# `sklearn.neighbors`.DistanceMetric¶

class `sklearn.neighbors.``DistanceMetric`

DistanceMetric class

This class provides a uniform interface to fast distance metric functions. The various metrics can be accessed via the get_metric class method and the metric string identifier (see below). For example, to use the Euclidean distance:

```>>> dist = DistanceMetric.get_metric('euclidean')
>>> X = [[0, 1, 2],
[3, 4, 5]])
>>> dist.pairwise(X)
array([[ 0.        ,  5.19615242],
[ 5.19615242,  0.        ]])
```

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 `sum(|x - y|^p)^(1/p)` “wminkowski” WMinkowskiDistance 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 NNZ / 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

 `dist_to_rdist` Convert the true distance to the reduced distance. `get_metric` Get the given distance metric from the string identifier. `pairwise` Compute the pairwise distances between X and Y `rdist_to_dist` Convert the Reduced distance to the true distance.
`__init__`()

x.__init__(...) initializes x; see help(type(x)) for signature

`dist_to_rdist`()

Convert the true distance to the reduced distance.

The reduced distance, defined for some metrics, is a computationally more efficent measure which preserves the rank of the true distance. For example, in the Euclidean distance metric, the reduced distance is the squared-euclidean distance.

`get_metric`()

Get the given distance metric from the string identifier.

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

Parameters: metric : string or class name The distance metric to use **kwargs : additional arguments will be passed to the requested metric
`pairwise`()

Compute the pairwise distances between X and Y

This is a convenience routine for the sake of testing. For many metrics, the utilities in scipy.spatial.distance.cdist and scipy.spatial.distance.pdist will be faster.

Parameters: X : array_like Array of shape (Nx, D), representing Nx points in D dimensions. Y : array_like (optional) Array of shape (Ny, D), representing Ny points in D dimensions. If not specified, then Y=X. Returns : ——- : dist : ndarray The shape (Nx, Ny) array of pairwise distances between points in X and Y.
`rdist_to_dist`()

Convert the Reduced distance to the true distance.

The reduced distance, defined for some metrics, is a computationally more efficent measure which preserves the rank of the true distance. For example, in the Euclidean distance metric, the reduced distance is the squared-euclidean distance.