機器學習EM演算法-硬幣問題-詳細可視化代碼

致讀者： 博主是一名資料科學與大資料專業大二的學生，真正的一個互聯網萌新，**寫博客一方面是為了記錄自己的學習程序中遇到的問題和思考，一方面是希望能夠幫助到很多和自己一樣處于困惑的讀者，

**> 由于水平有限，博客中難免會有一些錯誤，有紕漏之處懇請各位大佬不吝賜教！之后會寫大資料專業的文章哦，
GitHub鏈接https://github.com/wfy-belief
盡管現在我的水平可能還不太及格，但我會盡我自己所能，做到最好?，——天地有正氣，雜然賦流形，下則為河岳，上則為日星，

演算法簡介

演算法步驟

代碼效果展示

第一次

第二次

第n次

代碼實作

import math
import matplotlib.pyplot as plt


class Coin_Distribution():
    """
    硬幣的分布
    """

    def __init__(self, head, tail):
        """
        硬幣的正面和反面的個數
        """
        self.head = head
        self.tail = tail


class Solution():
    def __init__(self, theta_A, theta_B):
        """
        初始化條件
        """
        self.distribution1 = Coin_Distribution(5, 5)
        self.distribution2 = Coin_Distribution(9, 1)
        self.distribution3 = Coin_Distribution(8, 2)
        self.distribution4 = Coin_Distribution(4, 6)
        self.distribution5 = Coin_Distribution(7, 3)
        self.distribution = {
            '1': 0,
            '2': 0,
            '3': 0,
            '4': 0,
            '5': 0,
        }
        self.A = theta_A
        self.B = theta_B

    def get_distribution(self, head, tail, key):
        """
        求每個分布的概率,A投擲十次出現相應分布的概率
        """
        pa = math.pow(self.A, head) * math.pow(1 - self.A, tail)
        pb = math.pow(self.B, head) * math.pow(1 - self.B, tail)
        self.distribution[key] = pa / (pa + pb)
        # print(pa / (pa + pb))

    def get_five_distribution(self):
        self.get_distribution(self.distribution1.head,
                              self.distribution1.tail, '1')
        self.get_distribution(self.distribution2.head,
                              self.distribution2.tail, '2')
        self.get_distribution(self.distribution3.head,
                              self.distribution3.tail, '3')
        self.get_distribution(self.distribution4.head,
                              self.distribution4.tail, '4')
        self.get_distribution(self.distribution5.head,
                              self.distribution5.tail, '5')

    def M(self):
        sum_head_A = 0
        sum_tail_A = 0
        sum_head_B = 0
        sum_tail_B = 0
        # get A head
        # print(self.distribution['1'], self.distribution1.head)
        sum_head_A += self.distribution['1'] * self.distribution1.head
        sum_head_A += self.distribution['2'] * self.distribution2.head
        sum_head_A += self.distribution['3'] * self.distribution3.head
        sum_head_A += self.distribution['4'] * self.distribution4.head
        sum_head_A += self.distribution['5'] * self.distribution5.head
        # get A tail
        sum_tail_A += self.distribution['1'] * self.distribution1.tail
        sum_tail_A += self.distribution['2'] * self.distribution2.tail
        sum_tail_A += self.distribution['3'] * self.distribution3.tail
        sum_tail_A += self.distribution['4'] * self.distribution4.tail
        sum_tail_A += self.distribution['5'] * self.distribution5.tail

        # get B heBd
        sum_head_B += (1 - self.distribution['1']) * self.distribution1.head
        sum_head_B += (1 - self.distribution['2']) * self.distribution2.head
        sum_head_B += (1 - self.distribution['3']) * self.distribution3.head
        sum_head_B += (1 - self.distribution['4']) * self.distribution4.head
        sum_head_B += (1 - self.distribution['5']) * self.distribution5.head
        # get B tBil
        sum_tail_B += (1 - self.distribution['1']) * self.distribution1.tail
        sum_tail_B += (1 - self.distribution['2']) * self.distribution2.tail
        sum_tail_B += (1 - self.distribution['3']) * self.distribution3.tail
        sum_tail_B += (1 - self.distribution['4']) * self.distribution4.tail
        sum_tail_B += (1 - self.distribution['5']) * self.distribution5.tail

