随笔8

作业信息

| 作业课程 | [机器学习](https://edu.cnblogs.com/campus/ahgc/machinelearning/) |

|----------------------- |------------------------------|

| 作业要求 | [作业要求](https://edu.cnblogs.com/campus/ahgc/machinelearning/) |

| 学号 | 3180701241 |

一.实验目的

(1)理解K-近邻算法原理,能实现算法K近邻算法;

(2)掌握常见的距离度量方法;

(3)掌握K近邻树实现算法;

(4)针对特定应用场景及数据,能应用K近邻解决实际问题。

二.实验内容

(1)实现曼哈顿距离、欧氏距离、闵式距离算法,并测试算法正确性。

(2)实现K近邻树算法;

(3)针对iris数据集,应用sklearn的K近邻算法进行类别预测;

(4)针对iris数据集,编制程序使用K近邻树进行类别预测;

三.实验报告要求

(1)对照实验内容,撰写实验过程、算法及测试结果;

(2)代码规范化:命名规则、注释;

(3)分析核心算法的复杂度;

(4)查阅文献,讨论K近邻的优缺点; (5)举例说明K近邻的应用场景。

四.实验代码

1

距离度量

利用python代码遍历三个点中,与1点距离最近的点

import math
from itertools import combinations
def L(x, y, p=2):
# x1 = [1, 1], x2 = [5,1]
if len(x) == len(y) and len(x) > 1:
sum = 0
for i in range(len(x)):
sum += math.pow(abs(x[i] - y[i]), p)
return math.pow(sum, 1/p)
else:
return 0
x1 = [1, 1]
x2 = [5, 1]
x3 = [4, 4]

结果:

(3.0, '1-[4, 4]')
(3.0, '1-[4, 4]')
(3.0, '1-[4, 4]')
(3.0, '1-[4, 4]')

2.编写K-近邻算法

python实现,遍历所有数据点,找出n个距离最近的点的分类情况,少数服从多数(不使用直接的python中现有的K-近邻算法包)

# 导包
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from collections import Counter
复制代码
复制代码
# data 输入数据
iris = load_iris() # 获取python中鸢尾花Iris数据集
df = pd.DataFrame(iris.data, columns=iris.feature_names) # 将数据集使用DataFrame建表
df['label'] = iris.target # 将表的最后一列作为目标列
df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label'] # 定义表中每一列
# data = np.array(df.iloc[:100, [0, 1, -1]])

结果:

 

#数据进行可视化
#将标签为0、1的两种花,根据特征为长度和宽度打点表示
plt.scatter(df[:50]['sepal length'], df[:50]['sepal width'], label='0')
plt.scatter(df[50:100]['sepal length'], df[50:100]['sepal width'], label='1')
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()

结果:

#取数据,并且分成训练和测试集合
data = np.array(df.iloc[:100, [0, 1, -1]])
#按行索引,取出第0列第1列和最后一列,即取出sepal长度、宽度和标签
X, y = data[:,:-1], data[:,-1]#X为sepal length,sepal width y为标签 
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
# train_test_split函数用于将矩阵随机划分为训练子集和测试子集
复制代码
复制代码
# 建立一个类KNN,用于k-近邻的计算
class KNN:
    #初始化
    def __init__(self, X_train, y_train, n_neighbors=3, p=2): # 初始化数据,neighbor表示邻近点,p为欧氏距离
        self.n = n_neighbors
        self.p = p
        self.X_train = X_train
        self.y_train = y_train
    
    def predict(self, X):
        # X为测试集
        knn_list = []
        for i in range(self.n): # 遍历邻近点
            dist = np.linalg.norm(X - self.X_train[i], ord=self.p) # 计算训练集和测试集之间的距离
            knn_list.append((dist, self.y_train[i])) # 在列表末尾添加一个元素
            
        for i in range(self.n, len(self.X_train)): # 3-20
            max_index = knn_list.index(max(knn_list, key=lambda x: x[0])) # 找出列表中距离最大的点
            dist = np.linalg.norm(X - self.X_train[i], ord=self.p) # 计算训练集和测试集之间的距离
            if knn_list[max_index][0] > dist:   # 若当前数据的距离大于之前得出的距离,就将数值替换
                knn_list[max_index] = (dist, self.y_train[i])
                
        # 统计
        knn = [k[-1] for k in knn_list]
        count_pairs = Counter(knn)   # 统计标签的个数
        max_count = sorted(count_pairs, key=lambda x:x)[-1]  # 将标签升序排列
        return max_count
    
    # 计算测试算法的正确率
    def score(self, X_test, y_test):
        right_count = 0 
        n = 10
        for X, y in zip(X_test, y_test):
            label = self.predict(X)
            if label == y:
                right_count += 1
        return right_count / len(X_test)
复制代码
clf = KNN(X_train, y_train) # 调用KNN算法进行计算
clf.score(X_test, y_test) # 计算正确率

