Fisher算法+两类问题

文章目录

• 一、Fisher算法
• 二、蠓的分类问题：
• 三、代码实现：

一、Fisher算法

二、蠓的分类问题：

数据集：

APF = np.array([

    [1.14,1.78],[1.18,1.96],

    [1.20,1.86],[1.26,2.00],

    [1.30,2.00],[1.28,1.96]

])

AF = np.array([

    [1.24,1.72],[1.36,1.74],

    [1.38,1.64],[1.38,1.82],

    [1.38,1.90],[1.40,1.70],

    [1.48,1.82],[1.54,2.08],

    [1.56,1.78]

])

三、代码实现：

Fisher算法关键在于求出权向量W_和阈值W*，然后求出待测数据的映射y_test，最后与W*阈值作比较。

import numpy as np

APF = np.array([

    [1.14,1.78],[1.18,1.96],

    [1.20,1.86],[1.26,2.00],

    [1.30,2.00],[1.28,1.96]

])

AF = np.array([

    [1.24,1.72],[1.36,1.74],

    [1.38,1.64],[1.38,1.82],

    [1.38,1.90],[1.40,1.70],

    [1.48,1.82],[1.54,2.08],

    [1.56,1.78]

])

#获取样本均值

def getAvg(x):

    return np.mean(x, axis=0)

#求两类样本类内离散度矩阵Si

def getSi(x, x_mean):

    x_mean = x_mean.reshape(x.shape[1],1)

    Si = np.zeros((x.shape[1],x.shape[1]))

    for xi in x:

        temp_xi = xi.copy().reshape(x.shape[1],1)

        temp = (temp_xi-x_mean)

        Si = Si + np.dot(temp, temp.T)

    return Si

# 求权向量W_

def getW(x1_mean,x2_mean,Sw):

    return np.dot(np.linalg.inv(Sw),(x1_mean-x2_mean))

# 获取分类阈值w0和权向量W_

def get_w0(x1, x2):

    x1_mean = getAvg(x1)

    x2_mean = getAvg(x2)

    S1 = getSi(APF, x1_mean)

    S2 = getSi(AF, x2_mean)

    Sw = S1+S2

    W_ = getW(x1_mean,x2_mean,Sw)

    #获取投影点

    y1 = np.dot(x1, W_)

    y2 = np.dot(x2, W_)

    #求各类样本均值yi_mean

    y1_mean = np.mean(y1)

    y2_mean = np.mean(y2)

    #选取分类阈值w0

    w0 = (y1_mean + y2_mean) / 2

    return w0, W_

def Fisher(x1, x1_label, x2, x2_label, x_test):

    w0, W_ = get_w0(x1,x2)

    y_test = np.dot(x_test, W_)

    if y_test > w0:

        print('测试样本属于', x1_label)

    elif y_test <w0:

        print('测试样本属于',x2_label)

    else:

        print('测试样本可能属于%s，也可嫩属于%s'%x1_label%x2_label)

x_tests = np.array([

    [1.24,1.80],[1.28,1.84],[1.40,2.04]

])

i = 1

for x_test in x_tests:

    print('第%d个'%i,end='')

    i += 1

    Fisher(APF,'蠓APF',AF,'蠓AF',x_test)

预测结果如下：

第1个测试样本属于 蠓APF

第2个测试样本属于 蠓APF

第3个测试样本属于 蠓APF