def pcaTB(f, time, a=0.5, p=.99, no=5, parallel=True):
"""
This function computes tolerance bounds for functional data containing
phase and amplitude variation using fPCA
:param f: numpy ndarray of shape (M,N) of N functions with M samples
:param time: vector of size M describing the sample points
:param a: confidence level of tolerance bound (default = 0.05)
:param p: coverage level of tolerance bound (default = 0.99)
:param no: number of principal components (default = 5)
:param parallel: enable parallel processing (default = T)
:type f: np.ndarray
:type time: np.ndarray
:rtype: tuple of boxplot objects
:return warp: alignment data from time_warping
:return pca: functional pca from jointFPCA
:return tol: tolerance factor
"""
# Align Data
out_warp = fs.fdawarp(f, time)
out_warp.srsf_align( method="median", parallel=parallel)
# Calculate pca
out_pca = fpca.fdajpca(out_warp)
out_pca.calc_fpca(no)
# Calculate TB
tol = mvtol_region(out_pca.coef, a, p, 100000)
return warp, pca, tol
def joint_gauss_model(self, n=1, no=3):
"""
This function models the functional data using a joint Gaussian model
extracted from the principal components of the srsfs
:param n: number of random samples
:param no: number of principal components (default = 3)
:type n: integer
:type no: integer
"""
# Parameters
fn = self.fn
time = self.time
qn = self.qn
gam = self.gam
M = time.size
# Perform PCA
jfpca = fpca.fdajpca(self)
jfpca.calc_fpca(no=no)
s = jfpca.latent
U = jfpca.U
C = jfpca.C
mu_psi = jfpca.mu_psi
# compute mean and covariance
mq_new = qn.mean(axis=1)
mididx = jfpca.id
m_new = np.sign(fn[mididx, :]) * np.sqrt(np.abs(fn[mididx, :]))
mqn = np.append(mq_new, m_new.mean())
# generate random samples
vals = np.random.multivariate_normal(np.zeros(s.shape), np.diag(s), n)
tmp = np.matmul(U, np.transpose(vals))
qhat = np.tile(mqn.T, (n, 1)).T + tmp[0:M + 1, :]
tmp = np.matmul(U, np.transpose(vals) / C)
vechat = tmp[(M + 1):, :]
psihat = np.zeros((M, n))
gamhat = np.zeros((M, n))
for ii in range(n):
psihat[:, ii] = geo.exp_map(mu_psi, vechat[:, ii])
gam_tmp = cumtrapz(psihat[:, ii]**2,
np.linspace(0, 1, M),
initial=0.0)
gamhat[:, ii] = (gam_tmp - gam_tmp.min()) / (gam_tmp.max() -
gam_tmp.min())
ft = np.zeros((M, n))
fhat = np.zeros((M, n))
for ii in range(n):
fhat[:, ii] = uf.cumtrapzmid(
time, qhat[0:M, ii] * np.fabs(qhat[0:M, ii]),
np.sign(qhat[M, ii]) * (qhat[M, ii] * qhat[M, ii]), mididx)
ft[:, ii] = uf.warp_f_gamma(np.linspace(0, 1, M), fhat[:, ii],
gamhat[:, ii])
self.rsamps = True
self.fs = fhat
self.gams = gamhat
self.ft = ft
self.qs = qhat[0:M, :]
return
def calc_model(self,
pca_method="combined",
no=5,
smooth_data=False,
sparam=25,
parallel=False,
C=None):
"""
This function identifies a regression model with phase-variability
using elastic pca
:param pca_method: string specifing pca method (options = "combined",
"vert", or "horiz", default = "combined")
:param no: scalar specify number of principal components (default=5)
:param smooth_data: smooth data using box filter (default = F)
:param sparam: number of times to apply box filter (default = 25)
:param parallel: run in parallel (default = F)
:param C: scale balance parameter for combined method (default = None)
"""
if smooth_data:
self.f = fs.smooth_data(self.f, sparam)
N1 = self.f.shape[1]
# Align Data
self.warp_data = fs.fdawarp(self.f, self.time)
self.warp_data.srsf_align(parallel=parallel)
# Calculate PCA
if pca_method == 'combined':
out_pca = fpca.fdajpca(self.warp_data)
elif pca_method == 'vert':
out_pca = fpca.fdavpca(self.warp_data)
elif pca_method == 'horiz':
out_pca = fpca.fdahpca(self.warp_data)
else:
raise Exception('Invalid fPCA Method')
out_pca.calc_fpca(no)
# OLS using PCA basis
lam = 0
R = 0
Phi = np.ones((N1, no + 1))
Phi[:, 1:(no + 1)] = out_pca.coef
xx = dot(Phi.T, Phi)
inv_xx = inv(xx + lam * R)
xy = dot(Phi.T, self.y)
b = dot(inv_xx, xy)
alpha = b[0]
b = b[1:no + 1]
# compute the SSE
int_X = np.zeros(N1)
for ii in range(0, N1):
int_X[ii] = np.sum(out_pca.coef * b)
SSE = np.sum((self.y - alpha - int_X)**2)
self.alpha = alpha
self.b = b
self.pca = out_pca
self.SSE = SSE
self.pca_method = pca_method
return
def calc_model(self,
pca_method="combined",
no=5,
smooth_data=False,
sparam=25,
parallel=False):
"""
This function identifies a logistic regression model with phase-variability
using elastic pca
:param f: numpy ndarray of shape (M,N) of N functions with M samples
:param y: numpy array of N responses
:param time: vector of size M describing the sample points
:param pca_method: string specifing pca method (options = "combined",
"vert", or "horiz", default = "combined")
:param no: scalar specify number of principal components (default=5)
:param smooth_data: smooth data using box filter (default = F)
:param sparam: number of times to apply box filter (default = 25)
:param parallel: run model in parallel (default = F)
:type f: np.ndarray
:type time: np.ndarray
"""
if smooth_data:
self.f = fs.smooth_data(self.f, sparam)
N1 = self.f.shape[1]
# Align Data
self.warp_data = fs.fdawarp(self.f, self.time)
self.warp_data.srsf_align(parallel=parallel)
# Calculate PCA
if pca_method == 'combined':
out_pca = fpca.fdajpca(self.warp_data)
elif pca_method == 'vert':
out_pca = fpca.fdavpca(self.warp_data)
elif pca_method == 'horiz':
out_pca = fpca.fdahpca(self.warp_data)
else:
raise Exception('Invalid fPCA Method')
out_pca.calc_fpca(no)
# OLS using PCA basis
lam = 0
R = 0
Phi = np.ones((N1, no + 1))
Phi[:, 1:(no + 1)] = out_pca.coef
# Find alpha and beta using l_bfgs
b0 = np.zeros(self.n_classes * (no + 1))
out = fmin_l_bfgs_b(rg.mlogit_loss,
b0,
fprime=rg.mlogit_gradient,
args=(Phi, self.Y),
pgtol=1e-10,
maxiter=200,
maxfun=250,
factr=1e-30)
b = out[0]
B0 = b.reshape(no + 1, self.n_classes)
alpha = B0[0, :]
# compute the Loss
LL = rg.mlogit_loss(b, Phi, self.y)
b = B0[1:no + 1, :]
self.alpha = alpha
self.b = b
self.pca = out_pca
self.LL = LL
self.pca_method = pca_method
return