def PcaCustomFor2Variables(matrix):
#subtract average from each item
xAv = _math.AverageList(matrix[0])
yAv = _math.AverageList(matrix[1])
for i in range(len(matrix[0])):
matrix[0][i] = matrix[0][i] - xAv
for i in range(len(matrix[1])):
matrix[1][i] = matrix[1][i] - yAv
matrix = _matrix.Transpose(matrix)
covMatrix = _matrix.Covariance(matrix)
eValues = EigenValues(covMatrix)
eVector = EigenVector(covMatrix, eValues)
return eValues, _matrix.Transpose(eVector)
def LinearLeastSquares(matrix, y): # B = (X^T * X)^-1 * X^t * y
matrix = _matrix.AddBeginColumn(matrix, 1)
matrixtranspose = _matrix.Transpose(matrix)
section_1 = _matrix.Inverse(_matrix.Multiplication(matrixtranspose,
matrix),
1) # (X^T * X)^-1
section_2 = _matrix.Multiplication(section_1,
matrixtranspose) # (X^T * X)^-1 * X^t
section_3 = _matrix.Multiplication(section_2, y) # (X^T * X)^-1 * X^t * y
return section_3
def QuadraticLeastSquares(matrix, y): # B = (X^T * X)^-1 * X^t * y
matrix = _matrix.AddEndColumnPotentialLast(
_matrix.AddBeginColumn(matrix, 1), 2)
matrixtranspose = _matrix.Transpose(matrix)
section_1 = _matrix.Inverse(_matrix.Multiplication(matrixtranspose,
matrix),
1) # (X^T * X)^-1
section_2 = _matrix.Multiplication(section_1,
matrixtranspose) # (X^T * X)^-1 * X^t
section_3 = _matrix.Multiplication(section_2, y) # (X^T * X)^-1 * X^t * y
return section_3
def PcaNumpy(matrix):
covMatrix = _matrix.Covariance(_matrix.Transpose(matrix))
eigenValues, eigenVectors = np.linalg.eig(covMatrix)
auxZip = sorted(zip(eigenValues, eigenVectors.T))
eVector = []
eValues = []
for i in auxZip:
eValues.append(i[0])
eVector.append(i[1])
eValues = eValues[::-1]
eVector = np.asarray(eVector[::-1])
return eValues, eVector
def RobustLeastSquares(matrix, y): # B = (X^T * W.X)^-1 * X^t * W.y
matrixlinear = LinearLeastSquares(matrix, y)
newy = LinearPredictMatrix(matrix, matrixlinear)
w = _matrix.Copy(newy)
# calculating w
for i in range(len(w)):
w[i][0] = 1 / (abs(y[i][0] - newy[i][0]))
y = _matrix.MultiplicationEscalarMatrix(y, w)
matrix = _matrix.AddBeginColumn(matrix, 1)
matrix = _matrix.MultiplicationEscalarMatrix(matrix, w)
matrixtranspose = _matrix.Transpose(matrix)
section_1 = _matrix.Inverse(_matrix.Multiplication(matrixtranspose,
matrix),
1) # (X^T * X)^-1
section_2 = _matrix.Multiplication(section_1,
matrixtranspose) # (X^T * X)^-1 * X^t
section_3 = _matrix.Multiplication(section_2, y) # (X^T * X)^-1 * X^t * y
return section_3
def dataset_test(self, path, datatype="float"):
print(">>>>>> " + path + " <<<<<<")
originalMatrix = _matrix.ReadCsv(path, ";", datatype)
originalMatrix = _matrix.Transpose(originalMatrix)
auxMatrix = _matrix.Copy(originalMatrix)
eValues, eVectors = pca.Pca(auxMatrix)
_matrix.matrix_print("EigenVector", eVectors)
_matrix.matrix_print("EigenValue", [eValues])
# plot relevance components
pca.PlotRelevance(eValues, "Relevance Components " + path)
# plot data transformed in the new space
plot.SimplePointData2D(originalMatrix, "Original " + path, "PC1",
"PC2")
# plot data transformed in the new space
transformedData = pca.Transformation(originalMatrix, eVectors)
plot.SimplePointData2D(transformedData, "Transformed " + path, "PC1",
"PC2")
print("\n--------------------------------------------------")