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from PIL import Image
import numpy as np
先下載 MNIST 資料
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import os
import urllib
from urllib.request import urlretrieve
dataset = 'mnist.pkl.gz'
def reporthook(a,b,c):
print("\rdownloading: %5.1f%%"%(a*b*100.0/c), end="")
if not os.path.isfile(dataset):
origin = "https://github.com/mnielsen/neural-networks-and-deep-learning/raw/master/data/mnist.pkl.gz"
print('Downloading data from %s' % origin)
urlretrieve(origin, dataset, reporthook=reporthook)
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import gzip
import pickle
with gzip.open(dataset, 'rb') as f:
train_set, validation_set, test_set = pickle.load(f, encoding='latin1')
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# 設定好訓練及測試資料
train_X, train_y = train_set
test_X, test_y = test_set
# 設定成我們的格式
train_X = train_X[..., None]
test_X = test_X[..., None]
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# 有 10 種類別，輸入的是 784 維
print(train_X.shape)
np.unique(train_y)
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from IPython.display import display
def showX(X):
int_X = (X*255).clip(0,255).astype('uint8')
# N*784 -> N*28*28 -> 28*N*28 -> 28 * 28N
int_X_reshape = int_X.reshape(-1,28,28).swapaxes(0,1).reshape(28,-1)
display(Image.fromarray(int_X_reshape))
# 訓練資料， X 的前 20 筆
print(train_y[:20])
showX(train_X[:20])
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# 參考範例 softmax regression
W = np.random.normal(size=(10, 784))
b = np.random.normal(size=(10, 1))
n_data = train_X.shape[0]
# 紀錄 loss
loss_history = []
accuracy_history = []
for epoch in range(5000):
idx = np.random.choice(n_data, 300, replace=False)
X = train_X[idx]
y = train_y[idx]
one_y = np.eye(10)[y][..., None]
d = np.exp(W @ X + b)
q = d/d.sum(axis=(1,2), keepdims=True)
loss = -np.log(q[range(len(y)), y]).mean()
loss_history.append(loss)
accuracy = (q.argmax(axis=1).ravel() == y).mean()
accuracy_history.append(accuracy)
if epoch%100 == 0:
print(epoch, accuracy, loss)
grad_b_all = q - one_y
grad_b = grad_b_all.mean(axis=0)
grad_W_all = grad_b_all @ X.swapaxes(1,2)
grad_W = grad_W_all.mean(axis=0)
W -= grad_W
b -= grad_b
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# test data 的正確率
((W @ test_X + b).argmax(axis=1).ravel() == test_y).mean()
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%matplotlib inline
import matplotlib.pyplot as plt
# 準確率的圖
plt.plot(accuracy_history);
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# loss 的圖
plt.plot(loss_history);
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def softmax(x):
t = np.exp(x)
return t/t.sum(axis=(-2,-1),keepdims=True)
def relu(x):
return np.maximum(x, 0)
def sigmoid(x):
return 1/(1+np.exp(-x))
# 微分
def Drelu(x):
return (x>0).astype('float32')
def Dsigmoid(x):
q = sigmoid(x)
return q * (1-q)
# or
#return np.exp(x)/(1+np.exp(-x))**2
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# 參考範例 feedforward network
from time import time
accuracy_history = []
γ = 0.02
A = np.random.normal(size=(50,784))
b = np.random.normal(size=(50,1))
C = np.random.normal(size=(10,50))
d = np.random.normal(size=(10,1))
t0 = time()
for epochs in range(20):
idx = np.random.choice(n_data, n_data, replace=False)
for i in idx:
x = train_X[i]
y = train_y[i]
U_ = A@x+b
U = relu(U_)
q = softmax(C@U+d)
L = - np.log(q[y])[0]
p = np.eye(10)[y][:, None]
grad_d = q - p
grad_C = grad_d @ U.T
grad_b = (C.T @ grad_d ) * Drelu(U_)
grad_A = grad_b @ x.T
A -= γ * grad_A
b -= γ * grad_b
C -= γ * grad_C
d -= γ * grad_d
score = ((C@relu(A@test_X+b)+d).argmax(axis=1).ravel()==test_y).mean()
print(epochs, score, "%.1f"%(time()-t0), L)
print(time()-t0)
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