[机器学习]09-基于四种近邻算法的鸢尾花数据集分类

CONDIMENTTTT2025-08-19 10:54

基于四种不同的近邻判别方法对数据进行划分和分类

  1. 最近邻：每个测试样本的类别由其最近的一个训练样本决定。

  2. K近邻（KNN）：根据测试样本的9个最近邻的多数投票决定类别。相比NN更鲁棒，但对K值敏感。

  3. 剪辑近邻 ：训练中 迭代删除被KNN误分类的训练样本（剪辑噪声点）。测试中用剪辑后的训练集进行KNN分类。提升分类边界清晰度，减少过拟合。

  4. 压缩近邻 ：训练中 通过迭代将样本从Bag移到Store，仅保留对分类关键的样本。测试中 用Store中的样本进行最近邻分类。显著减少存储样本量，提升效率。

程序代码：

python 复制代码 
import math
import random
import matplotlib
import numpy as np
from matplotlib import pyplot as plt
from sklearn import svm

data_dict = {}
train_data = {}
test_data = {}

matplotlib.rcParams.update({'font.size': 7})

with open('Iris数据txt版.txt', 'r') as file:
    for line in file:
        line = line.strip()
        data = line.split('\t')
        if len(data) >= 3:
            try:
                category = data[0]
                attribute1 = eval(data[1])
                attribute2 = eval(data[3])
                if category in ['2', '3']:
                    if category not in data_dict:
                        data_dict[category] = {'Length': [], 'Width': []}

                    data_dict[category]['Length'].append(attribute1)
                    data_dict[category]['Width'].append(attribute2)
            except ValueError:
                print(f"Invalid data in line: {line}")
                continue
for category, attributes in data_dict.items():
    print(f'种类: {category}')
    print(len(attributes["Length"]))
    print(len(attributes["Width"]))
    print(f'属性1: {attributes["Length"]}')
    print(f'属性2: {attributes["Width"]}')

for category, attributes in data_dict.items():
    lengths = attributes['Length']
    widths = attributes['Width']
    train_indices = random.sample(range(len(lengths)), 45)
    test_indices = [i for i in range(len(lengths)) if i not in train_indices]

    train_data[category] = {
        'Length': [lengths[i] for i in train_indices],
        'Width': [widths[i] for i in train_indices]
    }

    test_data[category] = {
        'Length': [lengths[i] for i in test_indices],
        'Width': [widths[i] for i in test_indices]
    }


print(len(train_data['2']['Length']))
print(train_data['2'])
print(len(test_data['2']['Length']))
print(test_data['2'])
print(len(train_data['3']['Length']))
print(train_data['3'])
print(len(test_data['3']['Length']))
print(test_data['3'])
'''
#plt.scatter(train_data['1']['Length'], train_data['1']['Width'], color='paleturquoise', label='Category 1')
plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Basic Dataset Distribution')
plt.show()

#最近邻法
all_count = 0
right_count = 0
plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')
for category, attributes in test_data.items():
    for i in range(len(attributes['Length'])):
        test_point = (attributes['Length'][i], attributes['Width'][i])
        min_distance = math.inf
        n_category = None
        for train_category, train_attributes in train_data.items():
            for j in range(len(train_attributes['Length'])):
                train_point = (train_attributes['Length'][j], train_attributes['Width'][j])
                distance = np.sqrt((train_point[0] - test_point[0]) ** 2 + (train_point[1] - test_point[1]) ** 2)
                if distance < min_distance:
                    min_distance = distance
                    n_category = train_category
        all_count += 1
        if n_category != category:
            marker = 'x'
        else:
            marker = 'o'
            right_count += 1
        if category == '2':
            color = 'gray'
        else:
            color = 'darkgoldenrod'
        plt.scatter(test_point[0], test_point[1], color=color, marker=marker, label=f'Category {category} (Test)')

print("最近邻法准确率：",right_count/all_count)

plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Nearest Neighbor Classifier with Test Points and Predictions')
plt.show()

