For quadratic truncation, the minimal number of segments needed to recover a path from the barycenter of signature matrices is min(d, total segments) if all segment counts are even, and min(d, total segments minus the number of odd counts plus one) otherwise.
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Learning Barycenters from Signature Matrices
For quadratic truncation, the minimal number of segments needed to recover a path from the barycenter of signature matrices is min(d, total segments) if all segment counts are even, and min(d, total segments minus the number of odd counts plus one) otherwise.