文章目录

• 一、实验目的
• 二、实验环境
• 三、实验内容
• 四、实验要求
• 五、实验代码
• 六、实验结果

一、实验目的

让同学进一步了解分类器的设计概念，能够根据自己的设计对线性分类器有更深刻的认识，理解Fisher准则方法确定最佳线性分界面方法的原理，以及Lagrande乘子求解的原理。

二、实验环境

硬件：intel(R) Core(TM) i7-9750H CPU @ 2.60GHz  RAM 16GB
系统：Windows 10 
语言版本：Python 3.8.5 
编译环境：Visual Studio Code 1.56 、Anaconda 1.10
依赖库：numpy、matplotlib

三、实验内容

已知有两类数据ω_1和ω_2，二者的先验概率未知。
ω_1的数据点如下：
ω_1= [0.2331, 2.3385], [1.5207, 2.1946], [0.6499, 1.6730], [0.7757, 1.6365],
[1.0524, 1.7844], [1.1974, 2.0155], [0.2908, 2.0681], [0.2518, 2.1213],
[0.6682, 2.4797], [0.5622, 1.5118], [0.9023, 1.9692], [0.1333, 1.8340],
[-0.5431, 1.8704], [0.9407, 2.2948], [-0.2126, 1.7714], [0.0507, 2.3939],
[-0.0810, 1.5648], [0.7315, 1.9329], [0.3345, 2.2027], [1.0650, 2.4568],
[-0.0247, 1.7523], [0.1043, 1.6991], [0.3122, 2.4883], [0.6655, 1.7259],
[0.5838, 2.0466], [1.1653, 2.0226], [1.2653, 2.3757], [0.8137, 1.7987],
[-0.3399, 2.0828], [0.5152, 2.0798], [0.7226, 1.9449], [-0.2015, 2.3801],
[0.4070, 2.2373], [-0.1717, 2.1614], [-1.0573, 1.9235], [-0.2099, 2.2604]]
ω_2的数据点如下：
ω_2=[[1.4010, 1.0298], [1.2301, 0.9611], [2.0814, 0.9154], [1.1655, 1.4901],
[1.3740, 0.8200], [1.1829, 0.9399], [1.7632, 1.1405], [1.9739, 1.0678],
[2.4152, 0.8050], [2.5890, 1.2889], [2.8472, 1.4601], [1.9539, 1.4334],
[1.2500, 0.7091], [1.2864, 1.2942], [1.2614, 1.3744], [2.0071, 0.9387],
[2.1831, 1.2266], [1.7909, 1.1833], [1.3322, 0.8798], [1.1466, 0.5592],
[1.7087, 0.5150], [1.5920, 0.9983], [2.9353, 0.9120], [1.4664, 0.7126],
[2.9313, 1.2833], [1.8349, 1.1029], [1.8340, 1.2680], [2.5096, 0.7140],
[2.7198, 1.2446], [2.3148, 1.3392], [2.0353, 1.1808], [2.6030, 0.5503],
[1.2327, 1.4708], [2.1465, 1.1435], [1.5673, 0.7679], [2.9414, 1.1288]]
试用以上数据点作为样本点，按照Fisher准则求出w_0和W^*，画出判别面，并使用该模型判断[1, 1.5], [1.2, 1.0], [2.0, 0.9], [1.2, 1.5], [0.23, 2.33] 分别属于哪一类。

四、实验要求

1. 使用Python语言完成Fisher线性分类器的设计，要求程序有相应的说明文字。
2. 求出判别函数，画出分类线。
3. 对测试样本的类别进行判断，并画出数据分类的结果。

