def test_1D_array(self):
a = np.array([1, 2, 3, 4])
try:
vsplit(a, 2)
assert_(0)
except ValueError:
pass
def _removeNonTracklikeClusterCenters(self):
'''NOTE : Much of this code is copied from LPCMImpl.followXSingleDirection (factor out?)
'''
labels = self._meanShift.labels_
labels_unique = unique(labels)
cluster_centers = self._meanShift.cluster_centers_
rsp = lpcRandomStartPoints()
cluster_representatives = []
for k in range(len(labels_unique)):
cluster_members = labels == k
cluster_center = cluster_centers[k]
cluster = self._Xi[cluster_members,:]
mean_sub = cluster - cluster_center
cov_x = dot(transpose(mean_sub), mean_sub)
eigen_cov = eigh(cov_x)
sorted_eigen_cov = zip(eigen_cov[0],map(ravel,vsplit(eigen_cov[1].transpose(),len(eigen_cov[1]))))
sorted_eigen_cov.sort(key = lambda elt: elt[0], reverse = True)
rho = sorted_eigen_cov[1][0] / sorted_eigen_cov[0][0] #Ratio of two largest eigenvalues
if rho < self._lpcParameters['rho_threshold']:
cluster_representatives.append(cluster_center)
else: #append a random element of the cluster
random_cluster_element = rsp(cluster, 1)[0]
cluster_representatives.append(random_cluster_element)
return array(cluster_representatives)
def test_2D_array(self):
a = np.array([[1, 2, 3, 4],
[1, 2, 3, 4]])
res = vsplit(a, 2)
desired = [np.array([[1, 2, 3, 4]]), np.array([[1, 2, 3, 4]])]
compare_results(res, desired)
def _followxSingleDirection( self,
x,
direction = Direction.FORWARD,
forward_curve = None,
last_eigenvector = None,
weights = 1.):
'''Generates a partial lpc curve dictionary from the start point, x.
Arguments
---------
x : 1-dim, length m, numpy.array of floats, start point for the algorithm when m is dimension of feature space
direction : bool, proceeds in Direction.FORWARD or Direction.BACKWARD from this point (just sets sign for first eigenvalue)
forward_curve : dictionary as returned by this function, is used to detect crossing of the curve under construction with a
previously constructed curve
last_eigenvector : 1-dim, length m, numpy.array of floats, a unit vector that defines the initial direction, relative to
which the first eigenvector is biased and initial cos_neu_neu is calculated
weights : 1-dim, length n numpy.array of observation weights (can also be used to exclude
individual observations from the computation by setting their weight to zero.),
where n is the number of feature points
'''
x0 = copy(x)
N = self.Xi.shape[0]
d = self.Xi.shape[1]
it = self._lpcParameters['it']
h = array(self._lpcParameters['h'])
t0 = self._lpcParameters['t0']
rho0 = self._lpcParameters['rho0']
save_xd = empty((it,d))
eigen_vecd = empty((it,d))
c0 = ones(it)
cos_alt_neu = ones(it)
cos_neu_neu = ones(it)
lamb = empty(it) #NOTE this is named 'lambda' in the original R code
rho = zeros(it)
high_rho_points = empty((0,d))
count_points = 0
for i in range(it):
kernel_weights = self._kernd(self.Xi, x0, c0[i]*h) * weights
mu_x = average(self.Xi, axis = 0, weights = kernel_weights)
sum_weights = sum(kernel_weights)
mean_sub = self.Xi - mu_x
cov_x = dot( dot(transpose(mean_sub), numpy.diag(kernel_weights)), mean_sub) / sum_weights
