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Fermat distance documentation

class Fermat

init(self, alpha, path_method='L', k=None, landmarks=None, estimator='up', seed=None)

Parameters

  • alpha: float Parameter of the Fermat distance.

  • path_method: string ['FW','D','L']

    Options are:

    • 'FW': Computes the exact Fermat distance using the Floyd-Warshall algorithm.

    • 'D': Computes an approximation of the Fermat distance using k nearest neighbours and the Dijkstra algorithm.

    • 'L': Computes an approximation of the Fermat distance using landmarks and k-nn.

  • k: integer, optional Number of nearest neighbors to be considered. Incompatible with path_method == 'FW'

  • landmarks: integer, optional Number of landmarks considered in the Fermat distance computation. Only available when path_method = 'L'

  • estimator: string ['up', 'down', 'mean', 'no_lca'] (default: 'up')

    When computing an approximation of the Fermat distance, there are lower and upper bounds of the true value.

    • If estimator == 'no_lca', the distance for a pair of points is calculated as the minimum sum of the distance from both points to one of the landmarks.
    • If estimator == 'up', the distance for a pair of points is calculated as the minimum sum of the distance from both points to the lowest common ancestor in the distance tree of one of the landmarks.
    • If estimator == 'down', the distance for a pair of points is calculated as the maximum difference of thedistance from both points to one of the landmarks.
    • If estimator == 'mean', the mean between 'up' and 'down' estimators.

    Only available when path_method = 'L'

  • seed: int, optional Only available when path_method = 'L'

Methods

  • fit(X)

    • Parameters
      • X: input distances matrix
    • Return
      • self

  • get_distance(a, b)

    • Parameters
      • a: int, index of the first data point
      • b: int, index of the second data point
    • Return
      • float, the Fermat distance between poins a and b

  • get_distances()

    • Parameters
      • None
    • Return
      • np.matrix, Fermat distance between all pairs of points

Example of use