朴素贝叶斯算法

原理参考：
Python手写实现朴素贝叶斯（从原理到代码）
朴素贝叶斯算法的Python实现（多项式、高斯）
三种常用的朴素贝叶斯实现算法——高斯朴素贝叶斯、伯努利朴素贝叶斯、多项式朴素贝叶斯

- 伯努利模型
- 多项式模型
- 高斯模型

伯努利模型

python实现：

import numpy as np

class BernoulliNB(object):
    def __init__(self, alpha = 1.0, fit_prior=True):
        self.alpha = alpha
        self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
        self.class_prior = None    #类的先验几率，若指定则先验不能根据数据调整   
        self.classes = None
        self.conditional_prob = None
        self.predict_prob = None

    def fit(self,x,y):
        #计算类别y的先验几率
        self.classes = np.unique(y)
        if self.class_prior == None:#先验几率没有指定
            class_num = len(self.classes)
            self.class_prior = {}
            if not self.fit_prior:
                for d in self.classes:
                    self.class_prior[d] = 1.0/class_num 
            else:        
                for d in self.classes:
                    c_num = np.sum(np.equal(y,d))
                    self.class_prior[d]=(c_num+self.alpha) / (len(y) + class_num * self.alpha)          
        print(self.class_prior)
        #计算条件几率------伯努利模型
        self.conditional_prob = {}#{x1|y1:p1,x2|y1:p2,.....,x1|y2:p3,x2|y2:p4,.....}
        x_class = [0,1]
        y = list(y)
        for yy in self.class_prior.keys():          
            y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
            for i in range(len(x)):       
                for c in x_class:
                    x_index = [j for j,feature in enumerate(x[i]) if feature == c]
                    xy_count = len(set(x_index) & set(y_index))
                    pkey = str(c) + '|' + str(yy)
                    self.conditional_prob[pkey] = (xy_count+self.alpha) / (len(y_index)+2)
        print(self.conditional_prob)
        return self

    def predict(self, x):
        labels = []
        for i in range(x.shape[0]):
            self.predict_prob = {}
            for j in self.classes:
                self.predict_prob[j] = self.class_prior[j]          
                for d in x[i]:
                    self.predict_prob[j] = self.predict_prob[j]*self.conditional_prob[str(d) + '|'+ str(j)]
            print(self.predict_prob)
            label = max(self.predict_prob, key=self.predict_prob.get)
            labels.append(label)
        return labels


if __name__ == '__main__':   
    x = np.array([[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1],[0,1,1,0,0,0,1,1,1,1,1,1,1,1,1]])
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    bnb= BernoulliNB(alpha=1.0,fit_prior=True)
    bnb.fit(x, y)
    print('预测值为：', bnb.predict(np.array([[0,0]])))

python调包：

import numpy as np
from sklearn.naive_bayes import BernoulliNB

if __name__ == '__main__':   
    x = np.array([[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1],[0,1,1,0,0,0,1,1,1,1,1,1,1,1,1]]).T
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    bnb = BernoulliNB()
    bnb.fit(x,y)
    print('预测值为：', bnb.predict(np.array([[0,0]])))

C++实现：

#include 
#include 
#include 
#include 
#include 
#include 
#include 

class BernoulliNB
{
public:
	BernoulliNB(float alpha, bool fit_prior = true):m_alpha(alpha),m_fit_prior(fit_prior){}

	void fit(std::vector> x, std::vector y)
	{
		for (auto i : y)	
			m_classes.insert(i);
		if (m_class_prior.size() == 0)
		{
			int class_num = m_classes.size();
			if (!m_fit_prior)
			{
				for (auto d : m_classes)
					m_class_prior[d] = 1.0 / class_num;
			}
			else {
				for (auto d : m_classes)
				{
					int c_num = 0;
					for (auto i:y)	c_num += (d == i ? 1 : 0);
					m_class_prior[d] = (c_num + m_alpha) / (y.size() + class_num*m_alpha);
				}
			}
		}

		std::vector x_class = { 0, 1 };
		for (auto pa : m_class_prior)
		{
			//	std::cout << pa.first << " " << pa.second << std::endl;
			std::vector y_index;
			for (size_t i = 0; i < y.size(); i++)
			{
				if (y[i] == pa.first)	y_index.push_back(i);
			}

