import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
data = pd.read_csv('./mnist_train.csv')
print('Data: ', data)
print('Datatype: ', type(data))
print('Data_array: ', np.array(data))
print('Data_array_type: ', type(np.array(data)))
print('Data shape: ', data.shape)
# 首次通过 pandas.read_csv() 读入的数据为 pandas_Dataframe 实例
# 需要通过 np.array() 转换为 np.ndarray 类型
data = np.array(data)
Data: label 1x1 1x2 1x3 1x4 1x5 1x6 1x7 1x8 1x9 ... 28x19 28x20 \
0 5 0 0 0 0 0 0 0 0 0 ... 0 0
1 0 0 0 0 0 0 0 0 0 0 ... 0 0
2 4 0 0 0 0 0 0 0 0 0 ... 0 0
3 1 0 0 0 0 0 0 0 0 0 ... 0 0
4 9 0 0 0 0 0 0 0 0 0 ... 0 0
... ... ... ... ... ... ... ... ... ... ... ... ... ...
59995 8 0 0 0 0 0 0 0 0 0 ... 0 0
59996 3 0 0 0 0 0 0 0 0 0 ... 0 0
59997 5 0 0 0 0 0 0 0 0 0 ... 0 0
59998 6 0 0 0 0 0 0 0 0 0 ... 0 0
59999 8 0 0 0 0 0 0 0 0 0 ... 0 0
28x21 28x22 28x23 28x24 28x25 28x26 28x27 28x28
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0
... ... ... ... ... ... ... ... ...
59995 0 0 0 0 0 0 0 0
59996 0 0 0 0 0 0 0 0
59997 0 0 0 0 0 0 0 0
59998 0 0 0 0 0 0 0 0
59999 0 0 0 0 0 0 0 0
[60000 rows x 785 columns]
Datatype: <class 'pandas.core.frame.DataFrame'>
Data_array: [[5 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[4 0 0 ... 0 0 0]
...
[5 0 0 ... 0 0 0]
[6 0 0 ... 0 0 0]
[8 0 0 ... 0 0 0]]
Data_array_type: <class 'numpy.ndarray'>
Data shape: (60000, 785)
print('np.shape return type: ', type(data.shape))
# np.ndarray.shape 可以获得一个具有两个元素的 tuple 类型的返回值
m, n = data.shape # m rows, n columns
print('%d rows, %d columns.'%(m,n))
print('Data before shuffle:\n ', data)
# 将训练集随机打乱顺序
np.random.shuffle(data)
print('Data after shuffle:\n ', data)
print('Total training dataset shape: ', data.shape)
np.shape return type: <class 'tuple'>
60000 rows, 785 columns.
Data before shuffle:
[[5 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[4 0 0 ... 0 0 0]
...
[5 0 0 ... 0 0 0]
[6 0 0 ... 0 0 0]
[8 0 0 ... 0 0 0]]
Data after shuffle:
[[0 0 0 ... 0 0 0]
[4 0 0 ... 0 0 0]
[5 0 0 ... 0 0 0]
...
[4 0 0 ... 0 0 0]
[2 0 0 ... 0 0 0]
[3 0 0 ... 0 0 0]]
Total training dataset shape: (60000, 785)
# 取出 dev_dataset 将第一列的标签通过转置放到第一行
data_dev = data[0:1000].T
print('Dev dataset shape: ', data_dev.shape)
# 取出 dev_dataset 的样本和标签
Y_dev = data_dev[0] # 标签
print('Y_dev_data(label): ', Y_dev)
X_dev = data_dev[1:] # 样本
print('X_dev_data(example): ', X_dev)
# 验证样本数据行是否完整，一行就是一张图片的展开
print('Is flatten pic valid: %s'%('True' if len(X_dev[:,int(np.random.randn()*100)]) == 28 * 28 else 'False'))
