共计 3268 个字符，预计需要花费 9 分钟才能阅读完成。
本人跑的时候正确率 0.89
库
- numpy
- PIL(如果须要对理论图片进行预测)
后果
- minst 的四个文件解压之后和这四个 py 文件放在同级文件夹
- 运行完结后的权重 W 和偏移 b 也在同级文件夹下，csv 文件只用来看，用的是 bin 文件
softmax.py
和训练、测试无关的所有函数
#!/usr/bin/python
import numpy as np
np.random.seed(0)
# 定义 softmax 函数
def SoftMax(z):
if np.ndim(z) == 2:
axisn = 1
else:
axisn = 0
s = np.exp(z) / np.sum(np.exp(z), axis=axisn, keepdims=True)
return s
# b = np.array([1,2,4, 5,5,6]).reshape(2,3)
# print(SoftMax(b))
# 编码标签
def OneCode(y):
r = len(y)
c = len(np.unique(y))
one_hot = np.zeros((r,c))
one_hot[np.arange(len(y)), y.astype(int).T] = 1
return one_hot
# 定义 y_ 的计算函数
def CalcY_(x, w, b):
# w * X.T + b 前面 +b 是一个播送运算，y_ = np.dot(w, x.T) + b
return y_.T
# 定义损失函数 - 穿插熵
def cross_entropy(y, y_):
loss = -(1/len(y))*np.sum(y * np.log(y_))
return loss
# 定义训练函数
def train(tr_x, tr_y, N):
''''''
# 模型
# y = w1 * x1 + w2 * x2 + b
W = np.random.rand(10,784)
b = np.random.rand(10,1)
losss = []
losi = 0
y = OneCode(tr_y) # 把 1 2 3 4 转换成向量 0001 0010 0100 1000
for i in range(N):
# 计算 loss
x = tr_x
y_ = SoftMax(CalcY_(x, W, b))
loss = cross_entropy(y, y_)
losss.append(loss)
# 计算梯度
grad_w = (1/len(x)) * np.dot((y_ - y).T, x)
grad_b = (1/len(x)) * np.sum((y_ - y))
# 更新参数
# 学习率 × 梯度
W = W - 0.5 * grad_w
b = b - 0.5 * grad_b
delta = abs(losi - loss)
print(i , loss ,delta)
# 损失值低于 0.01 或者 其变动值低于 0.0001
if(loss < 0.01 or delta < 0.0001):
break
losi = loss
return W,b
# 定义测试函数
def check(te_x, te_y, W, b):
# te_x,te_y = Iread('te')
# te_x = te_x / 255
# te_y = te_y
# print(W)
# print(b)
y_ = SoftMax(CalcY_(te_x, W, b))
l = np.argmax(y_, axis=1).reshape(10000,1)
right = np.sum(l == te_y.astype())/10000
print('right rate:', right)
return rightIdata.py
文件读取函数
#!/usr/bin/python
import numpy as np
filename_train_data ='./train-images-idx3-ubyte'
filename_train_label='./train-labels-idx1-ubyte'
filename_test_data ='./t10k-images-idx3-ubyte'
filename_test_label ='./t10k-labels-idx1-ubyte'
def Iread_train_data():
fp = open(filename_train_data, 'rb')
fl = open(filename_train_label, 'rb')
fp.read(4*4)
fl.read(2*4)
nstrs=np.zeros((60000, 28*28))
l =np.zeros((60000, 1))
for i in range(60000):
fstr = fp.read(28*28)
lstr = fl.read(1)
l[i] = int.from_bytes(lstr,byteorder='big',signed=False)
nstrs[i,:] = np.frombuffer(fstr, dtype=np.uint8)
return nstrs,l
def Iread_test_data():
fp = open(filename_test_data, 'rb')
fl = open(filename_test_label, 'rb')
fp.read(4*4)
fl.read(2*4)
nstrs=np.zeros((10000, 28*28))
l =np.zeros((10000, 1))
for i in range(10000):
fstr = fp.read(28*28)
lstr = fl.read(1)
l[i] = int.from_bytes(lstr,byteorder='big',signed=False)
nstrs[i,:] = np.frombuffer(fstr, dtype=np.uint8)
return nstrs,l
def Iread(option):
if(option == 'tr'):
d,l = Iread_train_data()
return d,l
else if(option == 'te'):
d,l = Iread_test_data()
return d,l
else:
print('op err')minst.py
实现训练和测试的脚本
#!/usr/bin/python
import numpy as np
from Idata import Iread
from softmax import train,check
# 读数据
tr_x,tr_y = Iread('tr')
te_x,te_y = Iread('te')
# 训练集和测试集正规到 0-1 区间
tr_x = tr_x / 255
te_x = te_x / 255
# print(tr_x.shape, tr_y.shape)
# print(te_x.shape, te_y.shape)
# 训练
W,b = train(tr_x, tr_y, 1000)
# 而后保留参数
W.tofile('W.bin')
b.tofile('b.bin')
np.savetxt('w.csv', W, fmt='%f', delimiter=',')
np.savetxt('b.csv', b, fmt='%f', delimiter=',')
# 读取参数
W = np.fromfile('W.bin').reshape(10, 784)
b = np.fromfile('b.bin').reshape(10, 1)
# 测试
r = check(te_x, te_y, W, b)predict.py
用来对一个理论的手写数字图像识别的脚本
#!/usr/bin/python
import numpy as np
from softmax import SoftMax,CalcY_,cross_entropy,OneCode
from PIL import Image
# 图像文件必须是 28 × 28 的 0～255 灰度图像
fname = '4.bmp'
img = np.array(Image.open(fname))
te_x = img.reshape(1, 28*28)
te_x = te_x / 255
print(te_x)
W = np.fromfile('W.bin').reshape(10, 784)
b = np.fromfile('b.bin').reshape(10, 1)
y_ = SoftMax(CalcY_(te_x, W, b))
y_ = np.argmax(y_, axis=1)
print('pred:', y_)正文完