def get_covariance_matrix(data):
avg=get_average(data)
avg=[n[0] for n in avg]
centralized_matrix=[0]*len(data)
for i,item in enumerate(data):
centralized_matrix[i]=Vector.minus(item,avg)
res=Matrix.multiply(Matrix.transpose(centralized_matrix),centralized_matrix)
N=len(data)-1
return Matrix.multiply_integer(res, 1/N)
def run(self, file_name):
self.load_data(file_name)
for index in range(len(self.data_X)):
self.data_X[index] = [1] + self.data_X[index]
temp = Matrix.multiply(Matrix.transpose(self.data_X), self.data_X)
temp = Matrix.multiply(Matrix.inverse(temp), Matrix.transpose(self.data_X))
temp = Matrix.multiply(temp, self.data_Y)
return temp
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 run(self,file_name,k):
self.load_data(file_name)
self.set_distances()
self.iteration(k)
return Matrix.transpose(self.results);
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_determinant(self):
A=[[1,-9,13,7],[-2,5,-1,3],[3,-1,5,-5],[2,8,-7,-10]]
expected_result=-312
actual_result=Matrix.determinant(A)
self.assertEqual(expected_result, actual_result)
def test_append(self):
A=[[1,2,3],[4,5,6]]
B=[[1,2,3],[4,5,6]]
expected_result=[[1, 2, 3, 1, 2, 3], [4, 5, 6, 4, 5, 6]]
actual_result=Matrix.append(A, B)
self.assertEqual(expected_result, actual_result)
def test_eye(self):
N=3
expected_result=[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
actual_result=Matrix.eye(N)
self.assertEqual(expected_result, actual_result)
def test_inverse(self):
A=[[1,1,2],[-1,2,0],[1,1,3]]
expected_result=[[2.0, -0.3333333333333333, -1.3333333333333335], [1.0, 0.3333333333333333, -0.6666666666666666], [-1.0, 0.0, 1.0]]
actual_result=Matrix.inverse(A)
self.assertEqual(expected_result, actual_result)
def test_multiply_integer(self):
A=[[1,2,3],[4,5,6]]
N=2
expected_result=[[2,4,6],[8,10,12]]
actual_result=Matrix.multiply_integer(A,N)
self.assertEqual(expected_result, actual_result)
def test_transpose(self):
A=[[1,2,3],[4,5,6]]
expected_result=[[1,4],[2,5],[3,6]]
actual_result=Matrix.transpose(A)
self.assertEqual(expected_result, actual_result)
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)
def test_plus(self):
A=[[1,2,3],[4,5,6]]
B=[[6,5,4],[3,2,1]]
expected_result=[[7,7,7],[7,7,7]]
actual_result=Matrix.plus(A, B)
self.assertEqual(expected_result, actual_result)
def test_multiply(self):
A=[[1,2,3],[4,5,6]]
B=[[6,5],[4,3],[2,1]]
expected_result=[[20, 14], [56, 41]]
actual_result=Matrix.multiply(A, B)
self.assertEqual(expected_result, actual_result)