KNN&朴素贝叶斯（根据已知推测未知）

KNN（哲学思想：物以类聚，人以群分）

KNN算法原理及示例1：

向量化

画点，计算欧式距离：

可行代码展示：

#!/usr/bin/python
# coding=utf-8
#########################################
# kNN: k Nearest Neighbors

#  输入:      newInput:  (1xN)的待分类向量
#             dataSet:   (NxM)的训练数据集
#             labels:     训练数据集的类别标签向量
#             k:         近邻数

# 输出:     可能性最大的分类标签
#########################################

import numpy as np

# 创建一个数据集，包含2个类别共4个样本
def createDataSet():
    # 生成一个矩阵，每行表示一个样本
    group = np.array([[1.0, 0.9], [1.0, 1.0], [0.1, 0.2], [0.0, 0.1]])
    # 4个样本分别所属的类别
    labels = ['A', 'A', 'B', 'B']
    return group, labels

# KNN分类算法函数定义
def kNNClassify(newInput, dataSet, labels, k):
    numSamples = dataSet.shape[0]   # shape[0]表示行数
    diff = np.tile(newInput, (numSamples, 1)) - dataSet  # 按元素求差值
    squaredDiff = diff ** 2  # 将差值平方
    squaredDist = sum(squaredDiff)   # 按行累加
    distance = squaredDist ** 0.5  # 将差值平方和求开方，即得距离

    # # step 2: 对距离排序
    # argsort() 返回排序后的索引值
    sortedDistIndices = np.argsort(distance)
    classCount = {} # define a dictionary (can be append element)
    for i in range(k):
        # # step 3: 选择k个最近邻
        voteLabel = labels[sortedDistIndices[i]]

        # # step 4: 计算k个最近邻中各类别出现的次数
        # when the key voteLabel is not in dictionary classCount, get()
        # will return 0
        classCount[voteLabel] = classCount.get(voteLabel, 0) + 1

    # # step 5: 返回出现次数最多的类别标签
    maxCount = 0
    for key, value in classCount.items():
        if value > maxCount:
            maxCount = value
            maxIndex = key

    return maxIndex
	
if __name__ == '__main__':
    # 生成数据集和类别标签
    #	dataSet, labels = createDataSet()
    file_open = open('iris.txt', 'r')
    dataSet = []
    labels = []
    for l in file_open:
        line = l.strip().split(',')
        dataSet.append(list(map(float, line[:4])))
        labels.append(line[-1])
    dataSet = np.array(dataSet)
	# 定义一个未知类别的数
    testX = np.array([5.0,3.2,4.7,1.4])
    k = 3
	# 调用分类函数对未知数据分类
    outputLabel = kNNClassify(testX, dataSet, labels, 3)
    print("Your input is:", testX, "and classified to class: ", outputLabel)
    testX = np.array([1.6,1.6,1.0,0.2])
    outputLabel = kNNClassify(testX, dataSet, labels, 3)
    print("Your input is:", testX, "and classified to class: ", outputLabel)