#k近邻法
kn = 9
all_count = 0
right_count = 0
plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')
for category, attributes in test_data.items():
    for i in range(len(attributes['Length'])):
        test_point = (attributes['Length'][i], attributes['Width'][i])
        test_label = [0,0]
        n_category = None
        distances = []
        for train_category, train_attributes in train_data.items():
            for j in range(len(train_attributes['Length'])):
                train_point = (train_attributes['Length'][j], train_attributes['Width'][j])
                distances.append(np.sqrt((np.array(train_attributes['Length'][j]) - attributes['Length'][i]) ** 2 + (np.array(train_attributes['Width'][j]) - attributes['Width'][i]) ** 2))
        nearest_indices = np.argsort(distances)[:kn]
        print(nearest_indices)
        nearest_categories = [list(train_data.keys())[index // len(train_data['2']['Length'])] for index in nearest_indices]
        print(nearest_categories)
        for k in nearest_categories:
            if k == '2':
                test_label[0] += 1
            elif k == '3':
                test_label[1] += 1
        if test_label[0] > test_label[1]:
            n_category = '2'
        else:
            n_category = '3'
        all_count += 1
        if n_category != category:
            marker = 'x'
        else:
            marker = 'o'
            right_count += 1
        if category == '2':
            color = 'gray'
        else:
            color = 'darkgoldenrod'
        plt.scatter(test_point[0], test_point[1], color=color, marker=marker, label=f'Category {category} (Test)')

print("K邻法准确率：", right_count / all_count)
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('K-Neighbors Classifier with Test Points and Predictions')
plt.show()

'''
#剪辑近邻法

kn = 9
max_iterations = 1500
correct_iterations = 1000
iteration_sum = 0
pop_sum = 0

train_data_copy = {key: {'Length': value['Length'][:], 'Width': value['Width'][:]} for key, value in data_dict.items()}
print(train_data_copy)
iterations_without_error = 0

while iterations_without_error < correct_iterations and iteration_sum < max_iterations:
    selected_category = random.choice(list(train_data_copy.keys()))
    selected_attributes = train_data_copy[selected_category]
    selected_index = random.randint(0, len(selected_attributes['Length']) - 1)
    test_point = (selected_attributes['Length'][selected_index], selected_attributes['Width'][selected_index])

    test_label = [0, 0]
    n_category = None
    distances = []
    for train_category, train_attributes in train_data_copy.items():
        for j in range(len(train_attributes['Length'])):
            distance = np.sqrt((np.array(train_attributes['Length'][j]) - test_point[0]) ** 2 +
                               (np.array(train_attributes['Width'][j]) - test_point[1]) ** 2)
            distances.append(distance)
    nearest_indices = np.argsort(distances)[:kn]
    nearest_categories = [list(data_dict.keys())[index // len(data_dict['2']['Length'])] for index in nearest_indices]

    for k in nearest_categories:
        if k == '2':
            test_label[0] += 1
        elif k == '3':
            test_label[1] += 1

    if test_label[0] > test_label[1]:
        n_category = '2'
    else:
        n_category = '3'

    if n_category != selected_category:
        train_data_copy[selected_category]['Length'].pop(selected_index)
        train_data_copy[selected_category]['Width'].pop(selected_index)
        pop_sum += 1
        iterations_without_error = 0
    else:
        iterations_without_error += 1
    iteration_sum += 1

print("删除数据点数量：", pop_sum)
print("迭代次数：", iteration_sum)
#print(train_data_copy)

plt.scatter(train_data['2']['Length'], train_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(train_data['3']['Length'], train_data['3']['Width'], color='gold', label='Category 3')
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Basic Dataset Distribution')
plt.show()

for category, attributes in train_data_copy.items():
    if category == '2':
        color = 'silver'
        label = 'Category 2'
    elif category == '3':
        color = 'gold'
        label = 'Category 3'
    plt.scatter(attributes['Length'], attributes['Width'], color=color, label=label)

plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Remaining Training Dataset Distribution')
plt.show()

