Naive Bayesian python code implementation (watermelon book)
Summary:
Naive Bayesian machine learning is a very common method of classification for binary classification, and data collection time is characterized by discrete attributes,
use very convenient. Simple principle, training high efficiency, good fitting effect.
Naive Bayes
Bayesian formula:
Naive Bayes The reason that this is simple, because the assumption that the individual features are independent of each other, it is assumed that the following equation holds:
The formula for calculating Naive Bayes algorithm is as follows:
In the actual calculation, the above formula will be slightly modified as follows:
- Since the value of some characteristic properties of P (Xi | Ci) may be small, p = after multiplying a plurality of features may even be equal to about 0. Then both sides of the equation log may be taken as the multiplication becomes addition, to avoid the problem by class.
- P (Ci) and P (Xi | Ci) generally do not directly use the calculated frequency samples, typically using Laplacian smoothing.
In the above formula, the frequency of the category Dc, N denotes the number of all possible categories.
In the above formula, Dc, characterized in that XI attribute corresponding to the frequency, the frequency of the category Dc, Ni represents the number of possible properties of the feature.
Watermelon book corresponding data set
色泽 根蒂 敲声 纹理 脐部 触感 好瓜
青绿 蜷缩 浊响 清晰 凹陷 硬滑 是
乌黑 蜷缩 沉闷 清晰 凹陷 硬滑 是
乌黑 蜷缩 浊响 清晰 凹陷 硬滑 是
青绿 蜷缩 沉闷 清晰 凹陷 硬滑 是
浅白 蜷缩 浊响 清晰 凹陷 硬滑 是
青绿 稍蜷 浊响 清晰 稍凹 软粘 是
乌黑 稍蜷 浊响 稍糊 稍凹 软粘 是
乌黑 稍蜷 浊响 清晰 稍凹 硬滑 是
乌黑 稍蜷 沉闷 稍糊 稍凹 硬滑 否
青绿 硬挺 清脆 清晰 平坦 软粘 否
浅白 硬挺 清脆 模糊 平坦 硬滑 否
浅白 蜷缩 浊响 模糊 平坦 软粘 否
青绿 稍蜷 浊响 稍糊 凹陷 硬滑 否
浅白 稍蜷 沉闷 稍糊 凹陷 硬滑 否
乌黑 稍蜷 浊响 清晰 稍凹 软粘 否
浅白 蜷缩 浊响 模糊 平坦 硬滑 否
青绿 蜷缩 沉闷 稍糊 稍凹 硬滑 否python achieve
#encoding:utf-8
import pandas as pd
import numpy as np
class NaiveBayes:
def __init__(self):
self.model = {}#key 为类别名 val 为字典PClass表示该类的该类，PFeature:{}对应对于各个特征的概率
def calEntropy(self, y): # 计算熵
valRate = y.value_counts().apply(lambda x : x / y.size) # 频次汇总 得到各个特征对应的概率
valEntropy = np.inner(valRate, np.log2(valRate)) * -1
return valEntropy
def fit(self, xTrain, yTrain = pd.Series()):
if not yTrain.empty:#如果不传，自动选择最后一列作为分类标签
xTrain = pd.concat([xTrain, yTrain], axis=1)
self.model = self.buildNaiveBayes(xTrain)
return self.model
def buildNaiveBayes(self, xTrain):
yTrain = xTrain.iloc[:,-1]
yTrainCounts = yTrain.value_counts()# 频次汇总 得到各个特征对应的概率
yTrainCounts = yTrainCounts.apply(lambda x : (x + 1) / (yTrain.size + yTrainCounts.size)) #使用了拉普拉斯平滑
retModel = {}
for nameClass, val in yTrainCounts.items():
retModel[nameClass] = {'PClass': val, 'PFeature':{}}
propNamesAll = xTrain.columns[:-1]
allPropByFeature = {}
for nameFeature in propNamesAll:
allPropByFeature[nameFeature] = list(xTrain[nameFeature].value_counts().index)
#print(allPropByFeature)
for nameClass, group in xTrain.groupby(xTrain.columns[-1]):
for nameFeature in propNamesAll:
eachClassPFeature = {}
propDatas = group[nameFeature]
propClassSummary = propDatas.value_counts()# 频次汇总 得到各个特征对应的概率
for propName in allPropByFeature[nameFeature]:
if not propClassSummary.get(propName):
propClassSummary[propName] = 0#如果有属性灭有，那么自动补0
Ni = len(allPropByFeature[nameFeature])
propClassSummary = propClassSummary.apply(lambda x : (x + 1) / (propDatas.size + Ni))#使用了拉普拉斯平滑
for nameFeatureProp, valP in propClassSummary.items():
eachClassPFeature[nameFeatureProp] = valP
retModel[nameClass]['PFeature'][nameFeature] = eachClassPFeature
return retModel
def predictBySeries(self, data):
curMaxRate = None
curClassSelect = None
for nameClass, infoModel in self.model.items():
rate = 0
rate += np.log(infoModel['PClass'])
PFeature = infoModel['PFeature']
for nameFeature, val in data.items():
propsRate = PFeature.get(nameFeature)
if not propsRate:
continue
rate += np.log(propsRate.get(val, 0))#使用log加法避免很小的小数连续乘，接近零
#print(nameFeature, val, propsRate.get(val, 0))
#print(nameClass, rate)
if curMaxRate == None or rate > curMaxRate:
curMaxRate = rate
curClassSelect = nameClass
return curClassSelect
def predict(self, data):
if isinstance(data, pd.Series):
return self.predictBySeries(data)
return data.apply(lambda d: self.predictBySeries(d), axis=1)
dataTrain = pd.read_csv("xiguadata.csv", encoding = "gbk")
naiveBayes = NaiveBayes()
treeData = naiveBayes.fit(dataTrain)
import json
print(json.dumps(treeData, ensure_ascii=False))
pd = pd.DataFrame({'预测值':naiveBayes.predict(dataTrain), '正取值':dataTrain.iloc[:,-1]})
print(pd)
print('正确率:%f%%'%(pd[pd['预测值'] == pd['正取值']].shape[0] * 100.0 / pd.shape[0]))Export
{"否": {"PClass": 0.5263157894736842, "PFeature": {"色泽": {"浅白": 0.4166666666666667, "青绿": 0.3333333333333333, "乌 黑": 0.25}, "根蒂": {"稍蜷": 0.4166666666666667, "蜷缩": 0.3333333333333333, "硬挺": 0.25}, "敲声": {"浊响": 0.4166666666666667, "沉闷": 0.3333333333333333, "清脆": 0.25}, "纹理": {"稍糊": 0.4166666666666667, "模糊": 0.3333333333333333, "清晰": 0.25}, "脐部": {"平坦": 0.4166666666666667, "稍凹": 0.3333333333333333, "凹陷": 0.25}, "触感": {"硬滑": 0.6363636363636364, "软粘": 0.36363636363636365}}}, "是": {"PClass": 0.47368421052631576, "PFeature": {"色泽": {"乌黑": 0.45454545454545453, "青绿": 0.36363636363636365, "浅白": 0.18181818181818182}, "根蒂": {"蜷缩": 0.5454545454545454, "稍蜷": 0.36363636363636365, "硬挺": 0.09090909090909091}, "敲声": {"浊响": 0.6363636363636364, "沉闷": 0.2727272727272727, "清脆": 0.09090909090909091}, "纹理": {"清晰": 0.7272727272727273, "稍糊": 0.18181818181818182, "模糊": 0.09090909090909091}, "脐 部": {"凹陷": 0.5454545454545454, "稍凹": 0.36363636363636365, "平坦": 0.09090909090909091}, "触感": {"硬滑": 0.7, "软粘": 0.3}}}}
预测值 正取值
0 是 是
1 是 是
2 是 是
3 是 是
4 是 是
5 是 是
6 否 是
7 是 是
8 否 否
9 否 否
10 否 否
11 否 否
12 是 否
13 否 否
14 是 否
15 否 否
16 否 否
正确率:82.352941%to sum up:
- Bayesian classifier is a generative model, the classification result is not fitting directly, but the probability of fitting the posterior probability corresponding to formula after the classification.
- This article only describes the binary, can also be used to handle multiple classification problems.
- For small data sets, performed well.
- Based on features of the independence assumption.
- This is my github page https://github.com/fanchy, some interesting share.