数据如下

5.1,3.5,1.4,0.2,setosa
4.9,3.0,1.4,0.2,setosa
4.7,3.2,1.3,0.2,setosa
4.6,3.1,1.5,0.2,setosa
5.0,3.6,1.4,0.2,setosa
5.4,3.9,1.7,0.4,setosa
4.6,3.4,1.4,0.3,setosa
5.0,3.4,1.5,0.2,setosa
4.4,2.9,1.4,0.2,setosa
4.9,3.1,1.5,0.1,setosa
5.4,3.7,1.5,0.2,setosa
4.8,3.4,1.6,0.2,setosa
4.8,3.0,1.4,0.1,setosa
4.3,3.0,1.1,0.1,setosa
5.8,4.0,1.2,0.2,setosa
5.7,4.4,1.5,0.4,setosa
5.4,3.9,1.3,0.4,setosa
5.1,3.5,1.4,0.3,setosa
5.7,3.8,1.7,0.3,setosa
5.1,3.8,1.5,0.3,setosa
5.4,3.4,1.7,0.2,setosa
5.1,3.7,1.5,0.4,setosa
4.6,3.6,1.0,0.2,setosa
5.1,3.3,1.7,0.5,setosa
4.8,3.4,1.9,0.2,setosa
5.0,3.0,1.6,0.2,setosa
5.0,3.4,1.6,0.4,setosa
5.2,3.5,1.5,0.2,setosa
5.2,3.4,1.4,0.2,setosa
4.7,3.2,1.6,0.2,setosa
4.8,3.1,1.6,0.2,setosa
5.4,3.4,1.5,0.4,setosa
5.2,4.1,1.5,0.1,setosa
5.5,4.2,1.4,0.2,setosa
4.9,3.1,1.5,0.1,setosa
5.0,3.2,1.2,0.2,setosa
5.5,3.5,1.3,0.2,setosa
4.9,3.1,1.5,0.1,setosa
4.4,3.0,1.3,0.2,setosa
5.1,3.4,1.5,0.2,setosa
5.0,3.5,1.3,0.3,setosa
4.5,2.3,1.3,0.3,setosa
4.4,3.2,1.3,0.2,setosa
5.0,3.5,1.6,0.6,setosa
5.1,3.8,1.9,0.4,setosa
4.8,3.0,1.4,0.3,setosa
5.1,3.8,1.6,0.2,setosa
4.6,3.2,1.4,0.2,setosa
5.3,3.7,1.5,0.2,setosa
5.0,3.3,1.4,0.2,setosa
7.0,3.2,4.7,1.4,versicolor
6.4,3.2,4.5,1.5,versicolor
6.9,3.1,4.9,1.5,versicolor
5.5,2.3,4.0,1.3,versicolor
6.5,2.8,4.6,1.5,versicolor
5.7,2.8,4.5,1.3,versicolor
6.3,3.3,4.7,1.6,versicolor
4.9,2.4,3.3,1.0,versicolor
6.6,2.9,4.6,1.3,versicolor
5.2,2.7,3.9,1.4,versicolor
5.0,2.0,3.5,1.0,versicolor
5.9,3.0,4.2,1.5,versicolor
6.0,2.2,4.0,1.0,versicolor
6.1,2.9,4.7,1.4,versicolor
5.6,2.9,3.6,1.3,versicolor
6.7,3.1,4.4,1.4,versicolor
5.6,3.0,4.5,1.5,versicolor
5.8,2.7,4.1,1.0,versicolor
6.2,2.2,4.5,1.5,versicolor
5.6,2.5,3.9,1.1,versicolor
5.9,3.2,4.8,1.8,versicolor
6.1,2.8,4.0,1.3,versicolor
6.3,2.5,4.9,1.5,versicolor
6.1,2.8,4.7,1.2,versicolor
6.4,2.9,4.3,1.3,versicolor
6.6,3.0,4.4,1.4,versicolor
6.8,2.8,4.8,1.4,versicolor
6.7,3.0,5.0,1.7,versicolor
6.0,2.9,4.5,1.5,versicolor
5.7,2.6,3.5,1.0,versicolor
5.5,2.4,3.8,1.1,versicolor
5.5,2.4,3.7,1.0,versicolor
5.8,2.7,3.9,1.2,versicolor
6.0,2.7,5.1,1.6,versicolor
5.4,3.0,4.5,1.5,versicolor
6.0,3.4,4.5,1.6,versicolor
6.7,3.1,4.7,1.5,versicolor
6.3,2.3,4.4,1.3,versicolor
5.6,3.0,4.1,1.3,versicolor
5.5,2.5,4.0,1.3,versicolor
5.5,2.6,4.4,1.2,versicolor
6.1,3.0,4.6,1.4,versicolor
5.8,2.6,4.0,1.2,versicolor
5.0,2.3,3.3,1.0,versicolor
5.6,2.7,4.2,1.3,versicolor
5.7,3.0,4.2,1.2,versicolor
5.7,2.9,4.2,1.3,versicolor
6.2,2.9,4.3,1.3,versicolor
5.1,2.5,3.0,1.1,versicolor
5.7,2.8,4.1,1.3,versicolor
6.3,3.3,6.0,2.5,virginica
5.8,2.7,5.1,1.9,virginica
7.1,3.0,5.9,2.1,virginica
6.3,2.9,5.6,1.8,virginica
6.5,3.0,5.8,2.2,virginica
7.6,3.0,6.6,2.1,virginica
4.9,2.5,4.5,1.7,virginica
7.3,2.9,6.3,1.8,virginica
6.7,2.5,5.8,1.8,virginica
7.2,3.6,6.1,2.5,virginica
6.5,3.2,5.1,2.0,virginica
6.4,2.7,5.3,1.9,virginica
6.8,3.0,5.5,2.1,virginica
5.7,2.5,5.0,2.0,virginica
5.8,2.8,5.1,2.4,virginica
6.4,3.2,5.3,2.3,virginica
6.5,3.0,5.5,1.8,virginica
7.7,3.8,6.7,2.2,virginica
7.7,2.6,6.9,2.3,virginica
6.0,2.2,5.0,1.5,virginica
6.9,3.2,5.7,2.3,virginica
5.6,2.8,4.9,2.0,virginica
7.7,2.8,6.7,2.0,virginica
6.3,2.7,4.9,1.8,virginica
6.7,3.3,5.7,2.1,virginica
7.2,3.2,6.0,1.8,virginica
6.2,2.8,4.8,1.8,virginica
6.1,3.0,4.9,1.8,virginica
6.4,2.8,5.6,2.1,virginica
7.2,3.0,5.8,1.6,virginica
7.4,2.8,6.1,1.9,virginica
7.9,3.8,6.4,2.0,virginica
6.4,2.8,5.6,2.2,virginica
6.3,2.8,5.1,1.5,virginica
6.1,2.6,5.6,1.4,virginica
7.7,3.0,6.1,2.3,virginica
6.3,3.4,5.6,2.4,virginica
6.4,3.1,5.5,1.8,virginica
6.0,3.0,4.8,1.8,virginica
6.9,3.1,5.4,2.1,virginica
6.7,3.1,5.6,2.4,virginica
6.9,3.1,5.1,2.3,virginica
5.8,2.7,5.1,1.9,virginica
6.8,3.2,5.9,2.3,virginica
6.7,3.3,5.7,2.5,virginica
6.7,3.0,5.2,2.3,virginica
6.3,2.5,5.0,1.9,virginica
6.5,3.0,5.2,2.0,virginica
6.2,3.4,5.4,2.3,virginica
5.9,3.0,5.1,1.8,virginica

 

朴素贝叶斯（数学工具：贝叶斯公式）

1.数学原理：

2.一道大题：

根据原理求的是如下两个式子的概率，比较谁大，选取概率较大即可

利用贝叶斯公式将公式展开

因为分母是相同的，所以比较分子就可以知道谁大谁小了

因为高度，头发，眼睛是互不影响的，是独立时间，故可以拆开进行计算

通过比较可以发现，’－‘的概率是小于‘+’的概率的，故可以下结论：
预测该条件为‘+’值