test_data_copy = {}
rest_data = {}
for category, attributes in train_data_copy.items():
    lengthsx = attributes['Length']
    widthsx = attributes['Width']
    rest_indices = random.sample(range(len(lengthsx)), 40)
    test_indices_copy = [i for i in range(len(lengthsx)) if i not in rest_indices]
    test_data_copy[category] = {
        'Length': [lengthsx[i] for i in test_indices_copy],
        'Width': [widthsx[i] for i in test_indices_copy]
    }
    rest_data[category] = {
        'Length': [lengthsx[i] for i in rest_indices],
        'Width': [widthsx[i] for i in rest_indices]
    }
#print(test_data_copy['2'])
#print(test_data_copy['3'])
#print(rest_data['2'])
#print(rest_data['3'])
kn = 9
all_count = 0
right_count = 0
plt.scatter(rest_data['2']['Length'], rest_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(rest_data['3']['Length'], rest_data['3']['Width'], color='gold', label='Category 3')
for category, attributes in test_data_copy.items():
    for i in range(len(attributes['Length'])):
        test_point = (attributes['Length'][i], attributes['Width'][i])
        test_label = [0,0]
        n_category = None
        distances = []
        for train_category, rest_attributes in rest_data.items():
            for j in range(len(rest_attributes['Length'])):
                train_point = (rest_attributes['Length'][j], rest_attributes['Width'][j])
                distances.append(np.sqrt((np.array(rest_attributes['Length'][j]) - attributes['Length'][i]) ** 2 + (np.array(rest_attributes['Width'][j]) - attributes['Width'][i]) ** 2))
        nearest_ind = np.argsort(distances)[:kn]
        nearest_categories = [list(rest_data.keys())[index // len(rest_data['2']['Length'])] for index in nearest_ind]
        for k in nearest_categories:
            if k == '2':
                test_label[0] += 1
            elif k == '3':
                test_label[1] += 1
        if test_label[0] > test_label[1]:
            n_category = '2'
        else:
            n_category = '3'
        all_count += 1
        if n_category != category:
            marker = 'x'
        else:
            marker = 'o'
            right_count += 1
        if category == '2':
            color = 'gray'
        else:
            color = 'darkgoldenrod'
        plt.scatter(test_point[0], test_point[1], color=color, marker=marker, label=f'Category {category} (Test)')

print("剪辑近邻法准确率：", right_count / all_count)
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Trimming Neighbors Classifier with Test Points and Predictions')
plt.show()


#压缩近邻法

Store = []
Bag = []

# 将所有样本放入Garbbag
for category, attributes in train_data_copy.items():
    lengths = attributes['Length']
    widths = attributes['Width']
    for i in range(len(lengths)):
        Bag.append((lengths[i], widths[i], category))
random.shuffle(Bag)
#print(Bag)
#print(len(Bag))

x = random.choice(Bag)
Bag.remove(x)
Store.append(x)

max_iterations = 10000
correct_iterations = 1000
correct_sum = 0
iteration_sum = 0

while correct_sum < correct_iterations and iteration_sum < max_iterations:
    # 从Garbbag中随机选择一个样本
    x = random.choice(Bag)
    Bag.remove(x)
    lengthx, widthx, catx = x

    min_distance = math.inf
    n_category = None
    for i in Store:
        lengthy, widthy, caty = i
        distance = np.sqrt((lengthx - lengthy)**2 + (widthx - widthy)**2)
        if distance < min_distance:
            min_distance = distance
            n_category = caty
    if catx != n_category:
        Store.append(x)
        correct_sum = 0
    else:
        Bag.append(x)
        correct_sum += 1
    iteration_sum += 1

print("Store数据点数量：",len(Store))
print("迭代次数：",iteration_sum)

plt.scatter(rest_data['2']['Length'], rest_data['2']['Width'], color='silver', label='Category 2')
plt.scatter(rest_data['3']['Length'], rest_data['3']['Width'], color='gold', label='Category 3')
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Basic Dataset Distribution')
plt.show()

lengths = [sample[0] for sample in Store]
widths = [sample[1] for sample in Store]
categories = [sample[2] for sample in Store]

colors = ['silver' if category == '2' else 'gold' for category in categories]

plt.scatter(lengths, widths, c=colors, label='Store Data')
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Compressed Data Points')
plt.show()

test_data_copy = {}
for category, attributes in train_data_copy.items():
    lengthsx = attributes['Length']
    widthsx = attributes['Width']
    test_indices = random.sample(range(len(lengthsx)), 5)
    test_data_copy[category] = {
        'Length': [lengthsx[i] for i in test_indices],
        'Width': [widthsx[i] for i in test_indices]
    }

plt.scatter(lengths, widths, c=colors, label='Store Data')
for category, attributes in test_data_copy.items():
    for i in range(len(attributes['Length'])):
        test_point = (attributes['Length'][i], attributes['Width'][i])
        test_label = [0,0]
        n_category = None
        min_distance = math.inf
        for lengthz, widthz, catz in Store:
            distance = np.sqrt((lengthz - attributes['Length'][i]) ** 2 + (widthz - attributes['Width'][i]) ** 2)
            if distance < min_distance:
                min_distance = distance
                n_category = catz
        all_count += 1
        if n_category != category:
            marker = 'x'
        else:
            marker = 'o'
            right_count += 1
        if category == '2':
            color = 'gray'
        else:
            color = 'darkgoldenrod'
        plt.scatter(test_point[0], test_point[1], color=color, marker=marker, label=f'Category {category} (Test)')

print("压缩近邻法准确率：", right_count / all_count)
plt.xlabel('Length')
plt.ylabel('Width')
plt.legend()
plt.title('Zipping Neighbors Classifier with Test Points and Predictions')
plt.show()

