【DSW Gallery】使用Numpy实现卷积神经网络-阿里云开发者社区

直接使用

请打开使用Numpy实现卷积神经网络，并点击右上角 “ 在DSW中打开” 。

使用Numpy实现CNN的前向网络以及反向传播

本文用到的数据集来自Kaggle,可以在这里下载

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

本例中，我们定义一个只有两层的卷积神经网络

Activate function选的是 Relu,因为它可以有效的改善梯度弥散现象
最后会通过Softmax将各个神经元的输出结果转化为[0,1]之间的数字

前向传递

反向传递

参数更新的计算公式

根据上面的公式，定义activation function

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

定义前向传递的函数和反向传递的函数

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

定义预测、梯度下降还有计算精确度的函数

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

开始训练

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
Iteration:  360
[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()

下面我们选择几个输入，看一下我们的CNN模型是否能够正确识别图片中的字

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)

Prediction:  [9]
Label:  9.0

Prediction:  [7]
Label:  7.0

Prediction:  [2]
Label:  2.0

Prediction:  [7]
Label:  7.0

计算一下模型对整个的数据集的精确度

dev_predictions = make_predictions(X_dev, W1, b1, W2, b2)
print("Accuracy: ",get_accuracy(dev_predictions, Y_dev))

[6 3 0 4 8 6 8 0 8 4 9 7 5 9 9 8 1 8 8 8 9 9 8 4 6 0 9 4 1 7 5 6 4 0 4 7 0
 8 9 1 9 4 8 3 1 1 8 7 9 1 9 7 0 4 9 2 8 5 2 9 9 7 9 5 4 4 2 1 6 9 7 6 2 4
 0 9 5 5 1 8 7 6 3 3 8 4 8 4 9 2 2 3 0 9 7 7 6 9 9 9 9 3 4 7 8 9 7 1 1 3 0
 4 7 1 4 1 7 8 1 4 9 2 7 6 8 9 3 5 8 9 2 3 0 7 1 9 4 9 0 9 8 2 6 9 6 0 1 3
 4 5 4 9 4 0 0 4 8 1 9 0 9 7 8 8 1 5 5 7 8 0 2 5 5 3 6 3 9 3 4 1 0 1 1 9 8
 0 9 8 7 0 1 1 4 2 2 6 7 8 2 7 9 1 2 3 1 1 5 2 5 6 8 4 0 2 4 6 6 6 1 8 8 7
 7 2 2 3 4 0 6 9 8 0 5 9 4 1 2 7 8 3 7 9 9 7 7 9 1 3 2 0 5 9 3 6 8 8 6 3 1
 1 7 3 0 6 6 2 8 1 3 2 8 8 4 8 1 8 1 8 9 7 6 8 7 6 4 4 4 2 4 7 2 9 6 9 1 1
 9 8 0 1 0 8 8 9 3 2 1 7 1 8 4 0 9 9 9 2 6 0 3 6 0 4 0 1 7 0 4 2 5 2 2 9 2
 7 6 0 9 6 0 8 7 1 7 0 9 8 0 4 5 2 6 6 6 0 6 9 7 5 8 7 3 6 5 8 3 4 7 6 1 2
 2 9 9 9 6 3 0 2 9 1 6 7 9 5 1 9 4 9 4 9 2 1 7 6 8 6 3 7 5 0 8 4 3 1 1 0 6
 2 4 9 7 1 6 2 8 1 2 0 0 9 8 9 9 8 4 1 0 7 6 0 0 7 1 0 8 9 4 1 7 4 0 6 7 0
 7 5 4 1 9 9 6 7 4 1 0 1 6 9 1 8 3 4 1 7 7 1 8 0 2 7 2 0 0 2 7 7 2 3 3 5 3
 4 7 3 1 1 2 0 6 1 8 6 0 4 9 1 6 0 2 6 6 6 7 8 5 3 6 4 6 1 3 4 8 6 4 6 6 0
