def descs_to_sstats(xx, gmm):
""" Converts the descriptors to sufficient statistics.
Inputs
------
xx: array [nr_descs, nr_dimensions]
Data matrix containing the descriptors.
gmm: yael.gmm instance
Mixture of Gaussian object.
Output
------
Q_sum: array [nr_clusters, ]
Averaged posterior probabilities.
"""
K = gmm.k
N = xx.shape[0]
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K)
yael.free(Q_yael)
# Compute statistics.
Q_sum = sum(Q, 0) / N # 1xK
return np.array(Q_sum, dtype=np.float32)
def descs_to_sstats(xx, gmm):
""" Converts the descriptors to sufficient statistics.
Inputs
------
xx: array [nr_descs, nr_dimensions]
Data matrix containing the descriptors.
gmm: yael.gmm instance
Mixture of Gaussian object.
Output
------
sstats: array [nr_clusters + 2 * nr_clusters * nr_dimensions, ]
Concatenation of the averaged posterior probabilities `Q_sum`, the
first moment `Q_xx` and second-order moment `Q_xx_2`.
"""
xx = np.atleast_2d(xx)
N = xx.shape[0]
K = gmm.k
D = gmm.d
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K) # NxK
yael.free(Q_yael)
# Compute statistics.
sstats = np.zeros(K + 2 * K * D, dtype=np.float32)
sstats[:K] = np.sum(Q, 0) / N # 1xK
sstats[K:K + K * D] = dot(Q.T, xx).flatten() / N # 1xKD
sstats[K + K * D:K + 2 * K * D] = dot(Q.T, xx**2).flatten() / N # 1xKD
return sstats
def descs_to_sstats(xx, gmm):
""" Converts the descriptors to sufficient statistics.
Inputs
------
xx: array [nr_descs, nr_dimensions]
Data matrix containing the descriptors.
gmm: yael.gmm instance
Mixture of Gaussian object.
Output
------
sstats: array [nr_clusters + 2 * nr_clusters * nr_dimensions, ]
Concatenation of the averaged posterior probabilities `Q_sum`, the
first moment `Q_xx` and second-order moment `Q_xx_2`.
"""
xx = np.atleast_2d(xx)
N = xx.shape[0]
K = gmm.k
D = gmm.d
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K) # NxK
yael.free(Q_yael)
# Compute statistics.
sstats = np.zeros(K + 2 * K * D, dtype=np.float32)
sstats[: K] = np.sum(Q, 0) / N # 1xK
sstats[K: K + K * D] = dot(Q.T, xx).flatten() / N # 1xKD
sstats[K + K * D: K + 2 * K * D] = dot(
Q.T, xx ** 2).flatten() / N # 1xKD
return sstats
def descs_to_sstats(xx, gmm):
""" Converts the descriptors to sufficient statistics.
Inputs
------
xx: array [nr_descs, nr_dimensions]
Data matrix containing the descriptors.
gmm: yael.gmm instance
Mixture of Gaussian object.
Output
------
Q_sum: array [nr_clusters, ]
Averaged posterior probabilities.
"""
K = gmm.k
N = xx.shape[0]
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K)
yael.free(Q_yael)
# Compute statistics.
Q_sum = sum(Q, 0) / N # 1xK
return np.array(Q_sum, dtype=np.float32)
def gmm_predict_proba(xx, gmm):
"""Computes posterior probabilities using yael."""
N = xx.shape[0]
K = gmm.k
Q_yael = yael.fvec_new(N * K)
yael.gmm_compute_p(
N, yael.numpy_to_fvec_ref(xx), gmm, Q_yael, yael.GMM_FLAGS_W)
Q = yael.fvec_to_numpy(Q_yael, N * K).reshape(N, K)
yael.free(Q_yael)
return Q
def descs_to_spatial_sstats(xx, ll, gmm):
""" Computes spatial statistics from descriptors and their position.
Inputs
------
xx: array [N, D], required
N D-dimensional descriptors from an video (usually, after they are
processed with PCA).
ll: array [N, 3], required
Descriptor locations in an image; on each row, we have the triplet
(x, y, t).
gmm: instance of yael object gmm
Gauassian mixture object.
Output
------
ss: array [1, K + 2 * 3 * k]
Sufficient statistics in the form of a vector that concatenates
(i) the sum of posteriors, (ii) an expected value of the locations
ll under the posterior distribution Q and (iii) the second-order
moment of the locations ll under the posterior distribution Q.
"""
N = ll.shape[0]
K = gmm.k
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K)
yael.free(Q_yael)
# Compute statistics.
Q_sum = sum(Q, 0) / N # 1xK
Q_ll = dot(Q.T, ll).flatten() / N # 1x3K
Q_ll_2 = dot(Q.T, ll ** 2).flatten() / N # 1x3K
return np.array(hstack((Q_sum, Q_ll, Q_ll_2)), dtype=np.float32)
def descs_to_spatial_sstats(xx, ll, gmm):
""" Computes spatial statistics from descriptors and their position.
Inputs
------
xx: array [N, D], required
N D-dimensional descriptors from an video (usually, after they are
processed with PCA).
ll: array [N, 3], required
Descriptor locations in an image; on each row, we have the triplet
(x, y, t).
gmm: instance of yael object gmm
Gauassian mixture object.
Output
------
ss: array [1, K + 2 * 3 * k]
Sufficient statistics in the form of a vector that concatenates
(i) the sum of posteriors, (ii) an expected value of the locations
ll under the posterior distribution Q and (iii) the second-order
moment of the locations ll under the posterior distribution Q.
"""
N = ll.shape[0]
K = gmm.k
# Compute posterior probabilities using yael.
Q_yael = fvec_new(N * K)
gmm_compute_p(N, numpy_to_fvec_ref(xx), gmm, Q_yael, GMM_FLAGS_W)
Q = fvec_to_numpy(Q_yael, N * K).reshape(N, K)
yael.free(Q_yael)
# Compute statistics.
Q_sum = sum(Q, 0) / N # 1xK
Q_ll = dot(Q.T, ll).flatten() / N # 1x3K
Q_ll_2 = dot(Q.T, ll**2).flatten() / N # 1x3K
return np.array(hstack((Q_sum, Q_ll, Q_ll_2)), dtype=np.float32)
