Module provides various distance metrics - abstraction of the notion of distance in a metric space. More...

Classes
class	distance_metric
	Distance metric performs distance calculation between two points in line with encapsulated function, for example, euclidean distance or chebyshev distance, or even user-defined. More...

class	type_metric
	Enumeration of supported metrics in the module for distance calculation between two points. More...

Functions
def	euclidean_distance (point1, point2)
	Calculate Euclidean distance between two vectors. More...

def	euclidean_distance_numpy (object1, object2)
	Calculate Euclidean distance between two objects using numpy. More...

def	euclidean_distance_square (point1, point2)
	Calculate square Euclidean distance between two vectors. More...

def	euclidean_distance_square_numpy (object1, object2)
	Calculate square Euclidean distance between two objects using numpy. More...

def	manhattan_distance (point1, point2)
	Calculate Manhattan distance between between two vectors. More...

def	manhattan_distance_numpy (object1, object2)
	Calculate Manhattan distance between two objects using numpy. More...

def	chebyshev_distance (point1, point2)
	Calculate Chebyshev distance between between two vectors. More...

def	chebyshev_distance_numpy (object1, object2)
	Calculate Chebyshev distance between two objects using numpy. More...

def	minkowski_distance (point1, point2, degree=2)
	Calculate Minkowski distance between two vectors. More...

def	minkowski_distance_numpy (object1, object2, degree=2)
	Calculate Minkowski distance between objects using numpy. More...

def	canberra_distance (point1, point2)
	Calculate Canberra distance between two vectors. More...

def	canberra_distance_numpy (object1, object2)
	Calculate Canberra distance between two objects using numpy. More...

def	chi_square_distance (point1, point2)
	Calculate Chi square distance between two vectors. More...

def	chi_square_distance_numpy (object1, object2)
	Calculate Chi square distance between two vectors using numpy. More...

def	gower_distance (point1, point2, max_range)
	Calculate Gower distance between two vectors. More...

def	gower_distance_numpy (point1, point2, max_range)
	Calculate Gower distance between two vectors using numpy. More...

Detailed Description

Module provides various distance metrics - abstraction of the notion of distance in a metric space.

Authors: Andrei Novikov (pyclu.nosp@m.ster.nosp@m.ing@y.nosp@m.ande.nosp@m.x.ru)

Date: 2014-2019

Copyright: GNU Public License

Function Documentation

◆ canberra_distance()

def pyclustering.utils.metric.canberra_distance	(	point1,
		point2
	)

Calculate Canberra distance between two vectors.

$dist(a, b) = \sum_{i=0}^{N}\frac{\left | a_{i} - b_{i} \right |}{\left | a_{i} \right | + \left | b_{i} \right |};$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (float) Canberra distance between two objects.

Definition at line 499 of file metric.py.

◆ canberra_distance_numpy()

def pyclustering.utils.metric.canberra_distance_numpy	(	object1,
		object2
	)

Calculate Canberra distance between two objects using numpy.

Parameters

[in]	object1	(array_like): The first vector.
[in]	object2	(array_like): The second vector.

Returns: (float) Canberra distance between two objects.

Definition at line 524 of file metric.py.

◆ chebyshev_distance()

def pyclustering.utils.metric.chebyshev_distance	(	point1,
		point2
	)

Calculate Chebyshev distance between between two vectors.

$dist(a, b) = \max_{}i\left (\left | a_{i} - b_{i} \right |\right );$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (double) Chebyshev distance between two vectors.

See also: euclidean_distance_square, euclidean_distance, minkowski_distance

Definition at line 423 of file metric.py.

◆ chebyshev_distance_numpy()

def pyclustering.utils.metric.chebyshev_distance_numpy	(	object1,
		object2
	)

Calculate Chebyshev distance between two objects using numpy.

Parameters

[in]	object1	(array_like): The first array_like object.
[in]	object2	(array_like): The second array_like object.

Returns: (double) Chebyshev distance between two objects.

Definition at line 448 of file metric.py.

◆ chi_square_distance()

def pyclustering.utils.metric.chi_square_distance	(	point1,
		point2
	)

Calculate Chi square distance between two vectors.

$dist(a, b) = \sum_{i=0}^{N}\frac{\left ( a_{i} - b_{i} \right )^{2}}{\left | a_{i} \right | + \left | b_{i} \right |};$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (float) Chi square distance between two objects.

Definition at line 543 of file metric.py.

◆ chi_square_distance_numpy()

def pyclustering.utils.metric.chi_square_distance_numpy	(	object1,
		object2
	)

Calculate Chi square distance between two vectors using numpy.

Parameters

[in]	object1	(array_like): The first vector.
[in]	object2	(array_like): The second vector.

Returns: (float) Chi square distance between two objects.

Definition at line 566 of file metric.py.

◆ euclidean_distance()

def pyclustering.utils.metric.euclidean_distance	(	point1,
		point2
	)

Calculate Euclidean distance between two vectors.

The Euclidean between vectors (points) a and b is calculated by following formula:

$dist(a, b) = \sqrt{ \sum_{i=0}^{N}(a_{i} - b_{i})^{2} };$

Where N is a length of each vector.