 5 5 1 6 4 1 0 8 2 6 0 1 1 3 7 9 7 4 4 7 1 9 3 9 8 9 2 9 0 2 7 1 1 7 1 2 6
 4 9 7 3 3 4 9 3 2 2 2 0 0 6 2 1 3 7 4 4 8 1 2 3 7 5 8 8 5 8 2 5 2 3 8 1 0
 2 5 8 6 1 0 7 0 3 7 3 6 4 0 5 9 1 2 5 9 8 7 2 2 8 8 4 2 4 5 5 7 7 0 8 2 1
 0 3 0 4 5 0 7 9 9 2 4 0 4 6 2 9 2 2 6 9 0 4 0 8 8 2 4 6 1 9 7 5 4 4 6 1 7
 1 1 0 0 1 2 3 1 4 6 0 3 6 7 0 6 9 6 3 0 0 1 5 5 3 8 0 1 1 5 8 9 1 4 4 5 6
 7 9 6 4 4 8 1 4 0 2 6 2 0 7 4 9 4 8 9 1 9 1 4 0 6 3 7 5 1 0 0 8 0 0 6 2 7
 1 5 0 9 4 8 1 7 1 5 1 0 9 5 6 1 2 9 6 5 4 8 9 5 2 8 7 5 2 7 4 3 0 5 5 3 8
 5 9 8 1 8 8 5 4 8 0 2 6 1 0 7 4 0 3 7 4 0 0 4 7 6 6 2 5 1 4 7 4 9 3 5 3 2
 1 3 0 7 4 3 2 7 2 7 1 3 7 4 3 8 6 8 0 7 6 4 2 4 9 6 0 7 2 7 4 2 8 4 4 8 1
 9 4 7 2 2 8 6 0 3 2 8 2 1 4 4 8 4 6 0 0 2 3 6 7 6 8 7 0 4 6 2 1 4 2 1 6 1
 2 1 4 5 6 5 9 0 4 9 9 1 9 3 3 5 1 2 1 1 0 9 7 6 2 6 8 3 8 6 0 9 9 2 0 3 0
 5 6 4 3 8 6 1 1 6 0 9 4 9 2 4 6 8 9 0 2 3 0 1 1 3 3 5 4 0 1 2 8 0 9 8 6 7
 4 8 4 6 0 4 9 6 2 5 9 9 7 6 5 4 1 4 5 0 5 8 4 6 6 0 0 6 1 3 7 0 5 7 4 0 7
 2] [6. 5. 0. 4. 8. 6. 8. 2. 5. 4. 9. 7. 0. 9. 9. 8. 1. 3. 8. 8. 9. 9. 8. 8.
 6. 0. 9. 4. 1. 7. 5. 6. 4. 0. 4. 7. 0. 8. 9. 1. 5. 4. 8. 3. 1. 1. 8. 7.
 9. 1. 4. 7. 0. 4. 3. 8. 5. 5. 2. 9. 9. 7. 9. 3. 6. 4. 2. 1. 6. 9. 9. 6.
 2. 4. 0. 9. 5. 0. 1. 5. 7. 6. 3. 8. 8. 4. 8. 4. 4. 2. 2. 3. 0. 9. 7. 9.
 6. 9. 7. 4. 9. 3. 8. 7. 8. 4. 7. 1. 1. 3. 0. 4. 7. 2. 4. 1. 7. 3. 1. 8.
 9. 2. 7. 6. 8. 9. 3. 5. 8. 9. 2. 3. 5. 7. 3. 4. 4. 4. 0. 9. 8. 2. 6. 9.
 6. 0. 1. 3. 4. 5. 4. 7. 4. 2. 0. 4. 5. 1. 1. 0. 9. 7. 1. 8. 1. 5. 5. 7.
 3. 3. 2. 5. 5. 3. 6. 0. 9. 3. 7. 1. 0. 1. 1. 2. 8. 0. 9. 8. 7. 0. 1. 1.
 4. 2. 2. 6. 9. 8. 2. 8. 9. 1. 5. 3. 1. 1. 5. 2. 5. 4. 6. 4. 0. 2. 4. 6.
 6. 6. 2. 3. 8. 7. 7. 2. 2. 3. 4. 0. 6. 5. 8. 0. 5. 9. 4. 1. 2. 7. 1. 9.
 3. 4. 4. 9. 7. 9. 1. 3. 2. 0. 5. 9. 9. 6. 8. 8. 6. 8. 1. 1. 3. 3. 0. 6.
 6. 2. 8. 1. 3. 2. 5. 9. 4. 8. 1. 4. 1. 8. 8. 7. 6. 3. 7. 8. 4. 4. 4. 2.
 4. 9. 2. 9. 6. 9. 1. 1. 4. 8. 0. 1. 0. 8. 8. 7. 3. 2. 1. 7. 1. 8. 4. 0.
 9. 9. 4. 2. 6. 0. 3. 6. 0. 4. 6. 2. 9. 0. 5. 2. 1. 2. 2. 9. 2. 7. 6. 0.
 4. 6. 2. 8. 7. 1. 7. 0. 4. 8. 3. 4. 5. 2. 6. 6. 6. 0. 6. 9. 7. 5. 8. 7.
