def __init__(self, beta, mode='O', N=200, scale=True):
"""
fdacurve Construct an instance of this class
:param beta: (n,T,K) matrix defining n dimensional curve on T samples with K curves
:param mode: Open ('O') or closed curve ('C') (default 'O')
:param N: resample curve to N points
:param scale: scale curve to length 1 (true/false)
"""
self.mode = mode
self.scale = scale
K = beta.shape[2]
n = beta.shape[0]
q = zeros((n, N, K))
beta1 = zeros((n, N, K))
cent1 = zeros((n, K))
for ii in range(0, K):
beta1[:, :, ii] = cf.resamplecurve(beta[:, :, ii], N, mode)
a = -cf.calculatecentroid(beta1[:, :, ii])
beta1[:, :, ii] += tile(a, (N, 1)).T
q[:, :, ii] = cf.curve_to_q(beta1[:, :, ii], self.scale, self.mode)
cent1[:, ii] = -a
self.q = q
self.beta = beta1
self.cent = cent1
def preproc_open_curve(beta, T=100):
n, M, k = beta.shape
q = np.zeros((n, T, k))
beta2 = np.zeros((n, T, k))
for i in range(0, k):
beta1 = beta[:, :, i]
beta1, scale = cf.scale_curve(beta1)
beta1 = cf.resamplecurve(beta1, T)
centroid1 = cf.calculatecentroid(beta1)
beta1 = beta1 - np.tile(centroid1, [T, 1]).T
beta2[:, :, i] = beta1
q[:, :, i] = cf.curve_to_q(beta1)
return (q, beta2)
def curve_karcher_cov(betamean, beta, mode='O'):
"""
This claculates the mean of a set of curves
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param beta: numpy ndarray of shape (n, M, N) describing N curves
in R^M
:param mode: Open ('O') or closed curve ('C') (default 'O')
:rtype: tuple of numpy array
:return K: Covariance Matrix
"""
n, T, N = beta.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
# Compute Karcher covariance of uniformly sampled mean
betamean = cf.resamplecurve(betamean, T)
mu = cf.curve_to_q(betamean)
if mode == 1:
mu = cf.project_curve(mu)
basis = cf.find_basis_normal(mu)
v = zeros((n, T, N))
for i in range(0, N):
beta1 = beta[:, :, i]
w, dist = cf.inverse_exp_coord(betamean, beta1)
# Project to the tangent sapce of manifold to obtain v_i
if mode == 0:
v[:, :, i] = w
else:
v[:, :, i] = cf.project_tangent(w, mu, basis)
K = zeros((2*T, 2*T))
for i in range(0, N):
w = v[:, :, i]
wtmp = w.reshape((T*n, 1), order='C')
K = K + wtmp.dot(wtmp.T)
K = K/(N-1)
return(K)
def curve_karcher_cov(betamean, beta, mode='O'):
"""
This claculates the mean of a set of curves
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param beta: numpy ndarray of shape (n, M, N) describing N curves
in R^M
:param mode: Open ('O') or closed curve ('C') (default 'O')
:rtype: tuple of numpy array
:return K: Covariance Matrix
"""
n, T, N = beta.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
# Compute Karcher covariance of uniformly sampled mean
betamean = cf.resamplecurve(betamean, T)
mu = cf.curve_to_q(betamean)
if mode == 1:
mu = cf.project_curve(mu)
basis = cf.find_basis_normal(mu)
v = zeros((n, T, N))
for i in range(0, N):
beta1 = beta[:, :, i]
w, dist = cf.inverse_exp_coord(betamean, beta1)
# Project to the tangent sapce of manifold to obtain v_i
if mode == 0:
v[:, :, i] = w
else:
v[:, :, i] = cf.project_tangent(w, mu, basis)
K = zeros((2*T, 2*T))
for i in range(0, N):
w = v[:, :, i]
wtmp = w.reshape((T*n, 1), order='C')
K = K + wtmp.dot(wtmp.T)
K = K/(N-1)
return(K)
def geod_sphere(beta1, beta2, k=5):
"""
This function calculates the geodesics between open curves beta1 and
beta2 with k steps along path
:param beta1: numpy ndarray of shape (2,M) of M samples
:param beta2: numpy ndarray of shape (2,M) of M samples
:param k: number of samples along path (Default = 5)
:rtype: numpy ndarray
:return dist: geodesic distance
:return path: geodesic path
:return O: rotation matrix
"""
lam = 0.0
elastic = 1
rotation = 1
returnpath = 1
n, T = beta1.shape
beta1 = cf.resamplecurve(beta1, T)
beta2 = cf.resamplecurve(beta2, T)
centroid1 = cf.calculatecentroid(beta1)
beta1 = beta1 - tile(centroid1, [T, 1]).T
centroid2 = cf.calculatecentroid(beta2)
beta2 = beta2 - tile(centroid2, [T, 1]).T
q1 = cf.curve_to_q(beta1)
if rotation:
beta2, O1, tau = cf.find_rotation_and_seed_coord(beta1, beta2)
q2 = cf.curve_to_q(beta2)
else:
O1 = eye(2)
q2 = cf.curve_to_q(beta2)
if elastic:
# Find the optimal coorespondence
gam = cf.optimum_reparam_curve(q2, q1, lam)
gamI = uf.invertGamma(gam)
# Applying optimal re-parameterization to the second curve
beta2n = cf.group_action_by_gamma_coord(beta2, gamI)
q2n = cf.curve_to_q(beta2n)
if rotation:
beta2n, O2, tau = cf.find_rotation_and_seed_coord(beta1, beta2n)
centroid2 = cf.calculatecentroid(beta2n)
beta2n = beta2n - tile(centroid2, [T, 1]).T
q2n = cf.curve_to_q(beta2n)
O = O1.dot(O2)
else:
q2n = q2
O = O1
# Forming geodesic between the registered curves
dist = arccos(cf.innerprod_q2(q1, q2n))
if returnpath:
PsiQ = zeros((n, T, k))
PsiX = zeros((n, T, k))
for tau in range(0, k):
s = dist * tau / (k - 1.)
