I. KNN基本原理
关于KNN的基本原理可以参考我之前写的一篇文章：最简单的分类算法之一：KNN（原理解析+代码实现）
II. 数据处理
导入torchvision.datasets.MNIST数据集：
def load_data():
dataset_train = torchvision.datasets.MNIST(root='./data/', train=True, transform=transforms.ToTensor())
dataset_test = torchvision.datasets.MNIST(root='./data/', train=False, transform=transforms.ToTensor())
data_train = dataset_train.data
X_train = data_train.numpy()
X_test = dataset_test.data.numpy()
X_train = np.reshape(X_train, (60000, 784))
X_test = np.reshape(X_test, (10000, 784))
Y_train = dataset_train.targets.numpy()
Y_test = dataset_test.targets.numpy()
return X_train, Y_train, X_test, Y_test
训练集中含有60000条数据，测试集中含有10000条数据。任意输出一条数据：
print(X_train[0], Y_train[0])
结果为：
[ 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
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
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
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
0 0 0 0 0 0 0 0 3 18 18 18 126 136 175 26 166 255
247 127 0 0 0 0 0 0 0 0 0 0 0 0 30 36 94 154
170 253 253 253 253 253 225 172...] 5
x是一个维度为784的一维数组，y是标签。
III. 手写KNN
为了减少计算量，训练集长度改为30000，测试集长度改为1000。
def get_distance(x1, x2):
return np.linalg.norm(x1 - x2)
def get_vec(K, x, train_x, train_y):
res = []
for i in range(len(train_x)):
dis = get_distance(x, train_x[i])
res.append([dis, train_y[i]])
res = sorted(res, key=(lambda t: t[0]))
return res[:K]
def knn(K):
train_x, train_y, test_x, test_y = load_data()
train_x, train_y, test_x, test_y = train_x[:30000], train_y[:30000], test_x[:1000], test_y[:1000]
cnt = 0
for i in range(len(test_x)):
# print(i)
x = test_x[i]
y = test_y[i]
vec = get_vec(K, x, train_x, train_y)
weight = [] # 权重与序号
sum_distance = 0.0
for j in range(K):
sum_distance += vec[j][0] # 计算前K个距离的和
for j in range(K):
weight.append([1 - vec[j][0] / sum_distance, vec[j][1]]) # 权重+序号
# 将相同序号的加起来
num = [] # 统计有哪些序号
for j in range(K):
num.append(weight[j][1])
num = list(set(num)) # 去重
final_res = []
for j in range(len(num)):
res = 0.0
for k in range(len(weight)):
if weight[k][1] == num[j]: # 前K个标签一样的样本权值加起来
res += weight[k][0]
final_res.append([res, num[j]])
final_res = sorted(final_res, key=(lambda e: e[0]), reverse=True) # 按照权重从大到小排序
if y == final_res[0][1]:
cnt = cnt + 1
print(y, final_res[0][1])
print('accuracy:', cnt / len(test_x))
if __name__ == '__main__':
K = 10
knn(K)
如果想要提升精度，可以增加训练集容量。
IV. sklearn.KNeighborsClassifier
采用sklearn中的KNeighborsClassifier对数据进行训练和测试，此时训练集和测试集都包括完整的数据：
if __name__ == '__main__':
K = 10
train_x, train_y, test_x, test_y = load_data()
knn = KNeighborsClassifier(n_neighbors=K)
knn.fit(train_x, train_y)
acc = knn.score(test_x, test_y)
print('accuracy:', acc)
结果：
V. 完整代码
# -*- coding: utf-8 -*-
"""
@Time ： 2022/1/7 21:28
@Author ：KI
@File ：knn-mnist.py
@Motto：Hungry And Humble
"""
import numpy as np
import torchvision
import torchvision.transforms as transforms
from sklearn.neighbors import KNeighborsClassifier
def load_data():
dataset_train = torchvision.datasets.MNIST(root='./data/', train=True, transform=transforms.ToTensor())
dataset_test = torchvision.datasets.MNIST(root='./data/', train=False, transform=transforms.ToTensor())
data_train = dataset_train.data
X_train = data_train.numpy()
X_test = dataset_test.data.numpy()
X_train = np.reshape(X_train, (60000, 784))
X_test = np.reshape(X_test, (10000, 784))
Y_train = dataset_train.targets.numpy()
Y_test = dataset_test.targets.numpy()
return X_train, Y_train, X_test, Y_test
def get_distance(x1, x2):
return np.linalg.norm(x1 - x2)
def get_vec(K, x, train_x, train_y):
res = []
for i in range(len(train_x)):
dis = get_distance(x, train_x[i])
res.append([dis, train_y[i]])
res = sorted(res, key=(lambda t: t[0]))
return res[:K]
def knn(K):
train_x, train_y, test_x, test_y = load_data()
train_x, train_y, test_x, test_y = train_x[:30000], train_y[:30000], test_x[:1000], test_y[:1000]
cnt = 0
for i in range(len(test_x)):
# print(i)
x = test_x[i]
y = test_y[i]
vec = get_vec(K, x, train_x, train_y)
weight = [] # 权重与序号
sum_distance = 0.0
for j in range(K):
sum_distance += vec[j][0] # 计算前K个距离的和
for j in range(K):
weight.append([1 - vec[j][0] / sum_distance, vec[j][1]]) # 权重+序号
# 将相同序号的加起来
num = [] # 统计有哪些序号
for j in range(K):
num.append(weight[j][1])
num = list(set(num)) # 去重
final_res = []
for j in range(len(num)):
res = 0.0
for k in range(len(weight)):
if weight[k][1] == num[j]: # 前K个标签一样的样本权值加起来
res += weight[k][0]
final_res.append([res, num[j]])
final_res = sorted(final_res, key=(lambda e: e[0]), reverse=True) # 按照权重从大到小排序
if y == final_res[0][1]:
cnt = cnt + 1
print(y, final_res[0][1])
print('accuracy:', cnt / len(test_x))
if __name__ == '__main__':
K = 10
knn(K)
# train_x, train_y, test_x, test_y = load_data()
# knn = KNeighborsClassifier(n_neighbors=K)
# knn.fit(train_x, train_y)
# acc = knn.score(test_x, test_y)
# print('accuracy:', acc)