重写轮子之 GaussionNB

我仿照sk-learn 中 GaussionNB 的结构, 重写了该算法的轮子,命名为 MyGaussionNB, 如下:

# !/usr/bin/python
# -*- coding:utf-8 -*-

"""
Reimplement Gaussion naive Bayes algorithm as a practice
"""

# Author: 相忠良(Zhong-Liang Xiang) <ugoood@163.com>
# Finished at June 3, 2017

import numpy as np
from sklearn import datasets, cross_validation
import math
import matplotlib.pyplot as plt
from sklearn import naive_bayes

def load_data():
    iris = datasets.load_iris()
    return cross_validation.train_test_split(iris.data, iris.target, test_size=0.50, random_state=0)

class MyGaussianNB:
    """
    注意: 使用该分类器前, 必须把标签处理成 0,1,2,3.... 这样的形式
    """
    class_prior_dic = {}
    class_prior_arr = []

    class_count_dic = {}
    class_count_arr = []

    theta_ = []
    sigma_ = []

    predict_label = []  # 最终预测值

    def __init__(self):
        pass

    def fit(self, X, y):
        """
        Fit Gaussian naive Bayes according to X, y

        Parameters
        ----------
        X : array-like, shape(n-samples, m-features)
            X part of training data
        y : array-like, shape(n-samples,)
            labels of training data

        Returns:
        --------
        self : object
            Return self.
        """

        # calculate class_prior and class_count-------------
        dic = {}

        for item in y:
            if item in dic.keys():
                dic[item] += 1
            else:
                dic[item] = 1

        dic_temp = dic.copy()
        self.class_count_dic = dic_temp
        self.class_count_arr = dic_temp.values()

        for item in dic:
            dic[item] = float(dic[item]) / y.shape[0]

        self.class_prior_dic = dic
        self.class_prior_arr = dic.values()
        # --------------------------------------------------
        # 调用本类 私有方法
        self.__cal_theta_sigma_arr(X_train, y_train)

    def predict(self, X):
        """
        Predict class labels of X 

        Parameters
        ----------
        X : array-like, shape(n-samples, m-features)
            X a set of test data 

        Returns:
        --------
        a list of class labels of X
        """

        post_arr_matrix = []

        for c in self.class_prior_dic.keys():
            post_per_sample = []
            for sample in X:
                i = 0
                temp = 0.0
                for element in sample:
                    # 注意: 使用该分类器前, 必须把标签处理成 0,1,2,3.... 这样的形式
                    # 原因在 下面的 theta_[c][] 处
                    # 重要: 用 np.log(x)相加的形式, 因为有的概率值特别特别小, 导致后验概率为0
                    #       log sum 越大, post 概率 越大!
                    # 注意: 我们并未采用 -np.log(x)的形式
                    temp = temp + np.log(self.__Gaussion_function(element, self.theta_[c][i], self.sigma_[c][i]))

                    i += 1
                # print '在某类, 一个样例结束'
                temp = temp + np.log(self.class_prior_dic[c])  # temp - log(p(c))
                post_per_sample.append(temp)  # 某类下, X 中所有 sample 的 post 概率, shape(n-samples,)
                # print '某类, 所有样本概率', post_per_sample
            post_arr_matrix.append(post_per_sample)  # 各类下, X 中所有 sample 的 post 概率, shape(n-classes, n-samples)
        self.predict_label = np.argmax(post_arr_matrix, 0)  # 返回 matrix 每列最大值索引. 这里, 索引值恰好是每个 sample 的预测 label.

        return self.predict_label

    def score(self, X, y):
        # 返回正确率
        temp_1 = list(X)
        temp = list(temp_1 == y)

        return 1.0 * temp.count(True) / temp.__len__()

    # 私有方法: 计算 每类 各列的 均值theta 和 标准差sigma
    def __cal_theta_sigma_arr(self, X, y):
        theta_arr = []
        sigma_arr = []

        xxx = []  # including (X,y)
        for item in X:
            xxx.append(list(item))

        ii = 0
        for item in xxx:
            item.append(y[ii])
            ii += 1

        # 担心改了原数据
        sss = np.array(xxx).copy()
        ssss = np.array(xxx).copy()

        for k in self.class_count_dic.keys():
            row_mask = np.array(sss[:, -1] == k, dtype = bool)  # 行网子
            temp = sss[row_mask, :]  # 用 行 网 子 !
            theta_arr.append(np.mean(temp, axis = 0))  # axis=0 表示列

            row_mask_1 = np.array(ssss[:, -1] == k, dtype = bool)  # 行网子
            temp_1 = ssss[row_mask_1, :]  # 用 行 网 子 !
            sigma_arr.append(np.std(temp_1, axis = 0))

        self.theta_ = theta_arr
        self.sigma_ = sigma_arr
        return theta_arr, sigma_arr

    # Gaussian function
    def __Gaussion_function(self, x, theta, sigma):  # private method
        return np.exp(-(x - theta) ** 2 / (2 * sigma ** 2)) / (np.sqrt(2 * np.pi) * sigma)

X_train, X_test, y_train, y_test = load_data()
MGN = MyGaussianNB()
MGN.fit(X_train, y_train)

a = MGN.predict(X_test)
b = np.array(a)
# print b
# print X_test

print '预测值: ', a
print '实际值: ', y_test
print a == y_test
print 'MyGaussionNB 预测正确率: ', MGN.score(MGN.predict_label, y_test)

# sk-learn 中的 GaussionNB 的性能, 且和我的实现 比较一下, 验证我的 implementation 的正确性.
cls = naive_bayes.GaussianNB()
cls.fit(X_train, y_train)
result = cls.predict(X_test)
print 'sklearn 的 GaussionNB 预测正确率: ', MGN.score(result, y_test)
# 结果几乎完全一致,  但在 test_size=0.95 及 训练集更小时, 我的程序会出现问题 !

