Function ewca

ot/dr.py:426–594

r""" Entropic Wasserstein Component Analysis :ref:`[52] `. The function solves the following optimization problem: .. math:: \mathbf{U} = \mathop{\arg \min}_\mathbf{U} \quad W(\mathbf{X}, \mathbf{U}\mathbf{U}^T \mathbf

(
    X,
    U0=None,
    reg=1,
    k=2,
    method="BCD",
    sinkhorn_method="sinkhorn",
    stopThr=1e-6,
    maxiter=100,
    maxiter_sink=1000,
    maxiter_MM=10,
    verbose=0,
)

def ewca(
    X,
    U0=None,
    reg=1,
    k=2,
    method="BCD",
    sinkhorn_method="sinkhorn",
    stopThr=1e-6,
    maxiter=100,
    maxiter_sink=1000,
    maxiter_MM=10,
    verbose=0,
):
    r"""
    Entropic Wasserstein Component Analysis :ref:`[52] <references-entropic-wasserstein-component_analysis>`.

    The function solves the following optimization problem:

    .. math::
        \mathbf{U} = \mathop{\arg \min}_\mathbf{U} \quad
        W(\mathbf{X}, \mathbf{U}\mathbf{U}^T \mathbf{X})

    where :

    - :math:`\mathbf{U}` is a matrix in the Stiefel(`p`, `d`) manifold
    - :math:`W` is entropic regularized Wasserstein distances
    - :math:`\mathbf{X}` are samples

    Parameters
    ----------
    X : ndarray, shape (n, d)
        Samples from measure :math:`\mu`.
    U0 : ndarray, shape (d, k), optional
        Initial starting point for projection.
    reg : float, optional
        Regularization term >0 (entropic regularization).
    k : int, optional
        Subspace dimension.
    method : str, optional
        Eather 'BCD' or 'MM' (Block Coordinate Descent or Majorization-Minimization).
        Prefer MM when d is large.
    sinkhorn_method : str
        Method used for the Sinkhorn solver, see :ref:`ot.bregman.sinkhorn` for more details.
    stopThr : float, optional
        Stop threshold on error (>0).
    maxiter : int, optional
        Maximum number of iterations of the BCD/MM.
    maxiter_sink : int, optional
        Maximum number of iterations of the Sinkhorn solver.
    maxiter_MM : int, optional
        Maximum number of iterations of the MM (only used when method='MM').
    verbose : int, optional
        Print information along iterations.

    Returns
    -------
    pi : ndarray, shape (n, n)
        Optimal transportation matrix for the given parameters.