鸢尾花分类和手写数字识别（K近邻）

鸢尾花分类

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
import pandas as pd
import mglearn

# 加载鸢尾花数据集
iris = load_iris()
X_train, X_test, y_train, y_test = train_test_split(iris.data,
                                                    iris.target,
                                                    test_size=0.3,
                                                    random_state=0)

# 导入数据集
iris_dataframe = pd.DataFrame(X_train, columns=iris.feature_names)
# 绘制散点矩阵图
grr = pd.plotting.scatter_matrix(iris_dataframe, # 要绘制散点矩阵图的特征数据
                                 c=y_train, # 指定颜色映射的依据
                                 figsize=(15, 15),
                                 marker='o',
                                 hist_kwds={'bins': 20}, # 设置直方图的参数，将直方图分为 20 个区间
                                 s=60,
                                 alpha=.8,
                                 cmap=mglearn.cm3) # 设置颜色映射，这里是使用 mglearn.cm3 颜色映射

from sklearn.neighbors import KNeighborsClassifier

knn = KNeighborsClassifier(n_neighbors = 3)
knn.fit(X_train,y_train)

KNeighborsClassifier(n_neighbors=3)

import numpy as np
y_pred = knn.predict(X_test)
print("Test set predictions:\n{}".format(y_pred))
print("Test set score:{:.2f}".format(np.mean(y_pred == y_test)))

Test set predictions:
[2 1 0 2 0 2 0 1 1 1 2 1 1 1 1 0 1 1 0 0 2 1 0 0 2 0 0 1 1 0 2 1 0 2 2 1 0
 2 1 1 2 0 2 0 0]
Test set score:0.98

手写数字识别

import torch
from torch.utils.data import DataLoader
import torchvision.datasets as dsets
import torchvision.transforms as transforms

#指定每次训练迭代的样本数量
batch_size = 100
transform = transforms.ToTensor()  #将图片转化为PyTorch张量

train_dataset = dsets.MNIST(root='./data',
                            train=True,
                            transform=transforms.ToTensor(),
                            download=False)
test_dataset = dsets.MNIST(root='./data',
                           train=False,
                           transform=transforms.ToTensor(),
                           download=False)
#加载数据
train_loader = DataLoader(dataset=train_dataset,
                          batch_size=batch_size,
                          shuffle=True)
test_loader = DataLoader(dataset=test_dataset,
                         batch_size=batch_size,
                         shuffle=True)

print("train data:",train_dataset.data.size())
print("train labels:",train_dataset.targets.size())
print("test data:",test_dataset.data.size())
print("test labels:",test_dataset.targets.size())

train data: torch.Size([60000, 28, 28])
train labels: torch.Size([60000])
test data: torch.Size([10000, 28, 28])
test labels: torch.Size([10000])

import matplotlib.pyplot as plt

# 看下第99张图是什么
train = train_loader.dataset.data[98]
plt.imshow(train, cmap=plt.cm.binary)
plt.show()
print(train_loader.dataset.targets[98])

tensor(3)

# 若不进行图像预处理：
import numpy as np
import operator
 
# KNN分类器构建
class KNNClassifier:
    def __init__(self):
        self.Xtr = None
        self.ytr = None
 
    def fit(self, X_train, y_train):
        self.Xtr = X_train
        self.ytr = y_train
 
    def predict(self, k, dis, X_test):
        assert dis == 'E' or dis == 'M'  # E代表欧氏距离, M代表曼哈顿距离。确保变量dis的值必须是'E'或'M'，否则会抛出异常
        num_test = X_test.shape[0]
        labellist = []
 
        if dis == 'E':
            for i in range(num_test):
                distances = np.sqrt(np.sum(((self.Xtr - np.tile(X_test[i], (self.Xtr.shape[0],1))) ** 2), axis=1))
                nearest_k = np.argsort(distances)[:k]
                classCount = {self.ytr[i]: 0 for i in nearest_k}
                for i in nearest_k:
                    classCount[self.ytr[i]] += 1
                sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
                labellist.append(sortedClassCount[0][0])
 
        elif dis == 'M':
            for i in range(num_test):
                distances = np.sum(np.abs(self.Xtr - np.tile(X_test[i], (self.Xtr.shape[0], 1))), axis=1)
                nearest_k = np.argsort(distances)[:k]
                classCount = {self.ytr[i]: 0 for i in nearest_k}
                for i in nearest_k:
                    classCount[self.ytr[i]] += 1
                sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
                labellist.append(sortedClassCount[0][0])
 
        return np.array(labellist)

if __name__ == '__main__':
    X_train = train_loader.dataset.data.numpy()  # 转化为numpy
    X_train = X_train.reshape(X_train.shape[0], 28 * 28)
    y_train = train_loader.dataset.targets.numpy()
 
