fisher_rao_amplitude_distance#
- skfda.misc.metrics.fisher_rao_amplitude_distance(fdata1, fdata2, *, lam=0, eval_points=None, _check=True, **kwargs)[source]#
Compute the Fisher-Rao amplitude distance between two functional objects.
Let \(f_i\) and \(f_j\) be two functional observations, and let \(q_i\) and \(q_j\) be the corresponding SRSF (see
SRSF
), the Fisher-Rao amplitude distance is defined as\[d_{A}(f_i, f_j)=min_{\gamma \in \Gamma}d_{FR}(f_i \circ \gamma,f_j)\]A penalty term could be added to restrict the ammount of elasticity in the alignment used.
\[d_{\lambda}^2(f_i, f_j) =min_{\gamma \in \Gamma} \{ d_{FR}^2(f_i \circ \gamma, f_j) + \lambda \mathcal{R}(\gamma) \}\]Where \(d_{FR}\) is the Fisher-Rao distance and the penalty term is given by
\[\mathcal{R}(\gamma) = \|\sqrt{\gamma'}- 1 \|_{\mathbb{L}^2}^2\]See the [1] for a detailed explanation.
If the observations are defined in a domain different than (0,1) their domains are normalized to this interval with an affine transformation.
- Parameters:
- Returns:
Elastic distance.
- Raises:
ValueError – If the objects are not unidimensional.
- Return type:
NDArrayFloat
References