初始化数据

import numpy as np

# 训练集
with open('./minist_data/train-images.idx3-ubyte') as f:
    loaded = np.fromfile(file=f, dtype=np.uint8)
    train_data = loaded[16:60000 * 784 + 16].reshape((60000, 784))
with open('./minist_data/train-labels.idx1-ubyte') as f:
    loaded = np.fromfile(file=f, dtype=np.uint8)
    train_labels = loaded[8:60000 + 8].reshape(60000)
# 手写痕迹为1 背景为0
for i in range(60000):
    for n in range(784):
        if train_data[i][n] > 0:
            train_data[i][n] = 1
# 测试集
with open('./minist_data/t10k-images.idx3-ubyte') as f:
    loaded = np.fromfile(file=f, dtype=np.uint8)
    test_data = loaded[16:10000 * 784 + 16].reshape((10000, 784))
# 测试集标签
with open('./minist_data/t10k-labels.idx1-ubyte') as f:
    loaded = np.fromfile(file=f, dtype=np.uint8)
    test_labels = loaded[8:10000 + 8].reshape(10000)
# 手写痕迹为1 背景为0
for i in range(10000):
    for n in range(784):
        if test_data[i][n] > 0:
            test_data[i][n] = 1
np.save("./minist_data/train_data.npy", train_data)
np.save("./minist_data/train_labels.npy", train_labels)
np.save("./minist_data/test_data.npy", test_data)
np.save("./minist_data/test_labels.npy", test_labels)

训练

import numpy as np

# 载入参数
parameter = np.zeros((784, 10), dtype=np.float32)
bias = np.zeros(10, dtype=np.float32)
numbers = [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
           [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
# 迭代次数
the_times = 1
# 训练数量
train_numbers = 60000
train_data = np.load("./minist_data/train_data.npy")
train_labels = np.load("./minist_data/train_labels.npy")

# 求参数
for times in range(the_times):
    random_data = np.empty((train_numbers, 784), dtype=np.float32)
    random_labels = np.empty((train_numbers, 10), dtype=np.float32)
    for m in range(train_numbers):
        # ran = np.random.randint(0, 60000)
        ran = m
        random_data[m] = train_data[ran]
        random_labels[m] = numbers[train_labels[ran]]
    ATB = np.matmul(random_data.T, random_labels)
    ATA = np.matmul(random_data.T, random_data)
    # 逆
    # ATA_1 = np.linalg.inv(ATA)
    # 违逆
    ATA_1 = np.linalg.pinv(ATA)
    parameter += np.matmul(ATA_1, ATB) * (1 / the_times)
    print(times)

# 求偏置
output = np.matmul(train_data, parameter)
for m in range(60000):
    bias += output[m] - numbers[train_labels[m]]
bias /= 60000
np.save("./minist_data/parameter.npy", parameter)
np.save("./minist_data/bias.npy", bias)

测试

import numpy as np

test_data = np.load("./minist_data/test_data.npy")
test_labels = np.load("./minist_data/test_labels.npy")
parameter = np.load("./minist_data/parameter.npy")
bias = np.load("./minist_data/bias.npy")
test_number = 10000
# 映射对应的矩阵
numbers = [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
           [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
           [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
           [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]
right_sum = 0
worse_sum = 0
right = np.zeros(10, dtype=np.int16)
worse = np.zeros(10, dtype=np.int16)
output = np.matmul(test_data, parameter)
output = output + bias
for m in range(test_number):
    if test_labels[m] == np.argmax(output[m]):
        right_sum += 1
        right[test_labels[m]] += 1
    else:
        worse_sum += 1
        worse[test_labels[m]] += 1
    if m % 1000 == 0:
        print(test_labels[m], output[m])
# 识别正确数
print(right_sum, right)
# 识别错误数
print(worse_sum, worse)