Function solve_gromov

ot/solvers.py:604–1348

r"""Solve the discrete (Fused) Gromov-Wasserstein and return :any:`OTResult` object The function solves the following optimization problem: .. math:: \min_{\mathbf{T}\geq 0} \quad (1 - \alpha) \langle \mathbf{T}, \mathbf{M} \rangle_F + \alpha \sum_{i,j,k,l} L(\mathbf{C_1}_{

(
    Ca,
    Cb,
    M=None,
    a=None,
    b=None,
    loss="L2",
    symmetric=None,
    alpha=0.5,
    reg=None,
    reg_type="entropy",
    unbalanced=None,
    unbalanced_type="KL",
    n_threads=1,
    method=None,
    max_iter=None,
    plan_init=None,
    tol=None,
    verbose=False,
)

def solve_gromov(
    Ca,
    Cb,
    M=None,
    a=None,
    b=None,
    loss="L2",
    symmetric=None,
    alpha=0.5,
    reg=None,
    reg_type="entropy",
    unbalanced=None,
    unbalanced_type="KL",
    n_threads=1,
    method=None,
    max_iter=None,
    plan_init=None,
    tol=None,
    verbose=False,
):
    r"""Solve the discrete (Fused) Gromov-Wasserstein and return :any:`OTResult` object

    The function solves the following optimization problem:

    .. math::
        \min_{\mathbf{T}\geq 0} \quad (1 - \alpha) \langle \mathbf{T}, \mathbf{M} \rangle_F +
        \alpha \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} + \lambda_r R(\mathbf{T}) + \lambda_u U(\mathbf{T}\mathbf{1},\mathbf{a}) + \lambda_u U(\mathbf{T}^T\mathbf{1},\mathbf{b})

    The regularization is selected with `reg` (:math:`\lambda_r`) and
    `reg_type`. By default ``reg=None`` and there is no regularization. The
    unbalanced marginal penalization can be selected with `unbalanced`
    (:math:`\lambda_u`) and `unbalanced_type`. By default ``unbalanced=None``
    and the function solves the exact optimal transport problem (respecting the
    marginals).

    Parameters
    ----------
    Ca : array-like, shape (dim_a, dim_a)
        Cost matrix in the source domain
    Cb : array-like, shape (dim_b, dim_b)
        Cost matrix in the target domain
    M : array-like, shape (dim_a, dim_b), optional
        Linear cost matrix for Fused Gromov-Wasserstein (default is None).
    a : array-like, shape (dim_a,), optional
        Samples weights in the source domain (default is uniform)
    b : array-like, shape (dim_b,), optional
        Samples weights in the source domain (default is uniform)
    loss : str, optional
        Type of loss function, either ``"L2"`` or ``"KL"``, by default ``"L2"``
    symmetric : bool, optional
        Use symmetric version of the Gromov-Wasserstein problem, by default None
        tests whether the matrices are symmetric or True/False to avoid the test.
    reg : float, optional
        Regularization weight :math:`\lambda_r`, by default None (no reg., exact
        OT)
    reg_type : str, optional
        Type of regularization :math:`R`, by default "entropy" (only used when
        ``reg!=None``)