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
- Non-negativity: 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__()¶
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.
- static 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.