Return Bures Wasserstein distance between samples.
The function estimates the Bures-Wasserstein distance between two
empirical distributions source \(\mu_s\) and target \(\mu_t\),
discussed in remark 2.31 [1].
The Bures Wasserstein distance between source and target distribution \(\mathcal{W}\)
The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions \(\mathcal{N}(\mu_s,\Sigma_s)\)
and \(\mathcal{N}(\mu_t,\Sigma_t)\) as proposed in
[1] and discussed in remark 2.29 in
[2].
Return Bures Wasserstein distance from mean and covariance of distribution.
The function estimates the Bures-Wasserstein distance between two
empirical distributions source \(\mu_s\) and target \(\mu_t\),
discussed in remark 2.31 [1].
The Bures Wasserstein distance between source and target distribution \(\mathcal{W}\)
The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions \(\mathcal{N}(\mu_s,\Sigma_s)\)
and \(\mathcal{N}(\mu_t,\Sigma_t)\) as proposed in
[1] and discussed in remark 2.29 in
[2].
Return Gaussian Gromov-Wasserstein distance between samples.
The function estimates the Gaussian Gromov-Wasserstein distance between two
Gaussien distributions source \(\mu_s\) and target \(\mu_t\), whose
parameters are estimated from the provided samples \(\mathcal{X}_s\) and
\(\mathcal{X}_t\). See [57] Theorem 4.1 for more details.
Parameters:
xs (array-like (ns,d)) – samples in the source domain
xt (array-like (nt,d)) – samples in the target domain
ws (array-like (ns,1), optional) – weights for the source samples
wt (array-like (ns,1), optional) – weights for the target samples
Return Gaussian Gromov-Wasserstein mapping between samples.
The function estimates the Gaussian Gromov-Wasserstein mapping between two
Gaussien distributions source \(\mu_s\) and target \(\mu_t\), whose
parameters are estimated from the provided samples \(\mathcal{X}_s\) and
\(\mathcal{X}_t\). See [57] Theorem 4.1 for more details.
Parameters:
xs (array-like (ns,ds)) – samples in the source domain
xt (array-like (nt,dt)) – samples in the target domain
ws (array-like (ns,1), optional) – weights for the source samples
wt (array-like (ns,1), optional) – weights for the target samples
sign_eigs (array-like (min(ds,dt),) or string, optional) – sign of the eigenvalues of the mapping matrix, by default all signs will
be positive. If ‘skewness’ is provided, the sign of the eigenvalues is
selected as the product of the sign of the skewness of the projected data.
Return the Gaussian Gromov-Wasserstein value from [57].
This function return the closed form value of the Gaussian Gromov-Wasserstein
distance between two Gaussian distributions
\(\mathcal{N}(\mu_s,\Sigma_s)\) and \(\mathcal{N}(\mu_t,\Sigma_t)\)
when the OT plan is assumed to be also Gaussian. See [57] Theorem 4.1 for
more details.
Parameters:
Cov_s (array-like (ds,ds)) – covariance of the source distribution
Cov_t (array-like (dt,dt)) – covariance of the target distribution
Return the Gaussian Gromov-Wasserstein mapping from [57].
This function return the closed form value of the Gaussian
Gromov-Wasserstein mapping between two Gaussian distributions
\(\mathcal{N}(\mu_s,\Sigma_s)\) and \(\mathcal{N}(\mu_t,\Sigma_t)\)
when the OT plan is assumed to be also Gaussian. See [57] Theorem 4.1 for
more details.
Parameters:
mu_s (array-like (ds,)) – mean of the source distribution
mu_t (array-like (dt,)) – mean of the target distribution
Cov_s (array-like (ds,ds)) – covariance of the source distribution
Cov_t (array-like (dt,dt)) – covariance of the target distribution
Return Bures Wasserstein distance between samples.
The function estimates the Bures-Wasserstein distance between two
empirical distributions source \(\mu_s\) and target \(\mu_t\),
discussed in remark 2.31 [1].
The Bures Wasserstein distance between source and target distribution \(\mathcal{W}\)
The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions \(\mathcal{N}(\mu_s,\Sigma_s)\)
and \(\mathcal{N}(\mu_t,\Sigma_t)\) as proposed in
[1] and discussed in remark 2.29 in
[2].
Return Bures Wasserstein distance from mean and covariance of distribution.
The function estimates the Bures-Wasserstein distance between two
empirical distributions source \(\mu_s\) and target \(\mu_t\),
discussed in remark 2.31 [1].
The Bures Wasserstein distance between source and target distribution \(\mathcal{W}\)
The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions \(\mathcal{N}(\mu_s,\Sigma_s)\)
and \(\mathcal{N}(\mu_t,\Sigma_t)\) as proposed in
[1] and discussed in remark 2.29 in
[2].
Return Gaussian Gromov-Wasserstein distance between samples.
The function estimates the Gaussian Gromov-Wasserstein distance between two
Gaussien distributions source \(\mu_s\) and target \(\mu_t\), whose
parameters are estimated from the provided samples \(\mathcal{X}_s\) and
\(\mathcal{X}_t\). See [57] Theorem 4.1 for more details.
Parameters:
xs (array-like (ns,d)) – samples in the source domain
xt (array-like (nt,d)) – samples in the target domain
ws (array-like (ns,1), optional) – weights for the source samples
wt (array-like (ns,1), optional) – weights for the target samples
Return Gaussian Gromov-Wasserstein mapping between samples.
The function estimates the Gaussian Gromov-Wasserstein mapping between two
Gaussien distributions source \(\mu_s\) and target \(\mu_t\), whose
parameters are estimated from the provided samples \(\mathcal{X}_s\) and
\(\mathcal{X}_t\). See [57] Theorem 4.1 for more details.
Parameters:
xs (array-like (ns,ds)) – samples in the source domain
xt (array-like (nt,dt)) – samples in the target domain
ws (array-like (ns,1), optional) – weights for the source samples
wt (array-like (ns,1), optional) – weights for the target samples
sign_eigs (array-like (min(ds,dt),) or string, optional) – sign of the eigenvalues of the mapping matrix, by default all signs will
be positive. If ‘skewness’ is provided, the sign of the eigenvalues is
selected as the product of the sign of the skewness of the projected data.
Return the Gaussian Gromov-Wasserstein value from [57].
This function return the closed form value of the Gaussian Gromov-Wasserstein
distance between two Gaussian distributions
\(\mathcal{N}(\mu_s,\Sigma_s)\) and \(\mathcal{N}(\mu_t,\Sigma_t)\)
when the OT plan is assumed to be also Gaussian. See [57] Theorem 4.1 for
more details.
Parameters:
Cov_s (array-like (ds,ds)) – covariance of the source distribution
Cov_t (array-like (dt,dt)) – covariance of the target distribution
Return the Gaussian Gromov-Wasserstein mapping from [57].
This function return the closed form value of the Gaussian
Gromov-Wasserstein mapping between two Gaussian distributions
\(\mathcal{N}(\mu_s,\Sigma_s)\) and \(\mathcal{N}(\mu_t,\Sigma_t)\)
when the OT plan is assumed to be also Gaussian. See [57] Theorem 4.1 for
more details.
Parameters:
mu_s (array-like (ds,)) – mean of the source distribution
mu_t (array-like (dt,)) – mean of the target distribution
Cov_s (array-like (ds,ds)) – covariance of the source distribution
Cov_t (array-like (dt,dt)) – covariance of the target distribution