			for (size_t i = 0; i < x.size(); i++)
			{
				for (auto c : x_class)
				{
					std::vector x_index;
					for (size_t j = 0; j < x[i].size(); j++)
					{
						if (x[i][j] == c)	x_index.push_back(j);
					}

					std::sort(x_index.begin(), x_index.end());
					std::sort(y_index.begin(), y_index.end());
					std::vector xy_index;
					std::set_intersection(x_index.begin(), x_index.end(), y_index.begin(), y_index.end(), std::back_inserter(xy_index));//求交集 

					std::string pkey = std::to_string(c) + "|" + std::to_string(pa.first);
					//std::cout << pkey << std::endl;

					m_conditional_prob[pkey] = (xy_index.size() + m_alpha) / (y_index.size() + 2);
				}
			}
		}
		
		for (auto pa : m_conditional_prob)
			std::cout << pa.first << " " << pa.second << std::endl;
	}

	std::vector predict(std::vector> x)
	{
		std::vector labels;
		for (size_t i = 0; i < x.size(); i++)
		{
			m_predict_prob.clear();
			for (auto j : m_classes)
			{
				m_predict_prob[j] = m_class_prior[j];
				for (auto d : x[i])
				{
					m_predict_prob[j] *= m_conditional_prob[std::to_string(d) + "|" + std::to_string(j)];
				}
			}

			for (auto pa : m_predict_prob)
				std::cout << pa.first << " " << pa.second << std::endl;

			std::vector>  m_predict_prob_vec;
			for (std::map::iterator it = m_predict_prob.begin(); it != m_predict_prob.end(); it++)
			{
				m_predict_prob_vec.push_back(std::make_pair((*it).first, (*it).second));
			}
			std::sort(m_predict_prob_vec.begin(), m_predict_prob_vec.end(), [](std::pair p1, std::pair p2) {return p1.second < p2.second; });
			float label = m_predict_prob_vec.rbegin()->first;
			labels.push_back(label);
		}
	
		return labels;
	}

private:
	float m_alpha;
	bool m_fit_prior;
	std::map m_class_prior;
	std::set m_classes;
	std::map m_conditional_prob;
	std::map m_predict_prob;
};


int main(int argc, char* argv[])
{
	std::vector> x = { { 1,1,1,1,1,0,0,0,0,0,1,1,1,1,1 }, { 0,1,1,0,0,0,1,1,1,1,1,1,1,1,1 } };
	std::vector y = { -1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1 };

	BernoulliNB bnb = BernoulliNB(1.0, true);
	bnb.fit(x, y);
	std::cout << "预测值为：" << bnb.predict({ { 0,0 } })[0] << std::endl;

	system("pause");
	return EXIT_SUCCESS;
}

多项式模型

python实现：

import numpy as np

class MultinomialNB(object):
    def __init__(self, alpha = 1.0, fit_prior=True):
        self.alpha = alpha
        self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
        self.class_prior = None    #类的先验几率，若指定则先验不能根据数据调整   
        self.classes = None
        self.conditional_prob = None
        self.predict_prob = None

    def fit(self,x,y):
        #计算类别y的先验几率
        self.classes = np.unique(y)
        if self.class_prior == None:#先验几率没有指定
            class_num = len(self.classes)
            self.class_prior = {}
            if not self.fit_prior:
                for d in self.classes:
                    self.class_prior[d] = 1.0/class_num 
            else:        
                for d in self.classes:
                    c_num = np.sum(np.equal(y,d))
                    self.class_prior[d]=(c_num+self.alpha) / (len(y) + class_num * self.alpha)          
        print(self.class_prior)
        #计算条件几率------多项式模型
        self.conditional_prob = {}#{x1|y1:p1,x2|y1:p2,.....,x1|y2:p3,x2|y2:p4,.....}
        y = list(y)
        for yy in self.class_prior.keys():
            y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
            for i in range(len(x)):
                x_class = np.unique(x[i])
                #print(x_class)
                for c in list(x_class):
                    x_index = [j for j,feature in enumerate(x[i]) if feature == c]
                    xy_count = len(set(x_index) & set(y_index))
                    pkey = str(c) + '|' + str(yy)
                    self.conditional_prob[pkey] = (xy_count+self.alpha) / (len(y_index)+x_class.shape[0])
        print(self.conditional_prob)
        return self

