python-机器学习的两种传统算法-knn，k-means
2024-05-16 06:37:18
机器学习的两种传统算法
knn–监督学习-分类算法
- 概念：KNN（K- Nearest Neighbor）即K最邻近法。数据挖掘分类技术中最简单的方法之一。所谓K最近邻，就是K个最近的邻居的意思，说的是每个样本都可以用它最接近的K个邻近值来代表。近邻算法就是将数据集合中每一个记录进行分类的方法
- 核心思想：如果一个样本在特征空间中的K个最相邻的样本中的大多数属于某一个类别，则该样本也属于这个类别，并具有这个类别上样本的特性。该方法在确定分类决策上只依据最邻近的一个或者几个样本的类别来决定待分样本所属的类别。
- 优点：KNN方法思路简单，易于理解，易于实现，无需估计参数，无需训练。
- 缺点：1、当样本不平衡时，如一个类的样本容量很大，而其他类样本容量很小时，有可能导致当输入一个新样本时，该样本的K个邻居中大容量类的样本占多数 。2、计算量较大，因为对每一个待分类的文本都要计算它到全体已知样本的距离，才能求得它的K个最近邻点。
- 算法实现
已知有4个点 (1.0,1.2),(1.0,1.0), (0,0.1), (0.1,0.1) 前两个点属于A类用红色表示，后两个点属于B类用蓝色表示。求新给出的点的分类，并画出。
#对数据进行分类
import numpy as np
import matplotlib.pyplot as plt#创建数据
def createDataSet():#已知的点group = np.array([[1.0,1.2],[1.0,1.0],[0,0.1],[0.1,0.1]])#根据已知点猜一下已知位置 前两个设置为A类型，后两个设置为B类型labels = ['A','A','B','B'] # 标签#函数中返回的序列默认为元组return group,labels # 返回为元组类型#将数据展示到组坐标轴上
def show_data(group,labels):# 将list类型转换为numpy类型labels = np.array(labels)# 找出A类下标index_a = np.where(labels == 'A')# 找出类下标index_b = np.where(labels == 'B')
# 画点的两个函数 plot，scatter
# plot 只能画标量，scatter能画张量for i in labels:if i == 'A':#将A类点画为红色plt.scatter(group[index_a,0],group[index_a,1],c = 'red')#将B类点画为蓝色elif i == 'B':plt.scatter(group[index_b,0],group[index_b,1],c ='blue')plt.xlabel("x")plt.ylabel("y")plt.show()# knn 分类器
# 给一个新的数据，给这个数据分到已知的类中
def classify(inX,dataset,label,k): # inX：新数据，dataset,label,已知类# 求出元数据的总个数datasetSize = dataset.shape[0]# 求新的点到任意一点的距离diff = dataset-inXdiff_diff = diff**2diff_sum = diff_diff.sum(axis=1)distance = diff_sum ** 0.5# 对所有的距离进行索引排序sortDistanceIndex = distance.argsort()# print(sortDistanceIndex) #[2 3 1 0]#对该点分类进行投票classCount = {}# 选取k个邻居点for i in range(k):label1 = labels[sortDistanceIndex[i]]# 计数classCount[label1] = classCount.get(label1,0)+1# print(classCount)# 对投票结果进行排序(降序)sortedClassCount = sorted(classCount.items(),key=lambda kv:(kv[0],kv[1]),reverse=True)# print(sortedClassCount)# 对分类结果返回return sortedClassCount[0][0]if __name__ == '__main__':#导入数据data_set,labels = createDataSet()x = [0,0.5]# show_data(data_set, labels)#分类结果classname = classify(x,data_set,labels,3)print(f'该数据属于{classname}类')# 将新数据添加到已知数据并画图data_set = np.vstack((data_set,x))labels.append(classname)# show_data(data_set,labels)
结果：
k-means—非监督学习-分类算法
- 概念：k-means 是一种迭代求解的聚类分析算法，聚类是一个将数据集中在某些方面相似的数据成员进行分类组织的过程，聚类就是一种发现这种内在结构的技术，聚类技术经常被称为无监督学习。k均值聚类是最著名的划分聚类算法，由于简洁和效率使得他成为所有聚类算法中最广泛使用的。给定一个数据点集合和需要的聚类数目k，k由用户指定，k均值算法根据某个距离函数反复把数据分入k个聚类中。
- 核心思想：先随机选取K个对象作为初始的聚类中心。然后计算每个对象与各个种子聚类中心之间的距离，把每个对象分配给距离它最近的聚类中心。聚类中心以及分配给它们的对象就代表一个聚类。一旦全部对象都被分配了，每个聚类的聚类中心会根据聚类中现有的对象被重新计算。这个过程将不断重复直到满足某个终止条件。终止条件可以是以下任何一个：1)没有（或最小数目）对象被重新分配给不同的聚类。2)没有（或最小数目）聚类中心再发生变化。3)误差平方和局部最小。
- 算法实现
