# 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 Get the given distance metric from the string identifier.
get_metric()

Get the given distance metric from the string identifier.

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

Parameters:
metricstr 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_objinstance of the requested metric

An instance of the requested distance metric class.