    def predict(self, x):
        labels = []
        for i in range(x.shape[0]):
            self.predict_prob = {}
            for j in self.classes:
                self.predict_prob[j] = self.class_prior[j]          
                for d in x[i]:
                    self.predict_prob[j] = self.predict_prob[j]*self.conditional_prob[str(d) + '|'+ str(j)]
            print(self.predict_prob)
            label = max(self.predict_prob, key=self.predict_prob.get)
            labels.append(label)
        return labels


if __name__ == '__main__':
    x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]])
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    mnb = MultinomialNB(alpha=1.0,fit_prior=True)
    mnb.fit(x, y)
    print('预测值为：', mnb.predict(np.array([[2,1]])))

python调包：

import numpy as np
from sklearn.naive_bayes import MultinomialNB

if __name__ == '__main__':   
    x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]]).T
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    mnb = MultinomialNB()
    mnb.fit(x,y)
    print('预测值为：', mnb.predict(np.array([[2,1]])))

C++实现：

#include 
#include 
#include 
#include 
#include 
#include 
#include 

class MultinomialNB
{
public:
	MultinomialNB(float alpha, bool fit_prior = true) :m_alpha(alpha), m_fit_prior(fit_prior) {}

	void fit(std::vector> x, std::vector y)
	{
		for (auto i : y)
			m_classes.insert(i);
		if (m_class_prior.size() == 0)
		{
			int class_num = m_classes.size();
			if (!m_fit_prior)
			{
				for (auto d : m_classes)
					m_class_prior[d] = 1.0 / class_num;
			}
			else {
				for (auto d : m_classes)
				{
					int c_num = 0;
					for (auto i : y)	c_num += (d == i ? 1 : 0);
					m_class_prior[d] = (c_num + m_alpha) / (y.size() + class_num*m_alpha);
				}
			}
		}

		for (auto pa : m_class_prior)
		{
			//	std::cout << pa.first << " " << pa.second << std::endl;
			std::vector y_index;
			for (size_t i = 0; i < y.size(); i++)
			{
				if (y[i] == pa.first)	y_index.push_back(i);
			}

			for (size_t i = 0; i < x.size(); i++)
			{
				std::set x_class(x[i].begin(), x[i].end());
				for (auto c : x_class)
				{
					std::vector x_index;
					for (size_t j = 0; j < x[i].size(); j++)
					{
						if (x[i][j] == c)	x_index.push_back(j);
					}

					std::sort(x_index.begin(), x_index.end());
					std::sort(y_index.begin(), y_index.end());
					std::vector xy_index;
					std::set_intersection(x_index.begin(), x_index.end(), y_index.begin(), y_index.end(), std::back_inserter(xy_index));//求交集 

					std::string pkey = std::to_string(c) + "|" + std::to_string(pa.first);
					m_conditional_prob[pkey] = (xy_index.size() + m_alpha) / (y_index.size() + x_class.size());
				}
			}
		}

		for (auto pa : m_conditional_prob)
			std::cout << pa.first << " " << pa.second << std::endl;
	}

	std::vector predict(std::vector> x)
	{
		std::vector labels;
		for (size_t i = 0; i < x.size(); i++)
		{
			m_predict_prob.clear();
			for (auto j : m_classes)
			{
				m_predict_prob[j] = m_class_prior[j];
				for (auto d : x[i])
				{
					m_predict_prob[j] *= m_conditional_prob[std::to_string(d) + "|" + std::to_string(j)];
				}
			}

			for (auto pa : m_predict_prob)
				std::cout << pa.first << " " << pa.second << std::endl;

			std::vector>  m_predict_prob_vec;
			for (std::map::iterator it = m_predict_prob.begin(); it != m_predict_prob.end(); it++)
			{
				m_predict_prob_vec.push_back(std::make_pair((*it).first, (*it).second));
			}
			std::sort(m_predict_prob_vec.begin(), m_predict_prob_vec.end(), [](std::pair p1, std::pair p2) {return p1.second < p2.second; });
			float label = m_predict_prob_vec.rbegin()->first;
			labels.push_back(label);
		}

