sklearn.metrics
.DistanceMetric¶
- class sklearn.metrics.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.metrics 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 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, w
sum(w * |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))
Deprecated since version 1.1:
WMinkowskiDistance
is deprecated in version 1.1 and will be removed in version 1.3. UseMinkowskiDistance
instead. Note that inMinkowskiDistance
, the weights are applied to the absolute differences already raised to the p power. This is different fromWMinkowskiDistance
where weights are applied to the absolute differences before raising to the p power. The deprecation aims to remain consistent with SciPy 1.8 convention.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
(N - NTT) / 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 propertiesNon-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
Convert the true distance to the rank-preserving surrogate distance.
Get the given distance metric from the string identifier.
Compute the pairwise distances between X and Y
Convert the rank-preserving surrogate distance to the distance.
- dist_to_rdist()¶
Convert the true distance to the rank-preserving surrogate distance.
The surrogate distance is any measure that yields the same rank as the distance, but is more efficient to compute. For example, the rank-preserving surrogate distance of the Euclidean metric is the squared-euclidean distance.
- Parameters
- distdouble
True distance.
- Returns
- double
Surrogate distance.
- get_metric()¶
Get the given distance metric from the string identifier.
See the docstring of DistanceMetric for a list of available metrics.
- Parameters
- metricstr 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
- Xarray-like
Array of shape (Nx, D), representing Nx points in D dimensions.
- Yarray-like (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 rank-preserving surrogate distance to the distance.
The surrogate distance is any measure that yields the same rank as the distance, but is more efficient to compute. For example, the rank-preserving surrogate distance of the Euclidean metric is the squared-euclidean distance.
- Parameters
- rdistdouble
Surrogate distance.
- Returns
- double
True distance.