pyriemann_qiskit.optimization.distance.qdistance_logeuclid_to_convex_hull

pyriemann_qiskit.optimization.distance.qdistance_logeuclid_to_convex_hull(A, B, optimizer=<pyriemann_qiskit.optimization.docplex.ClassicalOptimizer object>)

Log-Euclidean distance to a convex hull of SPD matrices.

Log-Euclidean distance between a SPD matrix B and the convex hull of a set of SPD matrices A [1], formulated as a Constraint Programming Model (CPM) [2].

Parameters:

• A (ndarray, shape (n_matrices, n_channels, n_channels)) – Set of SPD matrices.

• B (ndarray, shape (n_channels, n_channels)) – SPD matrix.

• optimizer (pyQiskitOptimizer, default=ClassicalOptimizer()) – An instance of pyriemann_qiskit.optimization.docplex.pyQiskitOptimizer.

Returns:

distance – Log-Euclidean distance between the SPD matrix B and the convex hull of the set of SPD matrices A, defined as the distance between B and the matrix of the convex hull closest to matrix B.

Return type:

float

Notes

Added in version 0.2.0.

References

[1]

K. Zhao, A. Wiliem, S. Chen, and B. C. Lovell, ‘Convex Class Model on Symmetric Positive Definite Manifolds’, Image and Vision Computing, 2019.

[2]

http://ibmdecisionoptimization.github.io/docplex-doc/cp/creating_model.html