		return labels;
	}

private:
	float m_alpha;
	bool m_fit_prior;
	std::map m_class_prior;
	std::set m_classes;
	std::map m_conditional_prob;
	std::map m_predict_prob;
};


int main(int argc, char* argv[])
{
	std::vector> x = { { 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3 },{ 1,2,2,1,1,1,2,2,3,3,3,2,2,3,3 } };
	std::vector y = { -1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1 };

	MultinomialNB mnb = MultinomialNB(1.0, true);
	mnb.fit(x, y);
	std::cout << "预测值为：" << mnb.predict({ { 2,1 } })[0] << std::endl;

	system("pause");
	return EXIT_SUCCESS;
}

高斯模型

python实现：

import numpy as np

class GaussionNB(object):   #计算条件几率的方法不同
    def __init__(self, fit_prior=True):
        self.fit_prior = fit_prior #是否学习类的先验几率，False则使用统一的先验
        self.class_prior = None    #类的先验几率，若指定则先验不能根据数据调整  
        self.classes = None
        self.mean = None
        self.var = None
        self.predict_prob = None

    def fit(self,x,y):
        #计算类别y的先验几率
        self.classes = np.unique(y)
        if self.class_prior == None:#先验几率没有指定
            class_num = len(self.classes)
            self.class_prior = {}
            if not self.fit_prior:
                for d in self.classes:
                    self.class_prior[d] = 1.0/class_num 
            else:
                self.class_prior = {}
                for d in self.classes:
                    c_num = np.sum(np.equal(y,d))
                    self.class_prior[d]= c_num / len(y)
        print(self.class_prior)           
        #计算条件几率------高斯模型
        self.mean = {}
        self.var = {}
        y = list(y)
        for yy in self.class_prior.keys():
            y_index = [i for i,label in enumerate(y) if label == yy] #标签的先验几率
            #print(y_index)
            for i in range(len(x)):
                x_class =[]
                for j in y_index:
                    x_class.append(x[i][j])
                    pkey = str(i) + '|' + str(yy)
                    mean = np.mean(x_class)
                    var = np.var(x_class)
                    self.mean[pkey] = mean
                    self.var[pkey] = var
                #print(x_class)
        print(self.mean, self.var)
        return self

    def _calculat_prob_gaussion(self,mu,sigma,x):    
        return  1.0/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (x - mu)**2 / (2 * sigma**2)) 

    def predict(self,x):
        labels = []
        for i in range(x.shape[0]):
            self.predict_prob = {}
            for yy in self.class_prior.keys():
                self.predict_prob[yy] = self.class_prior[yy]
                for c,d in  enumerate(list(x[i])):
                    tkey = str(c)+'|'+str(yy)
                    mu = self.mean[tkey] 
                    sigma = self.var[tkey] 
                    print(mu,sigma)
                    self.predict_prob[yy] = self.predict_prob[yy]*self._calculat_prob_gaussion(mu,sigma,d)     
            print(self.predict_prob)
            label = max(self.predict_prob, key=self.predict_prob.get)
            labels.append(label)
        return labels


if __name__ == '__main__':
    x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]])
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    gnb = GaussionNB()
    gnb.fit(x, y)
    print('预测值为：', gnb.predict(np.array([[2,1]])))

python调包：

import numpy as np
from sklearn.naive_bayes import GaussianNB

if __name__ == '__main__':   
    x = np.array([[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3],[1,2,2,1,1,1,2,2,3,3,3,2,2,3,3]]).T
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    gnb = GaussianNB()
    gnb.fit(x,y)
    print('预测值为：', gnb.predict(np.array([[2,1]])))