PsiQ[:, :, tau] = (sin(dist-s)*q1+sin(s)*q2n)/sin(dist)
PsiX[:, :, tau] = cf.q_to_curve(PsiQ[:, :, tau])
path = PsiQ
else:
path = 0
return(dist, path, O)
def geod_sphere(beta1, beta2, k=5):
"""
This function caluclates the geodecis between open curves beta1 and
beta2 with k steps along path
:param beta1: numpy ndarray of shape (2,M) of M samples
:param beta2: numpy ndarray of shape (2,M) of M samples
:param k: number of samples along path (Default = 5)
:rtype: numpy ndarray
:return dist: geodesic distance
:return path: geodesic path
:return O: rotation matrix
"""
lam = 0.0
elastic = 1
rotation = 1
returnpath = 1
n, T = beta1.shape
beta1 = cf.resamplecurve(beta1, T)
beta2 = cf.resamplecurve(beta2, T)
centroid1 = cf.calculatecentroid(beta1)
beta1 = beta1 - tile(centroid1, [T, 1]).T
centroid2 = cf.calculatecentroid(beta2)
beta2 = beta2 - tile(centroid2, [T, 1]).T
q1 = cf.curve_to_q(beta1)
if rotation:
beta2, O1, tau = cf.find_rotation_and_seed_coord(beta1, beta2)
q2 = cf.curve_to_q(beta2)
else:
O1 = eye(2)
q2 = cf.curve_to_q(beta2)
if elastic:
# Find the optimal coorespondence
gam = cf.optimum_reparam_curve(q2, q1, lam)
gamI = uf.invertGamma(gam)
# Applying optimal re-parameterization to the second curve
beta2n = cf.group_action_by_gamma_coord(beta2, gamI)
q2n = cf.curve_to_q(beta2n)
if rotation:
beta2n, O2, tau = cf.find_rotation_and_seed_coord(beta1, beta2n)
centroid2 = cf.calculatecentroid(beta2n)
beta2n = beta2n - tile(centroid2, [T, 1]).T
q2n = cf.curve_to_q(beta2n)
O = O1.dot(O2)
else:
q2n = q2
O = O1
# Forming geodesic between the registered curves
dist = arccos(cf.innerprod_q2(q1, q2n))
if returnpath:
PsiQ = zeros((n, T, k))
PsiX = zeros((n, T, k))
for tau in range(0, k):
s = dist * tau / (k - 1.0)
PsiQ[:, :, tau] = (sin(dist - s) * q1 + sin(s) * q2n) / sin(dist)
PsiX[:, :, tau] = cf.q_to_curve(PsiQ[:, :, tau])
path = PsiQ
else:
path = 0
return (dist, path, O)
def predict(self, newdata=None):
"""
This function performs prediction on regression model on new data if available or current stored data in object
Usage: obj.predict()
obj.predict(newdata)
:param newdata: dict containing new data for prediction (needs the keys below, if None predicts on training data)
:type newdata: dict
:param beta: (n, M,N) matrix of curves
:param y: truth if available
"""
T = self.warp_data.beta_mean.shape[1]
if newdata != None:
beta = newdata['beta']
y = newdata['y']
n = beta.shape[2]
beta1 = np.zeros(beta.shape)
q = np.zeros(beta.shape)
for ii in range(0,n):
if (beta.shape[1] != T):
beta1[:,:,ii] = cf.resamplecurve(beta[:,:,ii],T)
else:
beta1[:,:,ii] = beta[:,:,ii]
a = -cf.calculatecentroid(beta1[:,:,ii])
beta1[:,:,ii] += np.tile(a, (T,1)).T
q[:,:,ii] = cf.curve_to_q(beta1[:,:,ii])[0]
mu = self.warp_data.q_mean
v = np.zeros(q.shape)
for ii in range(0,n):
qn_t, R, gamI = cf.find_rotation_and_seed_unique(mu, q[:,:,ii], 0, self.rotation)
qn_t = qn_t / np.sqrt(cf.innerprod_q2(qn_t,qn_t))
q1dotq2 = cf.innerprod_q2(mu,qn_t)
if (q1dotq2 > 1):
q1dotq2 = 1
d = np.arccos(q1dotq2)
u = qn_t - q1dotq2*mu
normu = np.sqrt(cf.innerprod_q2(u,u))
if (normu>1e-4):
v[:,:,ii] = u*np.arccos(q1dotq2)/normu
else:
v[:,:,ii] = np.zeros(qn_t.shape)
Utmp = self.warp_data.U.T
no = self.warp_data.U.shape[1]
VM = np.mean(self.warp_data.v,2)
VM = VM.flatten()
x = np.zeros((no,n))
for i in range(0,n):
tmp = v[:,:,i]
tmpv1 = tmp.flatten()
x[:,i] = Utmp.dot((tmpv1- VM))
self.y_pred = np.zeros(n)
for ii in range(0,n):
self.y_pred[ii] = self.alpha + np.dot(x[:,ii],self.b)
if y is None:
self.SSE = np.nan
else:
self.SSE = np.sum((y-self.y_pred)**2)
else:
n = self.warp_data.coef.shape[1]
self.y_pred = np.zeros(n)
for ii in range(0,n):
self.y_pred[ii] = self.alpha + np.dot(self.warp_data.coef[:,ii],self.b)
self.SSE = np.sum((self.y-self.y_pred)**2)
return