【DSW Gallery】Using Numpy to implement convolutional neural network

NumPy を使用して CNN の順伝播ネットワークと誤差逆伝播を実装
この記事では、Kaggle のデータセットを使用します。データはこちらからダウンロードできます。
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
data = pd.read_csv('train_numpy.csv')
data.shape
(2290, 785)
data = np.array(data)
m, n = data.shape
np.random.shuffle(data) # shuffle before splitting into dev and training sets
data_dev = data[0:1000].T
Y_dev = data_dev[0]
X_dev = data_dev[1:n]
X_dev = X_dev / 255.
data_train = data[1000:m].T
Y_train = data_train[0]
X_train = data_train[1:n]
X_train = X_train / 255.
_,m_train = X_train.shape
この例では、2 層のみの畳み込みニューラルネットワークを定義します
1. 活性化関数として ReLU を選択します。ReLU は勾配消散現象を効果的に緩和できるためです
2. 最後に、各ニューロンの出力は Softmax を通じて [0,1] の範囲の数値に変換されます
順伝播
逆伝播
パラメーター更新の計算式
上記の数式に従って、活性化関数を定義します
def init_params():
W1 = np.random.rand(10, 784) - 0.5
b1 = np.random.rand(10, 1) - 0.5
W2 = np.random.rand(10, 10) - 0.5
b2 = np.random.rand(10, 1) - 0.5
return W1, b1, W2, b2
def ReLU(Z):
return np. maximum(Z, 0)
def ReLU_deriv(Z):
return Z > 0
def softmax(Z):
A = np.exp(Z) / sum(np.exp(Z))
return A

順伝播と逆伝播の関数を定義します
def forward_prop(W1, b1, W2, b2, X):
Z1 = W1.dot(X) + b1
A1 = ReLU(Z1)
Z2 = W2.dot(A1) + b2
A2 = softmax(Z2)
return Z1, A1, Z2, A2
def one_hot(Y):
one_hot_Y = np.zeros((Y.size, int(Y.max()) + 1)).astype(int)
one_hot_Y[np.arange(Y.size), Y.astype(int)] = 1
one_hot_Y = one_hot_Y.T
return one_hot_Y
def backward_prop(Z1, A1, Z2, A2, W1, W2, X, Y):
one_hot_Y = one_hot(Y)
dZ2 = A2 - one_hot_Y
dW2 = 1 / m * dZ2.dot(A1.T)
db2 = 1 / m * np.sum(dZ2)
dZ1 = W2.T.dot(dZ2) * ReLU_deriv(Z1)
dW1 = 1 / m * dZ1.dot(X.T)
db1 = 1 / m * np.sum(dZ1)
return dW1, db1, dW2, db2
def update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha):
W1 = W1 - alpha * dW1
b1 = b1 - alpha * db1
W2 = W2 - alpha * dW2
b2 = b2 - alpha * db2
return W1, b1, W2, b2
予測、勾配降下法、精度計算を行う関数を定義します
def get_predictions(A2):
return np.argmax(A2, 0)
def get_accuracy(predictions, Y):
print(predictions, Y)
return np.sum(predictions == Y) / Y.size
def gradient_descent(X, Y, alpha, iterations):
W1, b1, W2, b2 = init_params()
for i in range(iterations):
Z1, A1, Z2, A2 = forward_prop(W1, b1, W2, b2, X)
dW1, db1, dW2, db2 = backward_prop(Z1, A1, Z2, A2, W1, W2, X, Y)
W1, b1, W2, b2 = update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha)
if i % 10 == 0:
print("Iteration: ", i)
predictions = get_predictions(A2)
print(get_accuracy(predictions, Y))
return W1, b1, W2, b2
トレーニングの開始
W1, b1, W2, b2 = gradient_descent(X_train, Y_train, 0.10, 500)
Iteration: 0
[2 2 2 ... 1 3 2] [9. 7. 2. ... 5. 6. 0.]
0.1263565891472868
Iteration: 10
[1 1 0 ... 1 3 6] [9. 7. 2. ... 5. 6. 0.]
0.1821705426356589
Iteration: 20
[1 1 2 ... 4 0 6] [9. 7. 2. ... 5. 6. 0.]
0.2372093023255814
Iteration: 30
[1 1 6 ... 0 0 6] [9. 7. 2. ... 5. 6. 0.]
0.29147286821705426
Iteration: 40
[1 1 6 ... 0 0 6] [9. 7. 2. ... 5. 6. 0.]
0.3333333333333333
Iteration: 50
[1 1 6 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.38527131782945734
Iteration: 60
[1 1 6 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.4325581395348837
Iteration: 70
[1 1 2 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.4906976744186046
Iteration: 80
[5 7 2 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.537984496124031
Iteration: 90
[5 7 2 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.5612403100775194
Iteration: 100
[5 7 2 ... 0 0 0] [9. 7. 2. ... 5. 6. 0.]
0.5844961240310077
Iteration: 110
[5 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.6069767441860465
Iteration: 120
[5 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.624031007751938
Iteration: 130
[5 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.6403100775193798
Iteration: 140
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.662015503875969
Iteration: 150
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.6713178294573643
Iteration: 160
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.6922480620155039
Iteration: 170
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.6992248062015504
Iteration: 180
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7116279069767442
Iteration: 190
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7162790697674418
Iteration: 200
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.724031007751938
Iteration: 210
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.727906976744186
Iteration: 220
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7333333333333333
Iteration: 230
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7395348837209302
Iteration: 240
[9 7 2 ... 0 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7434108527131783
Iteration: 250
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7550387596899225
Iteration: 260
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7581395348837209
Iteration: 270
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7697674418604651
Iteration: 280
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7751937984496124
Iteration: 290
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7798449612403101
Iteration: 300
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7821705426356589
Iteration: 310
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7883720930232558
Iteration: 320
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7937984496124031
Iteration: 330
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.7968992248062016
Iteration: 340
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8007751937984496
Iteration: 350
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8062015503875969
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8093023255813954
Iteration: 370
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8147286821705426
Iteration: 380
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8178294573643411
Iteration: 390
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8217054263565892
Iteration: 400
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8224806201550388
Iteration: 410
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8255813953488372
Iteration: 420
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8255813953488372
Iteration: 430
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8263565891472868
Iteration: 440
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8310077519379845
Iteration: 450
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8333333333333334
Iteration: 460
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8348837209302326
Iteration: 470
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8395348837209302
Iteration: 480
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8395348837209302
Iteration: 490
[9 7 2 ... 5 6 0] [9. 7. 2. ... 5. 6. 0.]
0.8418604651162791
def make_predictions(X, W1, b1, W2, b2):
_, _, _, A2 = forward_prop(W1, b1, W2, b2, X)
predictions = get_predictions(A2)
return predictions
def test_prediction(index, W1, b1, W2, b2):
current_image = X_train[:, index, None]
prediction = make_predictions(X_train[:, index, None], W1, b1, W2, b2)
label = Y_train[index]
print("Prediction: ", prediction)
print("Label: ", label)

current_image = current_image.reshape((28, 28)) * 255
plt. gray()
plt.imshow(current_image, interpolation='nearest')
plt. show()
いくつかの入力を選んで、CNN モデルが画像内の数字を正しく認識できるか確認してみましょう
test_prediction(0, W1, b1, W2, b2)
test_prediction(1, W1, b1, W2, b2)
test_prediction(2, W1, b1, W2, b2)
test_prediction(3, W1, b1, W2, b2)