def pca(d, headers, normalize=True):
if normalize:
A = normalize_columns_separately(headers, d).T
else:
A = d.get_data(headers).T
# assign to m the mean values of the columns of A
m = A.mean(axis=0)
# 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)
N = np.shape(A)[0]
# 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.
eigenvalues = 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 = (V * D.T).T
# create and return a PCA data object with the headers, projected data,
# eigenvectors, eigenvalues, and mean vector.
result = data.PCAData(headers, pdata, eigenvalues, V, m)
return result
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(d, headers)
else:
A = d.subset(headers)
# assign to m the mean values of the columns of A
m = np.mean(A, 0)
# 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.
eigenvalues = np.square(S) / (np.size(D, 0) - 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.
proj_data = V * D.T
# create and return a PCA data object with the headers, projected data,
# eigenvectors, eigenvalues, and mean vector.
return data.PCAData(proj_data.T, V, eigenvalues, m, headers)
def pca(d, headers, normalize=True):
# assign to A the desired data
if (normalize):
A = normalize_columns_separately(d, headers)
else:
A = d.get_data(headers)
# assign to m the mean values of the columns of A
m = np.mean(A, axis=0)
# assign to D the difference matrix A - m
D = A - m
# assign to U, S, and V the results of SVD
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.
evals = S*S/(A.shape[0]-1)
# project the data onto the eigenvectors.
# The eigenvectors match the order of the eigenvalues.
proj = (V*D.T).T
# create and return a PCA data object with the headers, projected data,
# eigenvectors, eigenvalues, and mean vector.
pca = data.PCAData(headers, proj, evals, V, m)
return pca
def pca(d, headers, normalize=True):
if normalize:
A = normalize_columns_separately(d, headers)
m = []
for i in range(A.shape[1]):
m.append(np.mean(A[:, i]))
else:
A = d.get_data(headers)
# mean values of the columns of A
m = np.matrix(mean(d, headers))
# the difference matrix
D = A - m
# singular value decomposition
U, S, V = np.linalg.svd(D, full_matrices=False)
# get eigenvalues
evals = []
for i in range(len(S)):
evals.append((math.pow(S[i], 2)) / (A.shape[0] - 1))
evals = np.matrix(evals)
# generate projected data
pdata = (V * D.T).T
return data.PCAData(headers, pdata, evals, V, m)
def pca(d, headers, prenormalize=True):
if prenormalize:
A = normalize_columns_separately(headers, d)
else:
A = d.limit_columns(headers)
#do the mean on A so that it's normalized if they wanted to normalize it
m = np.mean(A, axis=0)
D = A - m
U,S,V = np.linalg.svd(D, full_matrices=False)
#D*V.T are the eigenvectors
#V are the eigenvalues
return data.PCAData(D*V.T,V,((S**2)/(A.shape[0]-1)),m,headers)
def pca(d, headers, normalize=True):
'''Takes in a Data object and list of column headers. Returns a data.PCAData object.
By default, data will be prenormalized before pca analysis.'''
if (normalize):
A = normalize_columns_separately(headers, d)
else:
A = d.columns_data(headers)
m = np.mean(A, axis=0)
D = A - m
U, S, V = np.linalg.svd(D, full_matrices=False)
N = A.shape[0]
eigenVals = (S * S) / (N - 1)
projectedData = (V * D.T).T
return data.PCAData(projectedData, V, eigenVals, m, headers)
def pca(d, headers, normalize=True):
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)
# assign to D the difference matrix A - m
D = A - m
# assign to U, S, V the result of running np.svd on d
U, S, V = np.linalg.svd(D, full_matrices=False)
eVals = np.square(S) / (D.shape[0] - 1)
pmat = (V * D.T).T
return data.PCAData(pmat, V, eVals, m, headers)
def pca(d, headers, normalize=True):
print(headers)
if normalize:
A = normalize_columns_separately(headers, d)
else:
A = d.all_rows_specified_columns(headers)
m = numpy.mean(A, axis=0)
D = A - m
U, S, V = numpy.linalg.svd(D, full_matrices=False)
N = D.shape[0]
eigenvalues = S**2 / (N - 1)
pmat = (V * D.T).T
return dt.PCAData(pmat, V, eigenvalues, m, headers)
def pca(d,headers,normalized=True): if(normalized): A = normalize_columns_separately(d, headers) else: A=d.get_data(headers) m = np.mean(A, axis=0) D=A-m U,S,V=np.linalg.svd(D,full_matrices=False) N=A.shape[0] evals=(S*S)/(N-1) projected=(V*D.T).T pcaData= data.PCAData(headers,projected,evals,V,m) return pcaData
def pca(d, headers, normalize=True):
if normalize:
A = normalize_columns_separately(d, headers)
else:
A = d.get_data(headers)
m = A.mean(axis=0)
D = A - m
U, S, V = np.linalg.svd(D, full_matrices=False)
# evals = np.square(np.true_divide(S,S.shape[0]-1))
evals, evecs = np.linalg.eig(np.cov(A, rowvar=False))
evals[::-1].sort()
evecs = V.copy()
pdata = np.transpose(V * np.transpose(D))
return data.PCAData(headers, pdata, evals, evecs, m)
def pca(d, headers, normalize=True):
if normalize:
A = normalize_columns_separately(d, headers).T
else:
A = d.get_data(headers).T
C = np.cov(A, rowvar=False)
W, V = np.linalg.eig(C)
W = np.real(W)
V = np.real(V)
idx = W.argsort()
idx = idx[::-1]
W = W[idx]
V = V[:, idx].T
m = A.mean(0)
D = A - m
projd_data = V * D.T
return data.PCAData(headers, projd_data.T, W, V, m)
def pca(d, headers, normalize=True):
if normalize == True:
A = normalize_columns_separately(headers, d)
else:
A = d.get_data(headers)
m = mean(headers, d)
D = A - m
#calculate eigenvectors and eigenvalues
U, S, V = np.linalg.svd(D, full_matrices=False)
index = 0
#get the eigenvalues using the number of degress of freedom
for d in S:
e = (d * d) / (U.shape[0] - 1)
S[index] = e
index = index + 1
#the projected data
pdata = np.dot(V, (D.T))
pdata = pdata.T
pcad = data.PCAData(headers, pdata, S, V, m)
return pcad
# 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 = data.PCAData(pdata, evecs, evals, means, headers)
# Test all of the various new functions
print("Eigenvalues:")
print(pcad.get_eigenvalues())
print("\nEigenvectors:")
print(pcad.get_eigenvectors())
print("\nMeans:")
print(pcad.get_original_means())
print("\nOriginal Headers:")
print(pcad.get_original_headers())
# Test old functions
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 = data.PCAData( headers, pdata, evals, evecs, 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