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
sum(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:

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
“maching” 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.