In Fishers linear discriminant analysis, we search for a vector w such that all data points are well separately after they are projected to the direction defined by w. The input data points are x1=(4,3)T y1 = 1 x2=(2,2)T y2 = 1 x3=(1,1)T y3 = -1 x4=(-2,-1)T y4= -1 (Note that the first element in vector xi is NOT x0=1). Use Python to find a vector w=[w1,w2] with Fishers linear discriminant analysis. Steps of the python code and intermediate results are needed.

Use these example steps:

Sw = np.matrix(",;,")

m2 = np.matrix(";")

m1 = np.matrix(";")

from numpy.linalg import inv

W = inv(Sw) * (m2-m1)