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (double) Euclidean distance between two vectors.

See also: euclidean_distance_square, manhattan_distance, chebyshev_distance

Definition at line 313 of file metric.py.

◆ euclidean_distance_numpy()

def pyclustering.utils.metric.euclidean_distance_numpy	(	object1,
		object2
	)

Calculate Euclidean distance between two objects using numpy.

Parameters

[in]	object1	(array_like): The first array_like object.
[in]	object2	(array_like): The second array_like object.

Returns: (double) Euclidean distance between two objects.

Definition at line 336 of file metric.py.

◆ euclidean_distance_square()

def pyclustering.utils.metric.euclidean_distance_square	(	point1,
		point2
	)

Calculate square Euclidean distance between two vectors.

$dist(a, b) = \sum_{i=0}^{N}(a_{i} - b_{i})^{2};$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (double) Square Euclidean distance between two vectors.

See also: euclidean_distance, manhattan_distance, chebyshev_distance

Definition at line 349 of file metric.py.

Referenced by pyclustering.utils.metric.euclidean_distance().

◆ euclidean_distance_square_numpy()

def pyclustering.utils.metric.euclidean_distance_square_numpy	(	object1,
		object2
	)

Calculate square Euclidean distance between two objects using numpy.

Parameters

[in]	object1	(array_like): The first array_like object.
[in]	object2	(array_like): The second array_like object.

Returns: (double) Square Euclidean distance between two objects.

Definition at line 372 of file metric.py.

◆ gower_distance()

def pyclustering.utils.metric.gower_distance	(	point1,
		point2,
		max_range
	)

Calculate Gower distance between two vectors.

Implementation is based on the paper [13]. Gower distance is calculate using following formula:

$dist\left ( a, b \right )=\frac{1}{p}\sum_{i=0}^{p}\frac{\left | a_{i} - b_{i} \right |}{R_{i}},$

where $R_{i}$ is a max range for ith dimension. $R$ is defined in line following formula:

$R=max\left ( X \right )-min\left ( X \right )$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.
[in]	max_range	(array_like): Max range in each data dimension.

Returns: (float) Gower distance between two objects.

Definition at line 585 of file metric.py.

Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().

◆ gower_distance_numpy()

def pyclustering.utils.metric.gower_distance_numpy	(	point1,
		point2,
		max_range
	)

Calculate Gower distance between two vectors using numpy.

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.
[in]	max_range	(array_like): Max range in each data dimension.

Returns: (float) Gower distance between two objects.

Definition at line 616 of file metric.py.

Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().

◆ manhattan_distance()

def pyclustering.utils.metric.manhattan_distance	(	point1,
		point2
	)

Calculate Manhattan distance between between two vectors.

$dist(a, b) = \sum_{i=0}^{N}\left | a_{i} - b_{i} \right |;$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.

Returns: (double) Manhattan distance between two vectors.

See also: euclidean_distance_square, euclidean_distance, chebyshev_distance

Definition at line 385 of file metric.py.

◆ manhattan_distance_numpy()

def pyclustering.utils.metric.manhattan_distance_numpy	(	object1,
		object2
	)

Calculate Manhattan distance between two objects using numpy.

Parameters

[in]	object1	(array_like): The first array_like object.
[in]	object2	(array_like): The second array_like object.

Returns: (double) Manhattan distance between two objects.

Definition at line 410 of file metric.py.

◆ minkowski_distance()

def pyclustering.utils.metric.minkowski_distance	(	point1,
		point2,
		degree = `2`
	)

Calculate Minkowski distance between two vectors.

$dist(a, b) = \sqrt[p]{ \sum_{i=0}^{N}\left(a_{i} - b_{i}\right)^{p} };$

Parameters

[in]	point1	(array_like): The first vector.
[in]	point2	(array_like): The second vector.
[in]	degree	(numeric): Degree of that is used for Minkowski distance.

Returns: (double) Minkowski distance between two vectors.

See also: euclidean_distance

Definition at line 461 of file metric.py.

Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().

◆ minkowski_distance_numpy()

def pyclustering.utils.metric.minkowski_distance_numpy	(	object1,
		object2,
		degree = `2`
	)

Calculate Minkowski distance between objects using numpy.

Parameters

[in]	object1	(array_like): The first array_like object.
[in]	object2	(array_like): The second array_like object.
[in]	degree	(numeric): Degree of that is used for Minkowski distance.

Returns: (double) Minkowski distance between two object.

Definition at line 485 of file metric.py.

Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().

Classes

Functions

Detailed Description

Function Documentation

◆ canberra_distance()

◆ canberra_distance_numpy()

◆ chebyshev_distance()

◆ chebyshev_distance_numpy()

◆ chi_square_distance()

◆ chi_square_distance_numpy()

◆ euclidean_distance()

◆ euclidean_distance_numpy()

◆ euclidean_distance_square()

◆ euclidean_distance_square_numpy()

◆ gower_distance()

◆ gower_distance_numpy()

◆ manhattan_distance()

◆ manhattan_distance_numpy()

◆ minkowski_distance()

◆ minkowski_distance_numpy()