#assert (abs(cov_x.transpose() - cov_x)/abs(cov_x.transpose() + cov_x) < 1e-6).all(), 'Covariance matrix not symmetric, \n cov_x = {0}, mean_sub = {1}'.format(cov_x, mean_sub)
save_xd[i] = mu_x #save first point of the branch
count_points += 1
#calculate path length
if i==0:
lamb[0] = 0
else:
lamb[i] = lamb[i-1] + sqrt(sum((mu_x - save_xd[i-1])**2))
#calculate eigenvalues/vectors
#(sorted_eigen_cov is a list of tuples containing eigenvalue and associated eigenvector, sorted descending by eigenvalue)
eigen_cov = eigh(cov_x)
sorted_eigen_cov = zip(eigen_cov[0],map(ravel,vsplit(eigen_cov[1].transpose(),len(eigen_cov[1]))))
sorted_eigen_cov.sort(key = lambda elt: elt[0], reverse = True)
eigen_norm = sqrt(sum(sorted_eigen_cov[0][1]**2))
eigen_vecd[i] = direction * sorted_eigen_cov[0][1] / eigen_norm #Unit eigenvector corresponding to largest eigenvalue
#rho parameters
rho[i] = sorted_eigen_cov[1][0] / sorted_eigen_cov[0][0] #Ratio of two largest eigenvalues
if i != 0 and rho[i] > rho0 and rho[i-1] <= rho0:
high_rho_points = vstack((high_rho_points, x0))
#angle between successive eigenvectors
if i==0 and last_eigenvector is not None:
cos_alt_neu[i] = direction * dot(last_eigenvector, eigen_vecd[i])
if i > 0:
cos_alt_neu[i] = dot(eigen_vecd[i], eigen_vecd[i-1])
#signum flipping
if cos_alt_neu[i] < 0:
eigen_vecd[i] = -eigen_vecd[i]
cos_neu_neu[i] = -cos_alt_neu[i]
else:
cos_neu_neu[i] = cos_alt_neu[i]
#angle penalization
pen = self._lpcParameters['pen']
if pen > 0:
if i == 0 and last_eigenvector is not None:
a = abs(cos_alt_neu[i])**pen
eigen_vecd[i] = a * eigen_vecd[i] + (1-a) * last_eigenvector
if i > 0:
a = abs(cos_alt_neu[i])**pen
eigen_vecd[i] = a * eigen_vecd[i] + (1-a) * eigen_vecd[i-1]
#check curve termination criteria
if i not in (0, it-1):
#crossing
cross = self._lpcParameters['cross']
if forward_curve is None:
full_curve_points = save_xd[0:i+1]
else:
full_curve_points = vstack((forward_curve['save_xd'],save_xd[0:i+1])) #inefficient, initialize then append?
if not cross:
prox = where(ravel(cdist(full_curve_points,[mu_x])) <= mean(h))[0]
if len(prox) != max(prox) - min(prox) + 1:
break
#convergence
convergence_at = self._lpcParameters['convergence_at']
conv_ratio = abs(lamb[i] - lamb[i-1]) / (2 * (lamb[i] + lamb[i-1]))
if conv_ratio < convergence_at:
break
#boundary
boundary = self._lpcParameters['boundary']
if conv_ratio < boundary:
c0[i+1] = 0.995 * c0[i]
else:
c0[i+1] = min(1.01*c0[i], 1)
#step along in direction eigen_vecd[i]
x0 = mu_x + t0 * eigen_vecd[i]
#trim output in the case where convergence occurs before 'it' iterations
curve = { 'save_xd': save_xd[0:count_points],
'eigen_vecd': eigen_vecd[0:count_points],
'cos_neu_neu': cos_neu_neu[0:count_points],
'rho': rho[0:count_points],
'high_rho_points': high_rho_points,
'lamb': lamb[0:count_points],
'c0': c0[0:count_points]
}
return curve
def test_2D_array(self):
a = np.array([[1, 2, 3, 4], [1, 2, 3, 4]])
res = vsplit(a, 2)
desired = [np.array([[1, 2, 3, 4]]), np.array([[1, 2, 3, 4]])]
compare_results(res, desired)