print((X_dev / 255.)[:,0]) # 像素点色彩强度值归一化优化运算速度
Dev dataset shape: (785, 1000)
Y_dev_data(label): [0 4 5 3 1 8 0 2 5 3 4 4 3 4 3 0 5 2 4 4 5 8 3 0 1 5 0 9 7 4 9 8 3 6 8 2 4
3 6 2 9 8 3 5 3 2 3 3 6 3 2 4 3 4 8 8 5 8 9 4 8 3 3 3 3 7 9 7 4 3 1 8 2 2
4 2 2 6 9 4 0 4 3 3 6 6 6 5 9 9 3 8 7 5 7 1 4 2 0 9 1 7 5 7 2 0 6 2 5 1 8
6 8 3 5 3 7 8 0 2 9 4 7 4 5 1 3 1 1 7 2 7 7 5 9 5 4 0 7 3 6 6 3 0 8 4 8 0
1 2 7 5 4 1 1 5 6 7 1 0 3 9 0 6 8 9 3 2 8 6 1 5 5 8 6 5 1 0 7 1 9 3 1 4 9
3 0 1 9 2 2 3 0 6 1 5 5 0 1 4 7 5 2 7 1 3 7 7 8 3 7 5 4 4 5 1 6 3 2 2 0 3
4 7 9 3 1 9 0 8 7 9 3 2 0 1 9 5 0 2 2 2 2 0 9 3 2 8 1 0 5 4 7 4 8 6 4 5 4
5 5 7 9 3 5 3 7 8 7 9 4 7 1 2 5 1 3 9 5 4 2 8 7 3 7 6 2 8 2 3 3 8 4 1 3 8
2 4 5 6 8 8 8 0 8 5 9 9 2 2 3 3 3 0 4 9 4 0 5 9 0 1 1 0 9 1 5 9 6 0 4 8 7
4 0 0 3 4 8 6 7 6 9 7 2 5 5 4 7 9 4 5 4 6 1 4 4 6 1 2 3 5 3 8 9 5 6 7 7 0
6 9 7 4 2 6 4 7 0 0 3 4 3 1 4 1 4 3 9 1 1 8 0 9 4 2 1 9 5 3 4 7 0 9 1 5 3
7 7 8 3 5 5 0 8 3 8 3 7 7 4 3 6 5 9 9 5 4 4 0 6 1 2 5 8 8 5 7 3 3 5 3 3 4
8 8 5 6 9 8 4 3 4 9 1 7 9 0 7 6 7 8 0 8 7 7 7 2 9 9 1 7 0 8 1 4 8 6 5 4 8
4 1 5 3 4 9 0 6 4 8 1 1 9 1 5 4 8 5 9 1 1 9 6 2 8 7 2 8 5 9 0 4 9 8 1 2 8
8 6 6 0 9 4 6 4 3 1 6 7 3 7 5 0 4 8 1 1 4 1 9 4 4 2 4 9 3 8 4 1 9 4 4 4 2
1 0 5 0 8 4 6 1 7 4 2 0 4 4 5 9 8 7 4 5 4 8 7 8 4 1 4 8 5 6 8 1 7 8 5 6 3
4 6 7 2 6 5 6 4 7 6 7 9 3 1 1 4 7 3 7 1 8 3 3 3 4 7 0 1 5 7 9 9 7 8 1 6 6
0 4 6 3 8 2 1 9 7 7 9 7 9 5 7 7 5 9 2 6 6 0 9 2 4 1 6 0 1 0 9 2 6 5 8 2 9
2 2 6 1 4 9 7 2 1 4 2 7 1 5 3 5 2 2 8 3 5 1 6 3 3 0 7 5 3 0 3 0 6 7 8 9 3
0 3 2 3 5 8 7 2 2 2 1 5 6 4 0 0 2 3 5 1 4 1 8 4 9 0 1 0 1 1 1 7 6 1 7 7 5
4 8 3 5 9 7 6 2 8 4 7 2 8 0 8 0 8 8 1 2 8 6 1 0 0 7 4 4 6 0 5 2 0 3 3 7 0
8 9 7 1 9 6 4 9 8 7 6 1 6 7 6 9 7 7 3 5 1 6 9 8 1 7 3 2 1 0 7 9 3 7 5 9 4
9 4 8 3 1 5 2 7 9 5 2 1 5 0 2 1 8 5 1 1 1 3 0 0 9 9 2 5 5 6 8 5 7 1 8 1 9
4 1 0 1 7 9 1 3 5 8 9 7 8 8 3 4 6 5 1 5 1 8 0 3 0 4 1 0 5 9 5 0 4 9 6 6 0
3 7 5 0 8 4 1 1 2 6 0 9 6 3 0 5 8 2 3 5 1 1 5 1 8 9 3 1 6 8 8 3 9 5 7 3 4
6 6 2 5 8 3 3 3 6 5 0 7 7 7 5 7 3 3 1 0 9 1 7 0 1 8 2 7 6 0 9 9 3 6 8 3 8
2 6 4 0 9 9 0 8 1 2 4 0 7 3 0 3 7 5 1 7 3 8 3 1 4 5 4 6 6 1 4 0 7 4 1 6 7
8]
X_dev_data(example): [[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
Is flatten pic valid: True
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data_train = data[1000:m].T # 后 59000 个样本作为训练集
Y_train = data_train[0]
X_train = data_train[1:]
print('Data validation: %s'%('True' if len(X_train[:, int(np.random.rand()*1000)]) == 28 * 28 else 'False'))
# 色值归一化
X_train = X_train / 255.