运行结果：

种类: 2

50

50

属性1: [7.0, 6.4, 6.9, 5.5, 6.5, 5.7, 6.3, 4.9, 6.6, 5.2, 5.0, 5.9, 6.0, 6.1, 5.6, 6.7, 5.6, 5.8, 6.2, 5.6, 5.9, 6.1, 6.3, 6.1, 6.4, 6.6, 6.8, 6.7, 6.0, 5.7, 5.5, 5.5, 5.8, 6.0, 5.4, 6.0, 6.7, 6.3, 5.6, 5.5, 5.5, 6.1, 5.8, 5.0, 5.6, 5.7, 5.7, 6.2, 5.1, 5.7]

属性2: [4.7, 4.5, 4.9, 4.0, 4.6, 4.5, 4.7, 3.3, 4.6, 3.9, 3.5, 4.2, 4.0, 4.7, 3.6, 4.4, 4.5, 4.1, 4.5, 3.9, 4.8, 4.0, 4.9, 4.7, 4.3, 4.4, 4.8, 5.0, 4.5, 3.5, 3.8, 3.7, 3.9, 5.1, 4.5, 4.5, 4.7, 4.4, 4.1, 4.0, 4.4, 4.6, 4.0, 3.3, 4.2, 4.2, 4.2, 4.3, 3.0, 4.1]

种类: 3

50

50

属性1: [6.3, 5.8, 7.1, 6.3, 6.5, 7.6, 4.9, 7.3, 6.7, 7.2, 6.5, 6.4, 6.8, 5.7, 5.8, 6.4, 6.5, 7.7, 7.7, 6.0, 6.9, 5.6, 7.7, 6.3, 6.7, 7.2, 6.2, 6.1, 6.4, 7.2, 7.4, 7.9, 6.4, 6.3, 6.1, 7.7, 6.3, 6.4, 6.0, 6.9, 6.7, 6.9, 5.8, 6.8, 6.7, 6.7, 6.3, 6.5, 6.2, 5.9]

属性2: [6.0, 5.1, 5.9, 5.6, 5.8, 6.6, 4.5, 6.3, 5.8, 6.1, 5.1, 5.3, 5.5, 5.0, 5.1, 5.3, 5.5, 6.7, 6.9, 5.0, 5.7, 4.9, 6.7, 4.9, 5.7, 6.0, 4.8, 4.9, 5.6, 5.8, 6.1, 6.4, 5.6, 5.1, 5.6, 6.1, 5.6, 5.5, 4.8, 5.4, 5.6, 5.1, 5.1, 5.9, 5.7, 5.2, 5, 5.2, 5.4, 5.1]

45

{'Length': [6.1, 6.0, 5.5, 7.0, 5.7, 6.1, 5.8, 6.4, 5.7, 5.8, 6.3, 5.5, 5.5, 6.6, 6.3, 6.7, 5.6, 6.9, 6.6, 6.1, 6.0, 5.4, 5.6, 5.1, 5.9, 5.7, 6.8, 5.9, 6.7, 6.1, 5.7, 6.4, 6.5, 6.0, 5.6, 5.0, 5.2, 5.5, 6.7, 5.5, 6.2, 5.8, 5.6, 6.3, 6.0], 'Width': [4.6, 4.0, 3.8, 4.7, 3.5, 4.7, 3.9, 4.5, 4.2, 4.1, 4.4, 4.0, 4.0, 4.4, 4.9, 4.7, 4.2, 4.9, 4.6, 4.7, 4.5, 4.5, 3.6, 3.0, 4.8, 4.1, 4.8, 4.2, 5.0, 4.0, 4.2, 4.3, 4.6, 4.5, 4.1, 3.5, 3.9, 4.4, 4.4, 3.7, 4.3, 4.0, 4.5, 4.7, 5.1]}

