K近邻算法-1.原理及简单实现

淡淡的烟草味﹌ 2023-08-17 16:44 106阅读 0赞

# K近邻算法 #

K近邻算法，又称KNN算法，是机器学习入门的第一个算法，其解决的是分类问题，具有以下特点：

*  思想简单
 *  应用数学知识少
 *  效果好（后续会讨论其缺点）
 *  机器学习的入门算法

## 原理及简单实现 ##

**例：图为肿瘤时间与大小对于肿瘤的分类，红色代表良性肿瘤，蓝色代表了恶性肿瘤，当新来一个数据点（绿色数据点）如何判断它的类别？**  
![1465169-20190711201621373-1931397067.png][]

编程实现预测

import numpy as np
    import matplotlib.pyplot as plt
    # 定义十个样本和它的结果集，每个样本有两个特征值
    
    data_x = [
        [3.393533211, 2.331273381],
        [3.110073483, 1.781539638],
        [1.343808831, 3.368360954],
        [3.582294042, 4.679179110],
        [2.280362439, 2.866990263],
        [7.423436942, 4.696522875],
        [5.745051997, 3.533989803],
        [9.172168622, 2.511101045],
        [7.792783481, 3.424088941],
        [7.939820817, 0.791637231]
    ]
    data_y = [0,0,0,0,0,1,1,1,1,1]

把样本和结果 转化为numpy矩阵

x_train = np.array(data_x)  
    y_train = np.array(data_y)

输出结果：  
![1465169-20190711210813782-22943069.png][]

基于样本的两个属性（x和y坐标），绘制样本散点图，不同颜色代表不同结果

plt.scatter(x_train[y_train==0,0], x_train[y_train==0,1], color='g')
    plt.scatter(x_train[y_train==1,0], x_train[y_train==1,1], color='r')
    plt.show()

![1465169-20190711210917383-1050245838.png][]

来了一个新的样本 ，在样本集中表现出来

x = np.array([8.093607318, 3.365731514])
    plt.scatter(x_train[y_train==0,0], x_train[y_train==0,1], color='g')
    plt.scatter(x_train[y_train==1,0], x_train[y_train==1,1], color='r')
    plt.scatter(x[0], x[1], color='b')
    plt.show()

![1465169-20190711210933389-1972833356.png][]

## K近邻算法核心：分别求出新样本与已有样本的距离 ##

![1465169-20190711211334999-118746851.png][]

# 导入math包中求平方根
    from math import sqrt  
    distances = []
    for x_tep in x_train:
        d = sqrt(np.sum((x_tep - x)**2))
        distances.append(d)

![1465169-20190711211436183-1069097898.png][]

根据索引排序,返回的数据为和新样本的距离从小到大排列的原有样本的索引

nearest = np.argsort(distances)

![1465169-20190711211024202-886292181.png][]

找出距离此新样本最近的k个原始样本的结果

k = 6
    topk_y = [y_train[i] for i in nearest[:k]]

![1465169-20190711211125446-493402260.png][]

统计数组中的元素，及它出现的次数，找到票数最多的n个元素

from collections import Counter  
    votes = Counter(topk_y)
    votes.most_common(3)   #[（元素，票数）]

![1465169-20190711211739338-1166798366.png][]

**得到预测的值**

predict_y = votes.most_common()[0][0] #预测的值

![1465169-20190711211223866-163440948.png][]

转载于:https://www.cnblogs.com/shuai-long/p/11172421.html

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