给出一堆初始样本点，用k-maens算法进行分类。初始样本点如下图所示。
代码实现：
# k-means 代码实现步骤
#1.取出k个随机向量作为中心点用于初始化
#2.计算每个点与K个中心点的距离，然后将每个点聚集到与最近的中心点
#3.新的聚集出来后，计算每个聚集新的中心点
#4.迭代2，3 直至满足条件推出(中心点趋于收敛)
import numpy as np
import matplotlib.pyplot as plt
import copy#获取数据
def get_data(filename):data = np.loadtxt(filename,delimiter="\t")return data# 欧式距离计算
def get_dist(x,y):diff = (x-y)**2sum1 = np.sum(diff,axis=1)dis = sum1**0.5return dis# 初始化分区，随机获取初始中心点
def get_randcenter(dataSet,k):# 随机找到中心点的x轴坐标c_x = np.random.randint(0,np.max(dataSet)-20,size=k)c_y = np.random.randint(0,np.max(dataSet)-20,size=k)c = np.array(list(zip(c_x,c_y)),dtype=np.float32)return c# 画出初始数据和随机找的中心点图像
def draw_picture1(dataSet,x,k):m = np.shape(dataSet)[0]# plt.figure(figsize=(30,8),dpi=80)for i in range(m):plt.scatter(dataSet[i,0],dataSet[i,1],c="blue",s=4)for i in range(k):plt.scatter(x[i,0],x[i,1],marker='*',c="red",s=100)plt.show()
# k-means迭代
def K_means(dataSet,x,k):# 保存中心点更新前的坐标C_old = np.zeros(x.shape)# print(C_old)# 保存数据所属于哪个中心点clusters = np.zeros(len(dataSet))# 计算新的中心点和旧的中心点之间的距离diff_flag = get_dist(x,C_old)# 若中心点不再变化，则退出循环while diff_flag.any() != 0:# 循环计算出每个点对应的最近中心点for i in range(len(dataSet)):distant = get_dist(dataSet[i],x)# 标记离该样本点最近的中心点的下标cluster = np.argmin(distant)clusters[i] = cluster# 深拷贝当前中心点C_old = copy.deepcopy(x)# 寻找新的中心点--将属于每个中心的样本点放入一个数组中按照列方向取平均值for i in range(k):for j in range(len(dataSet)):if(clusters[j]==i):points=[dataSet[j]]x[i] = np.mean(points,axis=0)# 计算新旧节点之间的距离diff_flag = get_dist(C_old,x)# 返回中心点和clustersreturn x,clusters# 最终结果展示
def draw_picture2(dataSet,center,clusters,k):colors = ['r','g','b']for i in range(k):for j in range(len(dataSet)):if(clusters[j] == i):#画样本点plt.scatter(dataSet[j,0],dataSet[j,1],c = colors[i],s=3)for i in range(k):#画中心点plt.scatter(center[i,0],center[i,1],marker="*",c="black",s=100)plt.show()if __name__ == '__main__':data_set = get_data("test01.txt")get_randcenter(data_set,3)center = get_randcenter(data_set,3)# 初始数据展示图# draw_picture1(data_set,center,3)# 最终结果展示new_center, clusters = K_means(data_set,center,3)draw_picture2(data_set,new_center,clusters,3)
note：因为循环次数的原因，需要循环多次才能达到一个很好的效果。读者可以在循环处多加一个条件即可达到想要的结果。如下图：
结果：
本代码数据：
2.072345 -3.241693
17.93671 15.78481
1.083576 7.319176
11.12067 14.40678
23.71155 2.557729
24.16993 32.02478
21.66578 4.892855
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0.4075031 15.29705
7.314846 3.309312
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4.415292 22.81555
11.94122 8.122487
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-11.70671 8.073185
7.255978 14.63704
3.392373 1.220712
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