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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 (maximum metric) 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... | |
Module provides various distance metrics - abstraction of the notion of distance in a metric space.
| def pyclustering.utils.metric.canberra_distance | ( | point1, | |
| point2 | |||
| ) |
| def pyclustering.utils.metric.canberra_distance_numpy | ( | object1, | |
| object2 | |||
| ) |
| def pyclustering.utils.metric.chebyshev_distance | ( | point1, | |
| point2 | |||
| ) |
Calculate Chebyshev distance (maximum metric) between between two vectors.
Chebyshev distance is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.
![\[ dist(a, b) = \max_{}i\left (\left | a_{i} - b_{i} \right |\right ); \]](../../form_39.png)
| [in] | point1 | (array_like): The first vector. |
| [in] | point2 | (array_like): The second vector. |
| def pyclustering.utils.metric.chebyshev_distance_numpy | ( | object1, | |
| object2 | |||
| ) |
| def pyclustering.utils.metric.chi_square_distance | ( | point1, | |
| point2 | |||
| ) |
| def pyclustering.utils.metric.chi_square_distance_numpy | ( | object1, | |
| object2 | |||
| ) |
| 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:
![\[ dist(a, b) = \sqrt{ \sum_{i=0}^{N}(a_{i} - b_{i})^{2} }; \]](../../form_36.png)
Where N is a length of each vector.
| [in] | point1 | (array_like): The first vector. |
| [in] | point2 | (array_like): The second vector. |
| def pyclustering.utils.metric.euclidean_distance_numpy | ( | object1, | |
| object2 | |||
| ) |
| def pyclustering.utils.metric.euclidean_distance_square | ( | point1, | |
| point2 | |||
| ) |
Calculate square Euclidean distance between two vectors.
![\[ dist(a, b) = \sum_{i=0}^{N}(a_{i} - b_{i})^{2}; \]](../../form_37.png)
| [in] | point1 | (array_like): The first vector. |
| [in] | point2 | (array_like): The second vector. |
Definition at line 349 of file metric.py.
Referenced by pyclustering.utils.metric.euclidean_distance().
| def pyclustering.utils.metric.euclidean_distance_square_numpy | ( | object1, | |
| object2 | |||
| ) |
| 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:
![\[ dist\left ( a, b \right )=\frac{1}{p}\sum_{i=0}^{p}\frac{\left | a_{i} - b_{i} \right |}{R_{i}}, \]](../../form_43.png)
where 
is a max range for ith dimension. 
is defined in line following formula:
![\[ R=max\left ( X \right )-min\left ( X \right ) \]](../../form_46.png)
| [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. |
Definition at line 587 of file metric.py.
Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().
| def pyclustering.utils.metric.gower_distance_numpy | ( | point1, | |
| point2, | |||
| max_range | |||
| ) |
Calculate Gower distance between two vectors using numpy.
| [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. |
Definition at line 618 of file metric.py.
Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().
| def pyclustering.utils.metric.manhattan_distance | ( | point1, | |
| point2 | |||
| ) |
Calculate Manhattan distance between between two vectors.
![\[ dist(a, b) = \sum_{i=0}^{N}\left | a_{i} - b_{i} \right |; \]](../../form_38.png)
| [in] | point1 | (array_like): The first vector. |
| [in] | point2 | (array_like): The second vector. |
| def pyclustering.utils.metric.manhattan_distance_numpy | ( | object1, | |
| object2 | |||
| ) |
| def pyclustering.utils.metric.minkowski_distance | ( | point1, | |
| point2, | |||
degree = 2 |
|||
| ) |
Calculate Minkowski distance between two vectors.
![\[ dist(a, b) = \sqrt[p]{ \sum_{i=0}^{N}\left(a_{i} - b_{i}\right)^{p} }; \]](../../form_40.png)
| [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. |
Definition at line 463 of file metric.py.
Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().
| def pyclustering.utils.metric.minkowski_distance_numpy | ( | object1, | |
| object2, | |||
degree = 2 |
|||
| ) |
Calculate Minkowski distance between objects using numpy.
| [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. |
Definition at line 487 of file metric.py.
Referenced by pyclustering.utils.metric.distance_metric.disable_numpy_usage().
1.8.13 ![\[ dist(a, b) = \sum_{i=0}^{N}\frac{\left | a_{i} - b_{i} \right |}{\left | a_{i} \right | + \left | b_{i} \right |}; \]](../../form_41.png)
![\[ dist(a, b) = \sum_{i=0}^{N}\frac{\left ( a_{i} - b_{i} \right )^{2}}{\left | a_{i} \right | + \left | b_{i} \right |}; \]](../../form_42.png)