'''
下面是编程过程中留下的经验
'''

# 重要1:  判断column value真假,用mask,取想要rows的方法
# row_mask = np.array(a[:, -1] == 0, dtype=bool)
# print a[row_mask, :]
# print np.mean(a[mask, :], axis=0)

# 重要2:  提取字典的keys集合和values集合
# print MGN.class_count_dic.keys()
# print MGN.class_count_dic.values()

# 重要3: 用 np.log(x)相加的形式, 因为有的概率值特别特别小, 导致后验概率为0
#       log sum 越大, post 概率 越大!
# 注意: 我们并未采用 -np.log(x)的形式

# 重要4: Numpy中找出array中最大值所对应的行和列
# a = np.array([[.5, 2, 0],
#               [5, 3, 6],
#               [.5, 1, 0]])
#
# re = np.where(a == np.max(a[:,1]))   a中第一列最大元素 在a中的坐标
# print re

# 重要5: 找出 列 or 行 的最大值索引 np.argmax(a,0), a 是矩阵, 0:列, 1:行

# 重要6: 必须要有用于测试的小数据, 来探测每一个func的正确性.
#        下面是我用来测试的小矩阵. 不仅仅测试自己编写的函数,
#        还得对numpy, python 中的函数探测其功能和使用方法.
# a = np.array([[.5, 2, 0],
#               [.25, 3, 6],
#               [.51, 1, 0]])
#
# b = np.array([11, 22, 33])
# aa = np.array(zip(a, b))
#
# cc = [True, False, True, False, True, True]
# print cc.__len__()
# print cc.count(True)

################################################
# 以下内容是我编程过程中用于测试和探查的各种乱七八糟的代码
#
# 我抛弃了这种做法----->: Gaussion这种东西, 算出的值 极有可能非常小, 得用 -log 相加 处理.
# log sum 越小, post 概率 越大!
# 取而代之的是------->: 直接 log后 相加, 取和的最大值的 为 那个样例 应得的标签.

# def Gaussion_function(x, u, sig):
#     return np.exp(-(x - u) ** 2 / (2 * sig ** 2)) / (math.sqrt(2 * math.pi) * sig)

# x1 = Gaussion_function(6., 5.006, 0.34894699)
# x2 = Gaussion_function(2.2, 3.418, 0.37719491)
# x3 = Gaussion_function(4., 1.464, 0.17176728)
# x4 = Gaussion_function(1., 0.244, 0.10613199)

# x1 = Gaussion_function(5., 4.99574468, 0.35247299)
# x2 = Gaussion_function(2.2, 3.418, 0.37719491)
# x3 = Gaussion_function(4., 1.464, 0.17176728)
# x4 = Gaussion_function(1., 0.244, 0.10613199)

# print 'x1 ', x1
# print 'x2 ', x2
# print 'x3 ', x3
# print 'x4 ', x4
#
# x1 = -np.log(x1)
# x2 = -np.log(x2)
# x3 = -np.log(x3)
# x4 = -np.log(x4)
#
# pc = -np.log(0.33098591549295775)

# print 'x1 ', x1
# print 'x2 ', x2
# print 'x3 ', x3
# print 'x4 ', x4
# print 'pc ', pc
# print "x1-x4 log sum:", x1 + x2 + x3 + x4 + pc
#
# print MGN.class_prior_dic
# print MGN.theta_
# [array([ 5.006,  3.418,  1.464,  0.244,  0.   ]),
# array([ 5.93469388,  2.78163265,  4.26530612,  1.33265306,  1.        ]),
# array([ 6.60408163,  2.97755102,  5.56122449,  2.01836735,  2.        ])]
#

# print MGN.sigma_
# [array([ 0.34894699,  0.37719491,  0.17176728,  0.10613199,  0.        ]),
# array([ 0.51608851,  0.30282579,  0.4684107 ,  0.19207541,  0.        ]),
# array([ 0.62562921,  0.32151764,  0.54802664,  0.26929497,  0.        ])]

# print 'x=0, 均值为0, 方差为1', Gaussion_function(0, 0, 1)

# x1 = Gaussion_function(5.8, 5.006, 0.34894699)
# x2 = Gaussion_function(2.8, 3.418, 0.37719491)
# x3 = Gaussion_function(5.1, 1.464, 0.17176728)
# x4 = Gaussion_function(2.4, 0.244, 0.10613199)
# print 'x1 ', x1
# print 'x2 ', x2
# print 'x3 ', x3
# print 'x4 ', x4
# print "x1-x4乘积:", x1 * x2 * x3 * x4 * 1.0  # x1-x4乘积: 2.53455055621e-188

# print X_test
# print MGN.class_prior_dic.keys()

# print "标准差", MGN.sigma_
# print "均值", MGN.theta_

# print MGN.class_count_dic
# print MGN.class_prior_dic
# print 'theta: ', MGN.theta_[0][0]
# print 'sigma: ', MGN.sigma_
# print a.__len__()
# print len(X_test)*4
# print MGN.theta_
# print X_train
# print np.mean(X_train, axis=0)

# print MGN.class_count_dic.keys()

# print 'x_train: ', X_train
# print 'y_train: ', y_train
#
# print 'MGN.class_prior_arr: ', MGN.class_prior_arr
# print 'MGN.class_prior_dic: ', MGN.class_prior_dic
# print 'MGN.class_count_arr: ', MGN.class_count_arr
# print 'MGN.class_count_dic: ', MGN.class_count_dic

# print np.argmax(a, 0)
#
# re = np.where(a == np.max(a[:, 0]))
# print re
# print int(re[0])

# print a[[True,False,True],:]