五、实验代码

import numpy as np
import matplotlib.pyplot as plt


data1 = np.array([[0.2331, 2.3385], [1.5207, 2.1946], [0.6499, 1.6730], [0.7757, 1.6365],
[1.0524, 1.7844], [1.1974, 2.0155], [0.2908, 2.0681], [0.2518, 2.1213],
[0.6682, 2.4797], [0.5622, 1.5118], [0.9023, 1.9692], [0.1333, 1.8340],
[-0.5431, 1.8704], [0.9407, 2.2948], [-0.2126, 1.7714], [0.0507, 2.3939],
[-0.0810, 1.5648], [0.7315, 1.9329], [0.3345, 2.2027], [1.0650, 2.4568],
[-0.0247, 1.7523], [0.1043, 1.6991], [0.3122, 2.4883], [0.6655, 1.7259],
[0.5838, 2.0466], [1.1653, 2.0226], [1.2653, 2.3757], [0.8137, 1.7987],
[-0.3399, 2.0828], [0.5152, 2.0798], [0.7226, 1.9449], [-0.2015, 2.3801],
[0.4070, 2.2373], [-0.1717, 2.1614], [-1.0573, 1.9235], [-0.2099, 2.2604]]
)
data2 = np.array([[1.4010, 1.0298], [1.2301, 0.9611], [2.0814, 0.9154], [1.1655, 1.4901],
[1.3740, 0.8200], [1.1829, 0.9399], [1.7632, 1.1405], [1.9739, 1.0678],
[2.4152, 0.8050], [2.5890, 1.2889], [2.8472, 1.4601], [1.9539, 1.4334],
[1.2500, 0.7091], [1.2864, 1.2942], [1.2614, 1.3744], [2.0071, 0.9387],
[2.1831, 1.2266], [1.7909, 1.1833], [1.3322, 0.8798], [1.1466, 0.5592],
[1.7087, 0.5150], [1.5920, 0.9983], [2.9353, 0.9120], [1.4664, 0.7126],
[2.9313, 1.2833], [1.8349, 1.1029], [1.8340, 1.2680], [2.5096, 0.7140],
[2.7198, 1.2446], [2.3148, 1.3392], [2.0353, 1.1808], [2.6030, 0.5503],
[1.2327, 1.4708], [2.1465, 1.1435], [1.5673, 0.7679], [2.9414, 1.1288]]
)
#数据输入

data1_avr = np.mean(data1,axis=0)
data2_avr = np.mean(data2,axis=0)
#求均值向量

new_data1 = np.zeros(data1.shape)
new_data2 = np.zeros(data1.shape)
t = 0
for i in data1:
    new_data1[t] = i - data1_avr
    t += 1
t = 0
for j in data2:
    new_data2[t] = j - data2_avr
#计算x-x平均

S1 = np.zeros((data1.shape[1],data1.shape[1]))
S2 = np.zeros((data2.shape[1],data2.shape[1]))
for i in new_data1:
    temp = i.reshape(2,1)
    S1 += temp @ temp.T
for i in new_data2:
    temp = i.reshape(2,1)
    S2 += temp @ temp.T
#计算类内离散度矩阵S1和S2

Sw = S1 + S2
Sw_n = np.linalg.inv(Sw)
#计算总类内离散度矩阵及其逆矩阵

w = Sw_n @ (data1_avr - data2_avr)
#得到最佳投影向量

m1 = w.T @ data1_avr
m2 = w.T @ data2_avr
w0 = -(data1.shape[1]*m1 + data2.shape[1]*m2)/(data1.shape[1] + data2.shape[1])
#计算分界阈值点

test = np.array([[1, 1.5], [1.2, 1.0], [2.0, 0.9], [1.2, 1.5], [0.23, 2.33]])
test_class1 = []
test_class2 = []
for i in test:
    y = w.T @ i + w0
    if y >0:
        print('数据'+ str(i) + '被判别为第一类')
        test_class1.append(i)
    elif y ==0:
        print('数据'+ str(i) + '在判别面上 无法判别')
    else:
        print('数据'+ str(i) + '被判别为第二类')
        test_class2.append(i)
#判别测试集数据

test_class1 = np.array(test_class1)
test_class2 = np.array(test_class2)
x1 = data1[:,0]
y1 = data1[:,1]
x2 = data2[:,0]
y2 = data2[:,1]
x3 = test_class1[:,0]
y3 = test_class1[:,1]
x4 = test_class2[:,0]
y4 = test_class2[:,1]
avr = (data1_avr + data2_avr)/2
temp_x = np.arange(-1,2.5,0.1)
k = -w[0]/w[1]
b = avr[1]-avr[0]*k
temp_y = k * temp_x + b
#准备画图数据


plt.scatter(x3,y3,c='g',marker=',',s=25)
plt.scatter(x4,y4,c='c',marker=',',s=25)
plt.scatter(x1,y1,s=8)
plt.scatter(x2,y2,s=8)
plt.plot(temp_x,temp_y,'r')
plt.legend(['judge line','test class 1','test class 2','class 1','class 2',],loc='upper right')
plt.show()
#画图

六、实验结果