def predict_cluster(self, X, with_covariance=False):
"""Backward prediction
If with_covariance is True, the importance of one cluster is computed with the height of gaussian as well."""
N = X.shape[0]
prob = np.empty((self.K, N))
if with_covariance:
chols = np.linalg.cholesky(self.full_SigmakList)
dets = np.sum(np.log(np.array([np.diag(c) for c in chols])),
axis=1)
for k, ck, Gammak, pik in zip(range(self.K), self.ckList,
self.GammakList, self.pikList):
r = chol_loggausspdf(X.T, ck[:, None], Gammak) + np.log(pik)
if with_covariance: # poids = pik / sqrt( det(Sigma))
r = r - dets[k]
prob[k] = r
choice = np.argmax(prob, axis=0)
prob = np.exp(prob)
prob = prob / prob.sum(axis=0)
return choice, prob.T
def _helper_backward_conditionnal_density(self, X):
"""
Compute the mean Ak*Y + Bk and the quantities alpha depending of X in (6)
:param X: shape (L,D)
:return: mean shape(D,N,K) alpha shape (N,K)
"""
N = X.shape[0]
X = X.reshape((N, self.L))
proj = np.empty((self.D, N, self.K)) # AkS * X + BkS
logalpha = np.zeros((N, self.K)) # log N(ckS,GammakS)(X)
for (k, pik, Ak, bk, ck, Gammak) in zip(range(self.K), self.pikList,
self.AkList, self.bkList,
self.ckList, self.GammakList):
proj[:, :, k] = Ak.dot(X.T) + np.expand_dims(bk, axis=1)
logalpha[:, k] = np.log(pik) + chol_loggausspdf(
X.T, ck.reshape((self.L, 1)), Gammak)
log_density = logsumexp(logalpha, axis=1, keepdims=True)
logalpha -= log_density
alpha = np.exp(logalpha)
return proj, alpha
def forward_density(self, Y, X_points, marginals=None, sub_densities=0):
"""Return conditionnal density of X knowing Y, evaluated at X_points.
Return shape (N ,len(X_points) ).
If marginals is given, compute marginal density. In this case, X_points needs to have the marginal dimension.
Is sub_densities is a non negative integer, returns the density of sub_densitites dominant components."""
if (not marginals) and not X_points.shape[1] == self.L:
raise WrongContextError(
"Dimension of X samples doesn't match the choosen Lw")
proj, alpha, _ = self._helper_forward_conditionnal_density(Y)
NX, D = X_points.shape
N = Y.shape[0]
if marginals:
proj = proj[:, :, marginals] # len(marginals) , N , K
covs = self.SigmakListS[:,
marginals, :][:, :,
marginals] # K, len(marginals), len(marginals)
else:
covs = self.SigmakListS
densites = np.empty((N, NX))
sub_dens = np.empty((sub_densities, N, NX))
t = time.time()
for n, meann, alphan in zip(range(N), proj, alpha):
densites[n] = densite_melange(X_points, alphan, meann, covs)
if sub_densities:
dominants = dominant_components(alphan, meann,
covs)[0:sub_densities]
for i, (_, w, m, c) in enumerate(dominants):
sub_dens[i, n] = np.exp(
chol_loggausspdf(X_points.T, m.reshape((D, 1)), c)) * w
if self.verbose:
logging.debug("Density calcul time {:.3f}".format(time.time() - t))
return densites, sub_dens
def _helper_forward_conditionnal_density(self, Y):
"""
Compute the mean Ak*Y + Bk and the quantities alpha depending of Y in (7)
:param Y: shape (N,D)
:return: mean shape(N,K,L) alpha shape (N,K) , normalisation shape (N,1)
"""
N = Y.shape[0]
Y = Y.reshape((N, self.D))
YT = np.array(Y.T, dtype=float)
proj = np.empty((self.L, N, self.K)) # AkS * Y + BkS
logalpha = np.zeros((N, self.K)) # log N(ckS,GammakS)(Y)
for (k, pik, Ak, bk, ck,
Gammak) in zip(range(self.K), self.pikList, self.AkListS,
self.bkListS, self.ckListS, self.GammakListS):
proj[:, :, k] = Ak.dot(YT) + np.expand_dims(bk, axis=1)
logalpha[:, k] = np.log(pik) + chol_loggausspdf(
YT, ck.reshape((self.D, 1)), Gammak)
log_density = logsumexp(logalpha, axis=1, keepdims=True)
logalpha -= log_density
alpha, normalisation = np.exp(logalpha), np.exp(log_density)
return proj.transpose((1, 2, 0)), alpha, normalisation
def test_Hapke():
mu = np.ones(11)
T = np.tril(np.ones((11, 1 & 1))) * 0.456
cov = np.dot(T, T.T)
d = chol_loggausspdf(a.T, mu[:, None], cov)