5

{'Length': [5.7, 4.9, 6.2, 5.6, 5.0], 'Width': [4.5, 3.3, 4.5, 3.9, 3.3]}

45

{'Length': [7.4, 6.4, 6.1, 5.8, 6.0, 6.5, 7.7, 7.6, 7.1, 6.9, 5.7, 6.3, 6.4, 7.3, 7.2, 7.2, 5.6, 6.7, 6.9, 7.7, 6.3, 6.0, 6.2, 6.1, 6.8, 6.3, 6.2, 6.8, 6.4, 6.7, 6.7, 6.4, 6.4, 7.2, 7.7, 7.7, 6.3, 6.5, 6.7, 5.8, 5.9, 6.7, 6.3, 6.3, 7.9], 'Width': [6.1, 5.3, 5.6, 5.1, 5.0, 5.5, 6.7, 6.6, 5.9, 5.1, 5.0, 4.9, 5.6, 6.3, 6.1, 5.8, 4.9, 5.2, 5.7, 6.7, 5.6, 4.8, 4.8, 4.9, 5.5, 5.6, 5.4, 5.9, 5.6, 5.8, 5.7, 5.3, 5.5, 6.0, 6.9, 6.1, 5, 5.2, 5.6, 5.1, 5.1, 5.7, 6.0, 5.1, 6.4]}

5

{'Length': [5.8, 6.5, 4.9, 6.5, 6.9], 'Width': [5.1, 5.8, 4.5, 5.1, 5.4]}

{'2': {'Length': [7.0, 6.4, 6.9, 5.5, 6.5, 5.7, 6.3, 4.9, 6.6, 5.2, 5.0, 5.9, 6.0, 6.1, 5.6, 6.7, 5.6, 5.8, 6.2, 5.6, 5.9, 6.1, 6.3, 6.1, 6.4, 6.6, 6.8, 6.7, 6.0, 5.7, 5.5, 5.5, 5.8, 6.0, 5.4, 6.0, 6.7, 6.3, 5.6, 5.5, 5.5, 6.1, 5.8, 5.0, 5.6, 5.7, 5.7, 6.2, 5.1, 5.7], 'Width': [4.7, 4.5, 4.9, 4.0, 4.6, 4.5, 4.7, 3.3, 4.6, 3.9, 3.5, 4.2, 4.0, 4.7, 3.6, 4.4, 4.5, 4.1, 4.5, 3.9, 4.8, 4.0, 4.9, 4.7, 4.3, 4.4, 4.8, 5.0, 4.5, 3.5, 3.8, 3.7, 3.9, 5.1, 4.5, 4.5, 4.7, 4.4, 4.1, 4.0, 4.4, 4.6, 4.0, 3.3, 4.2, 4.2, 4.2, 4.3, 3.0, 4.1]}, '3': {'Length': [6.3, 5.8, 7.1, 6.3, 6.5, 7.6, 4.9, 7.3, 6.7, 7.2, 6.5, 6.4, 6.8, 5.7, 5.8, 6.4, 6.5, 7.7, 7.7, 6.0, 6.9, 5.6, 7.7, 6.3, 6.7, 7.2, 6.2, 6.1, 6.4, 7.2, 7.4, 7.9, 6.4, 6.3, 6.1, 7.7, 6.3, 6.4, 6.0, 6.9, 6.7, 6.9, 5.8, 6.8, 6.7, 6.7, 6.3, 6.5, 6.2, 5.9], 'Width': [6.0, 5.1, 5.9, 5.6, 5.8, 6.6, 4.5, 6.3, 5.8, 6.1, 5.1, 5.3, 5.5, 5.0, 5.1, 5.3, 5.5, 6.7, 6.9, 5.0, 5.7, 4.9, 6.7, 4.9, 5.7, 6.0, 4.8, 4.9, 5.6, 5.8, 6.1, 6.4, 5.6, 5.1, 5.6, 6.1, 5.6, 5.5, 4.8, 5.4, 5.6, 5.1, 5.1, 5.9, 5.7, 5.2, 5, 5.2, 5.4, 5.1]}}

删除数据点数量： 6

迭代次数： 1203

剪辑近邻法准确率： 0.9285714285714286

Store数据点数量： 10

迭代次数： 1336

压缩近邻法准确率： 0.9583333333333334

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