def gaussian(x,u,C):
res=(1/sqrt(2*math.pi*abs(Matrix.determinant(C))))
temp=Matrix.transpose(Matrix.minus(x, u))
temp=Matrix.multiply(temp, Matrix.inverse(C))
temp=Matrix.multiply(temp,Matrix.minus(x, u))
try:
res*=exp(-0.5*temp[0][0])
except:
print(temp[0][0])
print(x)
print(u)
print(C)
return res
def analysis(self,k):
# Calculate the empirical mean
means=Multi_Dimension_Data_Statictis.get_average(self.data)
# Calculate the deviations from the mean
deviations=Multi_Dimension_Data_Statictis.get_deviations(self.data) #unused
mean_subtracted_data=Matrix.minus(self.data, Matrix.multiply([[1] for _ in range(len(self.data))], Matrix.transpose(means)))
# Find the covariance matrix
covariance_matrix=Multi_Dimension_Data_Statictis.get_covariance_matrix(mean_subtracted_data)
# Find the eigenvectors and eigenvalues of the covariance matrix
x= np.mat(covariance_matrix)
eigenvalues,eigenvectors=np.linalg.eigh(x)
eigenvalues=eigenvalues.tolist()
eigenvectors=Matrix.transpose(eigenvectors.tolist())
# Rearrange the eigenvectors and eigenvalues
eigenvalue_and_eigenvector=[]
for i in range(len(eigenvalues)):
eigenvalue_and_eigenvector.append((eigenvalues[i],eigenvectors[i]))
eigenvalue_and_eigenvector=sorted(eigenvalue_and_eigenvector, reverse=True)
# Choosing k eigenvectors with the largest eigenvalues
transform_matrix=[]
for i in range(k):
transform_matrix.append(eigenvalue_and_eigenvector[i][1])
return Matrix.transpose(Matrix.multiply(transform_matrix,Matrix.transpose(self.data)))
def iteration(self):
A=Matrix.multiply(self.data_X, self.weights)
E=Matrix.minus(self.g_function(A),self.data_Y)
temp=Matrix.multiply_integer(Matrix.multiply(Matrix.transpose(self.data_X), E), self.learning_rate)
self.weights=Matrix.minus(self.weights,temp)
def test_minus(self):
A=[[1,2,3],[4,5,6]]
B=[[6,5,4],[3,2,1]]
expected_result=[[-5,-3,-1],[1,3,5]]
actual_result=Matrix.minus(A, B)
self.assertEqual(expected_result, actual_result)