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).Examples
>>> from sklearn.neighbors import DistanceMetric >>> 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
(N  NTT) / 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 propertiesNonnegativity: 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
Convert the true distance to the reduced distance.
Get the given distance metric from the string identifier.
Compute the pairwise distances between X and Y
Convert the Reduced distance to the true distance.

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
 metricstring 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
 Xarraylike
Array of shape (Nx, D), representing Nx points in D dimensions.
 Yarraylike (optional)
Array of shape (Ny, D), representing Ny points in D dimensions. If not specified, then Y=X.
 Returns
 ——
 distndarray
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.