结果:Out [12]:1.0

#预测点
test_point = [6.0, 3.0]
#预测结果
print('Test Point: {}'.format(clf.predict(test_point)))

结果:Test Point: 1.0

plt.scatter(df[:50]['sepal length'], df[:50]['sepal width'], label='0')
plt.scatter(df[50:100]['sepal length'], df[50:100]['sepal width'], label='1')
#打印预测点
plt.plot(test_point[0], test_point[1], 'bo', label='test_point')
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()

结果:

3.使用scikitlearn中编好的包直接调用实现K-近邻算法 

 

sklearn.neighbors.KNeighborsClassifier
n_neighbors: 临近点个数
p: 距离度量
algorithm: 近邻算法,可选{'auto', 'ball_tree', 'kd_tree', 'brute'}
weights: 确定近邻的权重

# 导包
from sklearn.neighbors import KNeighborsClassifier
# 调用
clf_sk = KNeighborsClassifier()
clf_sk.fit(X_train, y_train)

结果:

Out[16]:
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
metric_params=None, n_jobs=1, n_neighbors=5, p=2,
weights='uniform')

clf_sk.score(X_test, y_test) # 计算正确率
结果:Out [17]:1.0
4.针对iris数据集,编制程序使用K近邻树进行类别预测
# 建造kd树
# kd-tree 每个结点中主要包含的数据如下:
class KdNode(object):
    def __init__(self, dom_elt, split, left, right):
        self.dom_elt = dom_elt#结点的父结点
        self.split = split#划分结点
        self.left = left#做结点
        self.right = right#右结点

class KdTree(object):
    def __init__(self, data):
        k = len(data[0])#数据维度
        #print("创建结点")
        #print("开始执行创建结点函数!!!")
        def CreateNode(split, data_set):
            #print(split,data_set)
            if not data_set:#数据集为空
                return None
            #print("进入函数!!!")
            data_set.sort(key=lambda x:x[split])#开始找切分平面的维度
            #print("data_set:",data_set)
            split_pos = len(data_set)//2 #取得中位数点的坐标位置(求整)
            median = data_set[split_pos]
            split_next = (split+1) % k #(取余数)取得下一个节点的分离维数
            return KdNode(
                median,
                split,
                CreateNode(split_next, data_set[:split_pos]),#创建左结点
                CreateNode(split_next, data_set[split_pos+1:]))#创建右结点
        #print("结束创建结点函数!!!")
        self.root = CreateNode(0, data)#创建根结点
            
#KDTree的前序遍历
def preorder(root):
    print(root.dom_elt)
    if root.left:
        preorder(root.left)
    if root.right:
        preorder(root.right)
# 遍历kd树
#KDTree的前序遍历
def preorder(root):
    print(root.dom_elt)
    if root.left:
        preorder(root.left)
    if root.right:
        preorder(root.right)
               
from math import sqrt
from collections import namedtuple
# 定义一个namedtuple,分别存放最近坐标点、最近距离和访问过的节点数
result = namedtuple("Result_tuple",
                    "nearest_point  nearest_dist  nodes_visited")

#搜索开始
def find_nearest(tree, point):
    k = len(point)#数据维度
    
    def travel(kd_node, target, max_dist):
        if kd_node is None:
            return result([0]*k, float("inf"), 0)#表示数据的无
        
        nodes_visited = 1
        s = kd_node.split #数据维度分隔
        pivot = kd_node.dom_elt #切分根节点
        
        if target[s] <= pivot[s]:
            nearer_node = kd_node.left #下一个左结点为树根结点
            further_node = kd_node.right #记录右节点
        else: #右面更近
            nearer_node = kd_node.right
            further_node = kd_node.left
        temp1 = travel(nearer_node, target, max_dist)
        
        nearest = temp1.nearest_point# 得到叶子结点,此时为nearest
        dist = temp1.nearest_dist #update distance
        
        nodes_visited += temp1.nodes_visited
        print("nodes_visited:", nodes_visited)
        if dist < max_dist:
            max_dist = dist
        
        temp_dist = abs(pivot[s]-target[s])#计算球体与分隔超平面的距离
        if max_dist < temp_dist:
            return result(nearest, dist, nodes_visited)
        # -------
        #计算分隔点的欧式距离
        
        temp_dist = sqrt(sum((p1-p2)**2 for p1, p2 in zip(pivot, target)))#计算目标点到邻近节点的Distance
        
        if temp_dist < dist:
            
            nearest = pivot #更新最近点
            dist = temp_dist #更新最近距离
            max_dist = dist #更新超球体的半径
            print("输出数据:" , nearest, dist, max_dist)
            
