The key idea to generalize MLR to a Riemannian manifold is to change the margin to reflect the geometry of the considered manifold.
This requires the notions of hyperplanes and margin in the considered manifold that are referred to as hypergyroplanes and pseudo-gyrodistances.
The definition of hypergyroplanes in structure spaces, suggested by Proposition 3.2, can be given below.
The algorithm for computing the pseudo-gyrodistances is provided, demonstrating the contributions of the authors to this complex topic.
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