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scikit-learn 1.3.2
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# `sklearn.metrics`.DistanceMetric

class sklearn.metrics.DistanceMetric

  Uniform interface for fast distance metric functions.

  The `DistanceMetric` class provides a convenient way to compute pairwise distances between samples. It supports various distance metrics, such as Euclidean distance, Manhattan distance, and more.

  The `pairwise` method can be used to compute pairwise distances between samples in the input arrays. It returns a distance matrix representing the distances between all pairs of samples.

  The `get_metric` method allows you to retrieve a specific metric using its string identifier.

  Examples

      >>> from sklearn.metrics import DistanceMetric
      >>> dist = DistanceMetric.get_metric('euclidean')
      >>> X = [[1, 2], [3, 4], [5, 6]]
      >>> Y = [[7, 8], [9, 10]]
      >>> dist.pairwise(X,Y)
      array([[7.81..., 10.63...]
             [5.65...,  8.48...]
             [1.41...,  4.24...]])

  Available Metrics

  The following lists the string metric identifiers and the associated distance metric classes:

  Metrics intended for real-valued vector spaces:

  identifier | class name | args | distance function
  “euclidean” | EuclideanDistance |  | `sqrt(sum((x - y)^2))`
  “manhattan” | ManhattanDistance |  | `sum(|x - y|)`
  “chebyshev” | ChebyshevDistance |  | `max(|x - y|)`
  “minkowski” | MinkowskiDistance | p, w | `sum(w * |x - y|^p)^(1/p)`
  “seuclidean” | SEuclideanDistance | V | `sqrt(sum((x - y)^2 / V))`
  “mahalanobis” | MahalanobisDistance | V or VI | `sqrt((x - y)' V^-1 (x - y))`

  Metrics intended for two-dimensional vector spaces: Note that the haversine distance metric requires data in the form of [latitude, longitude] and both inputs and outputs are in units of radians.

  identifier | class name | distance function
  “haversine” | HaversineDistance | `2 arcsin(sqrt(sin^2(0.5*dx) + cos(x1)cos(x2)sin^2(0.5*dy)))`

  Metrics intended for integer-valued vector spaces: Though intended for integer-valued vectors, these are also valid metrics in the case of real-valued vectors.

  identifier | class name | distance function
  “hamming” | HammingDistance | `N_unequal(x, y) / N_tot`
  “canberra” | CanberraDistance | `sum(|x - y| / (|x| + |y|))`
  “braycurtis” | BrayCurtisDistance | `sum(|x - y|) / (sum(|x|) + sum(|y|))`

  Metrics intended for boolean-valued vector spaces: Any nonzero entry is evaluated to “True”. In the listings below, the following abbreviations are used:

  > - N : number of dimensions

  > - NTT : number of dims in which both values are True

  > - NTF : number of dims in which the first value is True, second is False

  > - NFT : number of dims in which the first value is False, second is True

  > - NFF : number of dims in which both values are False

  > - NNEQ : number of non-equal dimensions, NNEQ = NTF + NFT

  > - NNZ : number of nonzero dimensions, NNZ = NTF + NFT + NTT

  identifier | class name | distance function
  “jaccard” | JaccardDistance | NNEQ / NNZ
  “matching” | MatchingDistance | NNEQ / N
  “dice” | DiceDistance | NNEQ / (NTT + NNZ)
  “kulsinski” | KulsinskiDistance | (NNEQ + N - NTT) / (NNEQ + N)
  “rogerstanimoto” | RogersTanimotoDistance | 2 * NNEQ / (N + NNEQ)
  “russellrao” | RussellRaoDistance | (N - NTT) / N
  “sokalmichener” | SokalMichenerDistance | 2 * NNEQ / (N + NNEQ)
  “sokalsneath” | SokalSneathDistance | NNEQ / (NNEQ + 0.5 * NTT)

  User-defined distance:

  identifier | class name | args
  “pyfunc” | PyFuncDistance | func

  Here `func` is a function which takes two one-dimensional numpy arrays, and returns a distance. Note that in order to be used within the BallTree, the distance must be a true metric: i.e. it must satisfy the following properties

  1. Non-negativity: d(x, y) >= 0

  2. Identity: d(x, y) = 0 if and only if x == y

  3. Symmetry: d(x, y) = d(y, x)

  4. Triangle Inequality: d(x, y) + d(y, z) >= d(x, z)

  Because of the Python object overhead involved in calling the python function, this will be fairly slow, but it will have the same scaling as other distances.

  Methods

  `get_metric`(metric[, dtype]) | Get the given distance metric from the string identifier.

  classmethod get_metric(metric, dtype=<class 'numpy.float64'>, **kwargs)

    Get the given distance metric from the string identifier.

    See the docstring of DistanceMetric for a list of available metrics.

    Parameters:
      metric str or class name

        The string identifier or class name of the desired distance metric. See the documentation of the `DistanceMetric` class for a list of available metrics.

      dtype{np.float32, np.float64}, default=np.float64

        The data type of the input on which the metric will be applied. This affects the precision of the computed distances. By default, it is set to `np.float64`.

      **kwargs

        Additional keyword arguments that will be passed to the requested metric. These arguments can be used to customize the behavior of the specific metric.

    Returns:
      metric_obj instance of the requested metric

        An instance of the requested distance metric class.