        self.A = sum_head_A / (sum_head_A + sum_tail_A)
        self.B = sum_head_B / (sum_head_B + sum_tail_B)
        print(self.A, self.B)

    def init_image(self):
        fig = plt.figure('EM', figsize=(4.5, 7))
        plt.title('EM')
        plt.xticks([])
        plt.yticks([])

    def drow_image(self, num):
        plt.title('This is the %d time EM' % num)
        plt.plot([1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 3, 3],
                 [1, 8, 8, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 1])
        plt.text(2, 1.5, r'$%s$' % str('COIN-A'), ha='center', c='r')
        plt.text(4, 1.5, r'$%s$' % str('COIN-B'), ha='center', c='g')
        # coin A
        # print(self.distribution['1'], self.distribution1.head)

        plt.text(1.5, 2.5, r'$%.1fH,%.1fT$' % (self.distribution['1'] * self.distribution1.head,
                                               self.distribution['1'] * self.distribution1.tail), c='r')
        plt.text(1.5, 3.5, r'$%.1fH,%.1fT$' % (self.distribution['2'] * self.distribution1.head,
                                               self.distribution['2'] * self.distribution1.tail), c='r')
        plt.text(1.5, 4.5, r'$%.1fH,%.1fT$' % (self.distribution['3'] * self.distribution1.head,
                                               self.distribution['3'] * self.distribution1.tail), c='r')
        plt.text(1.5, 5.5, r'$%.1fH,%.1fT$' % (self.distribution['4'] * self.distribution1.head,
                                               self.distribution['4'] * self.distribution1.tail), c='r')
        plt.text(1.5, 6.5, r'$%.1fH,%.1fT$' % (self.distribution['5'] * self.distribution1.head,
                                               self.distribution['5'] * self.distribution1.tail), c='r')
        # coin B
        plt.text(3.5, 2.5, r'$%.1fH,%.1fT$' % ((1 - self.distribution['1']) * self.distribution1.head,
                                               (1 - self.distribution['1']) * self.distribution1.head), c='g')
        plt.text(3.5, 3.5, r'$%.1fH,%.1fT$' % ((1 - self.distribution['2']) * self.distribution1.head,
                                               (1 - self.distribution['2']) * self.distribution1.head), c='g')
        plt.text(3.5, 4.5, r'$%.1fH,%.1fT$' % ((1 - self.distribution['3']) * self.distribution1.head,
                                               (1 - self.distribution['3']) * self.distribution1.head), c='g')
        plt.text(3.5, 5.5, r'$%.1fH,%.1fT$' % ((1 - self.distribution['4']) * self.distribution1.head,
                                               (1 - self.distribution['4']) * self.distribution1.head), c='g')
        plt.text(3.5, 6.5, r'$%.1fH,%.1fT$' % ((1 - self.distribution['5']) * self.distribution1.head,
                                               (1 - self.distribution['5']) * self.distribution1.head), c='g')
        # coni A and B
        plt.text(1.2, 7.5, r'CoinA is $p_{A}(%.2f)$' % self.A, c='k')
        plt.text(3.2, 7.5, r'CoinB is $p_{B}(%.2f)$' % self.B, c='k')
        # describe
        plt.text(1.5, 8.5, r'Please click on the X to continue...', c='b')

    def set_ax(self):
        ax = plt.gca()
        ax.spines['right'].set_color('none')
        ax.spines['bottom'].set_color('none')
        ax.spines['top'].set_color('none')
        ax.spines['left'].set_color('none')
        ax.xaxis.set_ticks_position('top')
        ax.invert_yaxis()

    def show_image(self, num):
        self.init_image()
        self.set_ax()
        self.drow_image(num)
        plt.show()


if __name__ == "__main__":
    S = Solution(0.6, 0.5)
    for i in range(5):
        S.get_five_distribution()
        S.M()
        S.show_image(i + 1)