Fisher线性判别分析以及python实现

而如何定量分析找到这一最佳投影方向则是我们下面需要进行的任务

#导入所需库：import numpy as npfrom matplotlib import pyplot as plt

#创建样本集：X1 = np.array([[[1.2],[2.8]],               [[1.9],[3.7]],               [[2.5],[3.8]],               [[4.8],[7.9]],               [[5.6],[7.8]]])X2 = np.array([[[9.7],[12.6]],               [[10.8],[12.7]],               [[13.7],[22.7]],               [[7.48],[14.82]],               [[11.23],[17.16]]])N1 = X1.shape[0]N2 = X2.shape[0]

#类均值向量：m1 = np.array([[0],[0]])for i in range(0,N1):    m1 =m1+X1[i]m1 = m1/N1m2 = np.array([[0],[0]])for i in range(0,N2):    m2 =m2+X2[i]m2 = m2/N2

#类内离散度矩阵：S1 = np.zeros((2,2))for i in range(0,N1):    S1 = S1+np.dot(X1[i]-m1,np.transpose(X1[i]-m1))S2 = np.zeros((2,2))for i in range(0,N2):    S2 = S2+np.dot(X2[i]-m2,np.transpose(X2[i]-m2))Sw = S1+S2

#类间离散度矩阵：Sb = np.dot(m1-m2,np.transpose(m1-m2))

#方向向量：w = np.dot(np.linalg.inv(Sw),m1-m2)print(w)

#投影后均值：m11 = np.dot(np.transpose(w),m1)m21 = np.dot(np.transpose(w),m2)w0 = -(m11+m21)/2

#测试样本：x_test = np.array([[3.42],[5.86]])g = np.dot(np.transpose(w),x_test)+w0if g>0:    print('测试样本属于第一类！')else:    print('测试样本属于第二类！')

#可视化：for i in range(0,N1):    plt.scatter(X1[i,0],X1[i,1],c='r')for i in range(0,N2):    plt.scatter(X2[i,0],X2[i,1],c='b')plt.scatter(x_test[0],x_test[1],c='g')x = np.arange(0,15,0.01)y = w[1]*x/w[0]plt.plot(x,y,c='black')plt.show()

运行结果如图：

最终将测试样本分入第一类，从图像上来看是合理的

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