def pca(d, headers, normalize=True):
# assign to A the desired data. Use either normalize_columns_separately
# or get_data, depending on the value of the normalize argument.
if normalize:
A = normalize_columns_separately(headers, d)
else:
A = d.get_data(headers)
# assign to m the mean values of the columns of A
m = np.mean(A, axis=0)[0]
m = np.array(m)
M = m * np.ones(A.shape)
# assign to D the difference matrix A - m
D = A - M
# assign to U, S, V the result of running np.svd on D, with full_matrices=False
U, S, V = np.linalg.svd(D, full_matrices=False)
# the eigenvalues of cov(A) are the squares of the singular values (S matrix)
# divided by the degrees of freedom (N-1). The values are sorted.
N = d.get_num_rows()
eValues = (S * S) / (N - 1)
# project the data onto the eigenvectors. Treat V as a transformation
# matrix and right-multiply it by D transpose. The eigenvectors of A
# are the rows of V. The eigenvectors match the order of the eigenvalues.
pData = np.dot(V, D.T).T
# create and return a PCA data object with the headers, projected data,
# eigenvectors, eigenvalues, and mean vector.
pca_data = PCAData.PCAData(headers, pData, V, eValues, m)
return pca_data
def pca(headers, d, normalize=True): if normalize: A = clusterNormalizeColSeparate(headers, d) else: A = d.getDataNum(headers) m = np.mean(A, axis=0)[0] m = np.array(m) M = m*np.ones( A.shape ) # this is so the mean is setup as the same dimensions as A D = A - M # difference between matrix A and m U, S, V = np.linalg.svd(D, full_matrices=False) #V = Evecs, S/(N-1) = Evals pdata = np.dot(V, D.T).T return PCAData.PCAData(headers, pdata, (S*S)/(d.getNumRowNum()-1), V, m)
def pca(d, headers, normalize=True):
if normalize:
A = normalize_columns_separately(headers, d)
else:
A = d.get_LimitedHeaders(headers)
print(A)
m = np.mean(A, axis=0)
D = A - m
U, S, V = np.linalg.svd(D, full_matrices=False)
eigenvalues = np.square(S) / (A.shape[0] - 1)
projected_data = ((V) * (D.T)).T
return PCAData.PCAData(projected_data, V, eigenvalues, m, headers)
def pca( d, headers, normalized = True ): #takes in a data object, list of column headers, and optional normalized boolean. #returns a PCAData object with the original headers, projected data, eigen values, #eigen vectors, and data means. #data if normalized: A = normalize_columns_separately( headers,d ) else: A = d.get_data(headers) #means m = A.mean(axis=0) #difference matrix D = A-m #transformation matrix U,S,V = np.linalg.svd( D, full_matrices=False ) #eigen values evals = np.matrix( (S*S)/(A.shape[0]-1) ) #eigen vectors evecs = V #projected data pdata = D*V.T #PCAData object return PCAData.PCAData( headers, pdata, evals, evecs, m )
# means of the original data
means = np.matrix([3., 6.])
# eigenvalues of the original data
evals = np.matrix([16.13395443, 0.03271224])
# eigenvectors of the original data as rows
evecs = np.matrix([[0.4527601, 0.89163238], [-0.89163238, 0.4527601]])
# the original data projected onto the eigenvectors.
# pdata = (evecs * (orgdata - means).T).T
pdata = np.matrix([[-4.4720497, -0.02777563], [-2.23602485, -0.01388782],
[4.02623351, -0.19860441], [2.68184104, 0.24026787]])
# create a PCAData object
pcad = PCAData.PCAData(headers, pdata, evecs, evals, means)
# Test all of the various new functions
print "Eigenvalues:"
print pcad.get_eigenvalues()
print "\nEigenvectors:"
print pcad.get_eigenvectors()
print "\nMeans:"
print pcad.get_data_means()
print "\nOriginal Headers:"
print pcad.get_data_headers()
# Test old functions