C++实现：

#include 
#include 
#include 
#include 
#include 
#include 
#include 

#define PI 3.1415926

class GaussionNB
{
public:
	GaussionNB(bool fit_prior = true) : m_fit_prior(fit_prior) {}

	void fit(std::vector> x, std::vector y)
	{
		for (auto i : y)
			m_classes.insert(i);
		if (m_class_prior.size() == 0)
		{
			int class_num = m_classes.size();
			if (!m_fit_prior)
			{
				for (auto d : m_classes)
					m_class_prior[d] = 1.0 / class_num;
			}
			else {
				for (auto d : m_classes)
				{
					float c_num = 0;
					for (auto i : y)	c_num += (d == i ? 1 : 0);
					m_class_prior[d] = c_num / y.size();
				}
			}
		}

		for (auto pa : m_class_prior)
		{
			//std::cout << pa.first << " " << pa.second << std::endl;
			std::vector y_index;
			for (size_t i = 0; i < y.size(); i++)
			{
				if (y[i] == pa.first)	y_index.push_back(i);
			}
			//for (size_t j = 0; j < y_index.size(); j++) std::cout << y_index[j] << " "; std::cout << std::endl;
			
			for (size_t i = 0; i < x.size(); i++)
			{
				std::vector x_class;

				for (auto j:y_index)
				{
					x_class.push_back(x[i][j]);

					std::string pkey = std::to_string(i) + "|" + std::to_string(pa.first);
					
					float mean_val = 0;
					for (size_t k = 0; k < x_class.size(); k++)
					{
						mean_val += x_class[k];
					}
					mean_val /= x_class.size();
					m_mean[pkey] = mean_val;

					float var_val = 0;
					for (size_t k = 0; k < x_class.size(); k++)
					{
						var_val += pow(x_class[k] - mean_val, 2);
					}
					var_val /= x_class.size();
					m_var[pkey] = var_val;
				}

				//for (auto i : x_class)	std::cout << i << " "; std::cout << std::endl;
			}
		}

		//for (auto pa : m_mean)	std::cout << pa.first << " " << pa.second << std::endl;
		//for (auto pa : m_var)	std::cout << pa.first << " " << pa.second << std::endl;
	}

	float _calculat_prob_gaussion(float mu, float sigma, float x)
	{
		return 1.0 / (sigma*sqrt(2 * PI))*exp(-pow(x - mu, 2) / (2 * pow(sigma, 2)));
	}

	std::vector predict(std::vector> x)
	{
		std::vector labels;
		for (size_t i = 0; i < x.size(); i++)
		{
			m_predict_prob.clear();
			for (auto pa : m_class_prior)
			{
				m_predict_prob[pa.first] = m_class_prior[pa.first];
				for (size_t j = 0; j < x[i].size(); ++j)
				{
					std::string tkey = std::to_string(j) + "|" + std::to_string(pa.first);
					//std::cout << tkey << std::endl;

					float mu = m_mean[tkey];
					float sigma = m_var[tkey];
					//std::cout << mu << " " << sigma << std::endl;
					m_predict_prob[pa.first] *= _calculat_prob_gaussion(mu, sigma, x[i][j]);
				}
			}

			//for (auto pa : m_predict_prob)	std::cout << pa.first << " " << pa.second << std::endl;

			std::vector>  m_predict_prob_vec;
			for (std::map::iterator it = m_predict_prob.begin(); it != m_predict_prob.end(); it++)
			{
				m_predict_prob_vec.push_back(std::make_pair((*it).first, (*it).second));
			}
			std::sort(m_predict_prob_vec.begin(), m_predict_prob_vec.end(), [](std::pair p1, std::pair p2) {return p1.second < p2.second; });
			float label = m_predict_prob_vec.rbegin()->first;
			labels.push_back(label);
		}

		return labels;
	}

private:
	bool m_fit_prior;
	std::map m_class_prior;
	std::set m_classes;
	std::map m_mean;
	std::map m_var;
	std::map m_predict_prob;
};


int main(int argc, char* argv[])
{
	std::vector> x = { { 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3 },{ 1,2,2,1,1,1,2,2,3,3,3,2,2,3,3 } };
	std::vector y = { -1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1 };

	GaussionNB gnb = GaussionNB();
	gnb.fit(x, y);
	std::cout << "预测值为：" << gnb.predict({ { 2,1 } })[0] << std::endl;

	system("pause");
	return EXIT_SUCCESS;
}

朴素贝叶斯算法

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