        # 检查另一个子结点对应的区域是否有更近的点
        temp2 = travel(further_node, target, max_dist)

        nodes_visited += temp2.nodes_visited
        if temp2.nearest_dist < dist:  # 如果另一个子结点内存在更近距离
            nearest = temp2.nearest_point  # 更新最近点
            dist = temp2.nearest_dist  # 更新最近距离

        return result(nearest, dist, nodes_visited)

    return travel(tree.root, point, float("inf"))  # 从根节点开始递归
# 遍历kd树
#KDTree的前序遍历
def preorder(root):
    print(root.dom_elt)
    if root.left:
        preorder(root.left)
    if root.right:
        preorder(root.right)
               
from math import sqrt
from collections import namedtuple
# 定义一个namedtuple,分别存放最近坐标点、最近距离和访问过的节点数
result = namedtuple("Result_tuple",
                    "nearest_point  nearest_dist  nodes_visited")

#搜索开始
def find_nearest(tree, point):
    k = len(point)#数据维度
    
    def travel(kd_node, target, max_dist):
        if kd_node is None:
            return result([0]*k, float("inf"), 0)#表示数据的无
        
        nodes_visited = 1
        s = kd_node.split #数据维度分隔
        pivot = kd_node.dom_elt #切分根节点
        
        if target[s] <= pivot[s]:
            nearer_node = kd_node.left #下一个左结点为树根结点
            further_node = kd_node.right #记录右节点
        else: #右面更近
            nearer_node = kd_node.right
            further_node = kd_node.left
        temp1 = travel(nearer_node, target, max_dist)
        
        nearest = temp1.nearest_point# 得到叶子结点,此时为nearest
        dist = temp1.nearest_dist #update distance
        
        nodes_visited += temp1.nodes_visited
        print("nodes_visited:", nodes_visited)
        if dist < max_dist:
            max_dist = dist
        
        temp_dist = abs(pivot[s]-target[s])#计算球体与分隔超平面的距离
        if max_dist < temp_dist:
            return result(nearest, dist, nodes_visited)
        # -------
        #计算分隔点的欧式距离
        
        temp_dist = sqrt(sum((p1-p2)**2 for p1, p2 in zip(pivot, target)))#计算目标点到邻近节点的Distance
        
        if temp_dist < dist:
            
            nearest = pivot #更新最近点
            dist = temp_dist #更新最近距离
            max_dist = dist #更新超球体的半径
            print("输出数据:" , nearest, dist, max_dist)
            
        # 检查另一个子结点对应的区域是否有更近的点
        temp2 = travel(further_node, target, max_dist)

        nodes_visited += temp2.nodes_visited
        if temp2.nearest_dist < dist:  # 如果另一个子结点内存在更近距离
            nearest = temp2.nearest_point  # 更新最近点
            dist = temp2.nearest_dist  # 更新最近距离

        return result(nearest, dist, nodes_visited)

    return travel(tree.root, point, float("inf"))  # 从根节点开始递归
复制代码
# 数据测试
data= [[2,3],[5,4],[9,6],[4,7],[8,1],[7,2]]
kd=KdTree(data)
preorder(kd.root)

结果:

 

# 导包
from time import clock
from random import random

# 产生一个k维随机向量,每维分量值在0~1之间
def random_point(k): 
    return [random() for _ in range(k)]

# 产生n个k维随机向量
def random_points(k, n):
    return [random_point(k) for _ in range(n)]
复制代码
# 输入数据进行测试
ret = find_nearest(kd, [3,4.5])
print (ret)

结果:

Result_tuple(nearest_point=[2, 3], nearest_dist=1.8027756377319946, nodes_visited=4)

N = 400000
t0 = clock()
kd2 = KdTree(random_points(3, N)) # 构建包含四十万个3维空间样本点的kd树
ret2 = find_nearest(kd2, [0.1,0.5,0.8]) # 四十万个样本点中寻找离目标最*的点
t1 = clock()
print ("time: ",t1-t0, "s")
print (ret2)

结果:

7.299844505209247 s
Result_tuple(nearest_point=[0.10505669630674175, 0.49542598718931097, 0.803316691954
3026], nearest_dist=0.007582362181450973, nodes_visited=53)

实验小结

k-近邻算法的核心思想是未标记样本的类别,由距离其最近的k个邻居投票来决定。此算法对于欠拟合的现象很难处理,没有很好的措施来解决,在建立模型的时候不能使用较为简单的模型,否则就无法很好的拟合出很好的训练样本。



posted @ 2021-05-19 17:58  雪舞长空  阅读(48)  评论(0编辑  收藏  举报