# 训练集大小
_, m_train = X_train.shape
print('X_train_col: ', m_train) # (x1, x2, ... , x58999, x59000)
Y_train
Data validation: True
X_train_col: 59000
array([1, 3, 2, ..., 4, 2, 3], dtype=int64)
# 可以发现 np.random.rand() 范围是 (0, 1), np.random.randn()
# for _ in range(10):
# print(np.random.rand(1,2), np.random.randn(1,2))
# 生成一个 randn() 矩阵
# test_randn_arr = np.array([np.random.randn() for _ in range(5000)]) # np.random.randn((5000)) 相同效果
# test_randn_arr
# 当数量足够大时，np.random.randn() 生成的数字其均值趋近0，可知 np.random.randn() 生成正态分布
# print(np.mean(test_randn_arr))
# np.max() & np.maximum()
# np.max() 求序列的最值，最少接受一个参数
# np.maximum() 两个序列逐位比较，最少接受两个参数，返回每一位比较后的最大值组成的序列
# test_arr = np.random.rand(3,3)-0.5
# 如果是 0 矩阵，相当于 broadcast 为 0 矩阵，常数则是 n 倍全 1 矩阵
# print(np.maximum(test_arr, 2)) # 返回 3*3 的 2 倍 全 1 矩阵
# 生成初始权重偏置(随机值)
def init_params():
# 减去 0.5 使 W1 的区间在 (-0.5, 0.5)
W1 = np.random.rand(30, 28*28) - 0.5
b1 = np.random.rand(30, 1) - 0.5
W2 = np.random.rand(10, 30) - 0.5
b2 = np.random.rand(10, 1) - 0.5
return W1, b1, W2, b2
# ReLU进行激活
def ReLU(Z):
return np.maximum(Z, 0)
# ReLU导数
def deriv_ReLU(Z):
return Z > 0
# 将输出结果归一化(概率化)
# 出现数值溢出，弃用
# def softmax(Z):
# return np.exp(Z) / sum(np.exp(Z))
# 优化softmax函数避免溢出
def softmax(x):
max = np.max(x)
return np.exp(x-max)/sum(np.exp(x-max))
# Z = np.array([
# [1,2,3],
# [4,5,6],
# [7,8,9]
# ])
# 前向传播
def forward_propagation(W1, b1, W2, b2, X):
Z1 = np.dot(W1, X) + b1
A1 = ReLU(Z1)
Z2 = np.dot(W2, A1) + b2
A2 = softmax(Z2)
return Z1, A1, Z2, A2
# 标签 one-hot 编码
def one_hot(Y):
one_hot_Y = np.zeros((Y.size, Y.max() + 1))
one_hot_Y[np.arange(Y.size), Y] = 1
one_hot_Y = one_hot_Y.T
return one_hot_Y
# 反向传播
def backward_propagation(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) * deriv_ReLU(Z1)
dW1 = 1 / m * dZ1.dot(X.T)
db1 = 1 / m * np.sum(dZ1)
return dW1, db1, dW2, db2
# 使用反向传播得到的ΔW和Δb进行原参数的调整(梯度下降法)
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
# 从10*m输出中找到softmax值最大者
def get_predictions(A2):
return np.argmax(A2, 0)
# 返回预测正确者在测试集(Y_dev)中的占比，作为准确度
def get_accuracy(predictions, Y):
print(predictions, Y)
return np.sum(predictions == Y) / Y.size
# 进行iterations次的迭代，完成梯度下降法对参数的调整
def gradient_descent(X, Y, alpha, iterations):
W1, b1, W2, b2 = init_params()
for i in range(iterations):
Z1, A1, Z2, A2 = forward_propagation(W1, b1, W2, b2, X)
dW1, db1, dW2, db2 = backward_propagation(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
W1, b1, W2, b2 = gradient_descent(X_train, Y_train, 0.10, 500)
Iteration: 0
[9 6 9 ... 7 7 9] [1 3 2 ... 4 2 3]
0.08171186440677966
Iteration: 10
[3 6 6 ... 2 7 5] [1 3 2 ... 4 2 3]
0.22979661016949152
Iteration: 20
[5 9 6 ... 2 7 5] [1 3 2 ... 4 2 3]
0.35710169491525423
Iteration: 30
[5 9 6 ... 2 7 5] [1 3 2 ... 4 2 3]
0.4587457627118644
Iteration: 40
[5 9 6 ... 2 4 3] [1 3 2 ... 4 2 3]
0.5425254237288135
Iteration: 50
[5 8 6 ... 2 4 3] [1 3 2 ... 4 2 3]
0.6005932203389831
Iteration: 60
[5 8 6 ... 2 4 3] [1 3 2 ... 4 2 3]
0.6429322033898305
Iteration: 70
[5 8 6 ... 4 4 3] [1 3 2 ... 4 2 3]
0.673864406779661
Iteration: 80
[5 8 6 ... 4 4 3] [1 3 2 ... 4 2 3]
0.6992372881355933
Iteration: 90
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.717728813559322
Iteration: 100
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7345423728813559
Iteration: 110
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7476440677966102
Iteration: 120
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7585762711864407
Iteration: 130
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7692033898305085
Iteration: 140
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.778
Iteration: 150
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7866271186440678
Iteration: 160
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.7936101694915254
Iteration: 170