 3. 6. 5. 8. 8. 4. 9. 6. 1. 2. 2. 9. 9. 9. 2. 3. 0. 2. 9. 1. 6. 7. 9. 3.
 1. 9. 4. 9. 7. 9. 2. 5. 7. 6. 8. 8. 3. 7. 5. 0. 8. 4. 3. 1. 1. 0. 4. 2.
 4. 9. 9. 1. 6. 2. 5. 1. 2. 0. 0. 9. 8. 9. 9. 3. 4. 1. 0. 7. 6. 5. 0. 7.
 1. 0. 8. 9. 4. 2. 7. 4. 0. 6. 7. 5. 7. 3. 4. 1. 9. 7. 6. 9. 4. 1. 7. 1.
 0. 9. 1. 8. 3. 4. 1. 7. 7. 1. 8. 0. 0. 7. 4. 0. 0. 2. 9. 7. 2. 3. 3. 5.
 3. 4. 9. 3. 1. 1. 2. 0. 4. 1. 8. 6. 0. 4. 9. 1. 5. 0. 2. 6. 6. 5. 7. 8.
 5. 3. 2. 4. 9. 2. 3. 9. 9. 6. 4. 6. 6. 0. 5. 5. 1. 6. 4. 3. 0. 8. 2. 6.
 0. 1. 1. 3. 7. 9. 7. 4. 9. 5. 1. 9. 3. 9. 8. 9. 2. 9. 0. 2. 7. 1. 5. 7.
 2. 2. 6. 4. 4. 7. 3. 3. 4. 7. 2. 2. 2. 2. 0. 0. 5. 2. 1. 3. 7. 7. 4. 8.
 1. 2. 5. 7. 5. 9. 8. 5. 8. 2. 5. 2. 2. 8. 1. 0. 2. 5. 5. 6. 1. 0. 7. 0.
 3. 7. 3. 2. 4. 0. 5. 9. 6. 2. 5. 9. 8. 7. 6. 2. 8. 4. 4. 2. 4. 5. 5. 7.
 7. 0. 8. 2. 1. 0. 3. 0. 4. 5. 0. 7. 9. 9. 2. 4. 5. 4. 6. 2. 9. 2. 2. 6.
 4. 0. 4. 7. 8. 9. 2. 0. 6. 1. 9. 7. 8. 4. 4. 9. 1. 7. 1. 1. 0. 2. 2. 2.
 3. 1. 9. 6. 0. 3. 6. 7. 3. 2. 9. 6. 3. 2. 0. 1. 8. 5. 3. 5. 5. 1. 1. 5.
 8. 4. 1. 4. 9. 5. 6. 7. 4. 6. 4. 4. 8. 1. 4. 0. 2. 6. 2. 0. 7. 4. 9. 4.
 8. 9. 1. 9. 1. 4. 0. 6. 3. 7. 5. 1. 0. 6. 5. 0. 0. 6. 2. 2. 1. 5. 0. 4.
 4. 8. 1. 8. 1. 3. 5. 0. 9. 3. 6. 8. 2. 9. 6. 5. 6. 8. 9. 5. 2. 1. 9. 5.
 2. 7. 4. 3. 5. 5. 3. 3. 8. 5. 4. 8. 1. 5. 8. 5. 5. 8. 0. 3. 6. 1. 0. 7.
 9. 0. 7. 7. 4. 6. 0. 4. 7. 6. 3. 2. 5. 1. 9. 7. 4. 3. 3. 5. 3. 2. 1. 3.
 0. 7. 4. 3. 2. 7. 2. 7. 1. 8. 7. 4. 3. 5. 6. 8. 3. 7. 6. 4. 2. 4. 4. 6.
 0. 7. 2. 7. 6. 2. 5. 4. 4. 8. 2. 9. 4. 3. 2. 2. 8. 6. 0. 3. 2. 8. 2. 1.
 4. 4. 9. 4. 6. 5. 0. 2. 0. 6. 7. 2. 8. 5. 3. 5. 6. 2. 7. 6. 2. 1. 6. 1.
 2. 1. 4. 5. 6. 5. 9. 0. 4. 9. 4. 1. 9. 3. 8. 5. 1. 8. 1. 1. 2. 8. 5. 6.
 2. 6. 8. 3. 2. 6. 0. 4. 4. 2. 0. 3. 0. 5. 6. 6. 3. 8. 7. 1. 1. 6. 0. 9.
 4. 9. 5. 4. 2. 5. 9. 0. 2. 3. 0. 1. 1. 3. 3. 5. 9. 0. 7. 2. 8. 6. 7. 8.
 4. 7. 4. 8. 4. 6. 0. 4. 4. 6. 2. 4. 4. 9. 7. 6. 5. 4. 1. 9. 4. 0. 8. 8.
 4. 1. 6. 0. 0. 6. 6. 3. 4. 0. 3. 7. 4. 0. 9. 8.]
Accuracy:  0.784

【DSW Gallery】使用Numpy实现卷积神经网络

直接使用

使用Numpy实现CNN的前向网络以及反向传播

人工智能平台PAI

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