率的圖片,可以獲取到成功實現(xiàn)了手寫數(shù)字識別。
隨著訓(xùn)練批次的增加,準(zhǔn)確率逐漸增大接近于1,說明訓(xùn)練過程按著正確擬合的方向前進(jìn)。
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