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8004745762711865
Iteration: 180
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8065593220338984
Iteration: 190
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8118983050847458
Iteration: 200
[5 5 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8164915254237288
Iteration: 210
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8213898305084746
Iteration: 220
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8257457627118644
Iteration: 230
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8292372881355933
Iteration: 240
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8325762711864407
Iteration: 250
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8360677966101695
Iteration: 260
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8393220338983051
Iteration: 270
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8421525423728814
Iteration: 280
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8444745762711865
Iteration: 290
[5 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8469491525423729
Iteration: 300
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8492542372881355
Iteration: 310
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8509152542372881
Iteration: 320
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8524406779661017
Iteration: 330
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8550169491525423
Iteration: 340
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8570677966101695
Iteration: 350
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8587288135593221
Iteration: 360
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8604237288135593
Iteration: 370
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8619661016949153
Iteration: 380
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8637457627118644
Iteration: 390
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8653220338983051
Iteration: 400
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8664237288135593
Iteration: 410
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.867457627118644
Iteration: 420
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8688474576271187
Iteration: 430
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8702203389830508
Iteration: 440
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8714745762711864
Iteration: 450
[3 3 6 ... 4 2 3] [1 3 2 ... 4 2 3]
0.873135593220339
Iteration: 460
[3 3 2 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8742881355932204
Iteration: 470
[3 3 2 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8754406779661017
Iteration: 480
[3 3 2 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8764406779661017
Iteration: 490
[3 3 2 ... 4 2 3] [1 3 2 ... 4 2 3]
0.8772542372881356
~87.7% accuracy on training set.
# 进行一次前向传播得到预测值
def make_predictions(X, W1, b1, W2, b2):
_, _, _, A2 = forward_propagation(W1, b1, W2, b2, X)
predictions = get_predictions(A2)
return predictions
# 以当前的权重和偏置值作为参数进行一次预测
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()
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: [3]
Label: 1
Prediction: [3]
Label: 3
Prediction: [2]
Label: 2
Prediction: [6]
Label: 6
import cv2 as cv
current_image = cv.imread('./8.png')
gray_image = cv.cvtColor(current_image, cv.COLOR_BGR2GRAY)
plt.imshow(gray_image)
plt.show()
gray_image = gray_image.reshape(784, 1)
gray_image.reshape(784, 1) / 255
# print(gray_image.shape)
def test_user_prediction(gray_image, W1, b1, W2, b2):
prediction = make_predictions(gray_image, W1, b1, W2, b2)
print("Prediction: ", prediction)
# current_image = X_train[:, 1, None]
# current_image.shape
test_user_prediction(gray_image, W1, b1, W2, b2)
Prediction: [8]
current_image = X_train[:, 12, None]
current_image.shape
(784, 1)