Fisher's Linear Discriminant Analysis (LDA) is a dimension reduction technique that can be used for classification

fishers_lda.py

import numpy as np

class_1 = np.array([[4,1],[2,4],[2,3],[3,6],[4,4]], dtype=np.float64)
class_2 = np.array([[9,10],[6,8],[9,5],[8,7],[10,8]], dtype=np.float64)
m_1, m_2, s_1, s_2, s_w = ([] for i in range(5))

m_1 = np.append(m_1, np.sum(class_1, axis=0)/len(class_1), axis=0)
m_2 = np.append(m_2, np.sum(class_2, axis=0)/len(class_2), axis=0)

print("m_1:", m_1, "\nm_2:", m_2)

for i in range(0, len(class_1), 1):
  a = m_1 - class_1[i]
  s_1.append(a.reshape(-1,1)*a)
s_1 = np.sum(s_1, axis=0)

for i in range(0, len(class_2), 1):
  a = m_2 - class_2[i]
  s_2.append(a.reshape(-1,1)*a)
s_2 = np.sum(s_2, axis=0)

s_w = np.sum([s_1 , s_2], axis=0)

print("s_1:\n", s_1, "\ns_2:\n", s_2, "\ns_w:\n", s_w)

w = np.sum(np.linalg.inv(s_w)*(m_1-m_2), axis=1)
print("w:",w)

output

m_1:
 [3.  3.6] 
m_2:
 [8.4 7.6]
 
s_1:
 [[ 4.  -2. ]
 [-2.  13.2]] 
s_2:
 [[ 9.2 -0.2]
 [-0.2 13.2]] 
s_w:
 [[13.2 -2.2]
 [-2.2 26.4]]
 
w:
 [-0.44046095 -0.18822023]