    X_test = test_loader.dataset.data[:1000].numpy()
    X_test = X_test.reshape(X_test.shape[0], 28 * 28)
    y_test = test_loader.dataset.targets[:1000].numpy()
 
    num_test = y_test.shape[0]
 
    knn = KNNClassifier()
    knn.fit(X_train, y_train)
 
    
    y_test_pred = knn.predict(5, 'M', X_test)
 
    num_correct = np.sum(y_test_pred == y_test)
    accuracy = float(num_correct) / num_test
    print('Got %d / %d correct => accuracy: %f' % (num_correct, num_test, accuracy))

Got 368 / 1000 correct => accuracy: 0.368000

KNN算法在计算距离时对特征的尺度非常敏感。如果图像的尺寸或像素值范围（亮度或颜色深度）不统一，可能会导致距离计算偏向于尺度较大的特征。如：将所有图像归一化到同一尺寸和/或将像素值标准化到同一范围（如0到1），可以确保不同的特征对距离的贡献均衡，从而使KNN分类器更公平、更准确。

KNN算法是基于距离度量（如欧氏距离或曼哈顿距离）来确定每个测试点的“邻居”，因此确保所有特征具有相似的尺度是至关重要的。对于KNN来说，由于它对数据的尺度敏感，选择均值方差归一化通常是更好的选择。

# 代码改进:添加一个均值方差归一化函数

def standardize_image(image): #均值方差归一化
    mean = np.mean(image)
    std = np.std(image)
    return (image - mean) / std

 # 图像（归一化）
train = train_loader.dataset.data[:1000].numpy()
digit_01 = train[33]
digit_02 = standardize_image(digit_01)
plt.imshow(digit_01, cmap=plt.cm.binary)
plt.show()
plt.imshow(digit_02, cmap=plt.cm.binary)
plt.show()
print(train_loader.dataset.targets[33])
print("Before standardization: mean = {}, std = {}".format(np.mean(digit_01), np.std(digit_01)))
print("After standardization: mean = {}, std = {}".format(np.mean(digit_02), np.std(digit_02)))

tensor(9)
Before standardization: mean = 27.007653061224488, std = 70.88341925375865
After standardization: mean = 5.890979314337566e-17, std = 1.0

虽然归一化前后的图像在视觉上似乎并无明显的差异，但通过打印归一化前后的像素值平均值和标准差可以发现标准化后，数据的平均值为5.890979314337566e-17，接近0（浮点数计算的微小误差，这在数值计算中可以视为0），这是标准化的预期结果，旨在将数据的均值中心化到0；标准差为1.0，确保数据的尺度一致。

if __name__ == '__main__':
    #训练数据
    X_train = train_loader.dataset.data.numpy()  #转化为numpy
    X_train = X_train.reshape(X_train.shape[0], 28 * 28)
    X_train = standardize_image(X_train) #均值方差归一化处理
    y_train = train_loader.dataset.targets.numpy()
 
    #测试数据
    X_test = test_loader.dataset.data[:1000].numpy()
    X_test = X_test.reshape(X_test.shape[0], 28 * 28)
    X_test = standardize_image(X_test)
    y_test = test_loader.dataset.targets[:1000].numpy()
 
    num_test = y_test.shape[0]
 
    knn = KNNClassifier()
    knn.fit(X_train,y_train)
 
   # y_test_pred = kNN_classify(5,'M',X_train,y_train,X_test)
    y_test_pred = knn.predict(5,'M',X_test)
 
    num_correct = np.sum(y_test_pred == y_test)
    accuracy = float(num_correct) / num_test
    print('Got %d / %d correct => accuracy: %f' % (num_correct,num_test,accuracy))

Got 950 / 1000 correct => accuracy: 0.950000