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 realvalued 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 twodimensional 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 integervalued vector spaces: Though intended for integervalued vectors, these are also valid metrics in the case of realvalued 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 booleanvalued 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 nonequal 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) Userdefined distance:
identifier class name args “pyfunc” PyFuncDistance func Here
func
is a function which takes two onedimensional 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 Nonnegativity: d(x, y) >= 0
 Identity: d(x, y) = 0 if and only if x == y
 Symmetry: d(x, y) = d(y, x)
 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__
(self, /, *args, **kwargs)¶ Initialize self. See help(type(self)) for accurate signature.

dist_to_rdist
()¶ Convert the true distance to the reduced distance.
The reduced distance, defined for some metrics, is a computationally more efficient measure which preserves the rank of the true distance. For example, in the Euclidean distance metric, the reduced distance is the squaredeuclidean 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 efficient measure which preserves the rank of the true distance. For example, in the Euclidean distance metric, the reduced distance is the squaredeuclidean distance.