metric.py

"""!

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

@authors Andrei Novikov (pyclustering@yandex.ru)
@date 2014-2020
@copyright GNU Public License

@cond GNU_PUBLIC_LICENSE
    PyClustering is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    PyClustering is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
@endcond

"""


import numpy

from enum import IntEnum


class type_metric(IntEnum):
    """!
    @brief Enumeration of supported metrics in the module for distance calculation between two points.

    """

    
    EUCLIDEAN = 0

    
    EUCLIDEAN_SQUARE = 1

    
    MANHATTAN = 2

    
    CHEBYSHEV = 3

    
    MINKOWSKI = 4

    
    CANBERRA = 5

    
    CHI_SQUARE = 6

    
    GOWER = 7

    
    USER_DEFINED = 1000



class distance_metric:
    """!
    @brief Distance metric performs distance calculation between two points in line with encapsulated function, for
            example, euclidean distance or chebyshev distance, or even user-defined.

    @details

    Example of Euclidean distance metric:
    @code
        metric = distance_metric(type_metric.EUCLIDEAN)
        distance = metric([1.0, 2.5], [-1.2, 3.4])
    @endcode

    Example of Chebyshev distance metric:
    @code
        metric = distance_metric(type_metric.CHEBYSHEV)
        distance = metric([0.0, 0.0], [2.5, 6.0])
    @endcode

    In following example additional argument should be specified (generally, 'degree' is a optional argument that is
     equal to '2' by default) that is specific for Minkowski distance:
    @code
        metric = distance_metric(type_metric.MINKOWSKI, degree=4)
        distance = metric([4.0, 9.2, 1.0], [3.4, 2.5, 6.2])
    @endcode

    User may define its own function for distance calculation. In this case input is two points, for example, you
    want to implement your own version of Manhattan distance:
    @code
        from pyclustering.utils.metric import distance_metric, type_metric

        def my_manhattan(point1, point2):
            dimension = len(point1)
            result = 0.0
            for i in range(dimension):
                result += abs(point1[i] - point2[i]) * 0.1
            return result

        metric = distance_metric(type_metric.USER_DEFINED, func=my_manhattan)
        distance = metric([2.0, 3.0], [1.0, 3.0])
    @endcode

    """
    def __init__(self, metric_type, **kwargs):
        """!
        @brief Creates distance metric instance for calculation distance between two points.

        @param[in] metric_type (type_metric):
        @param[in] **kwargs: Arbitrary keyword arguments (available arguments: 'numpy_usage' 'func' and corresponding additional argument for
                    for specific metric types).

        <b>Keyword Args:</b><br>
            - func (callable): Callable object with two arguments (point #1 and point #2) or (object #1 and object #2) in case of numpy usage.
                                This argument is used only if metric is 'type_metric.USER_DEFINED'.
            - degree (numeric): Only for 'type_metric.MINKOWSKI' - degree of Minkowski equation.
            - max_range (array_like): Only for 'type_metric.GOWER' - max range in each dimension. 'data' can be used
                                       instead of this parameter.
            - data (array_like): Only for 'type_metric.GOWER' - input data that used for 'max_range' calculation.
                                 'max_range' can be used instead of this parameter.
            - numpy_usage (bool): If True then numpy is used for calculation (by default is False).

        """
        self.__type = metric_type
        self.__args = kwargs
        self.__func = self.__args.get('func', None)
        self.__numpy = self.__args.get('numpy_usage', False)

        self.__calculator = self.__create_distance_calculator()


    def __call__(self, point1, point2):
        """!
        @brief Calculates distance between two points.

        @param[in] point1 (list): The first point.
        @param[in] point2 (list): The second point.

        @return (double) Distance between two points.

        """
        return self.__calculator(point1, point2)


    def get_type(self):
        """!
        @brief Return type of distance metric that is used.

        @return (type_metric) Type of distance metric.

        """
        return self.__type


    def get_arguments(self):
        """!
        @brief Return additional arguments that are used by distance metric.

        @return (dict) Additional arguments.

        """
        return self.__args


    def get_function(self):
        """!
        @brief Return user-defined function for calculation distance metric.

        @return (callable): User-defined distance metric function.

        """
        return self.__func


    def enable_numpy_usage(self):
        """!
        @brief Start numpy for distance calculation.
        @details Useful in case matrices to increase performance. No effect in case of type_metric.USER_DEFINED type.

        """
        self.__numpy = True
        if self.__type != type_metric.USER_DEFINED:
            self.__calculator = self.__create_distance_calculator()


    def disable_numpy_usage(self):
        """!
        @brief Stop using numpy for distance calculation.
        @details Useful in case of big amount of small data portion when numpy call is longer than calculation itself.
                  No effect in case of type_metric.USER_DEFINED type.

        """
        self.__numpy = False
        self.__calculator = self.__create_distance_calculator()


    def __create_distance_calculator(self):
        """!
        @brief Creates distance metric calculator.

        @return (callable) Callable object of distance metric calculator.

        """
        if self.__numpy is True:
            return self.__create_distance_calculator_numpy()

        return self.__create_distance_calculator_basic()


    def __create_distance_calculator_basic(self):
        """!
        @brief Creates distance metric calculator that does not use numpy.

        @return (callable) Callable object of distance metric calculator.

        """
        if self.__type == type_metric.EUCLIDEAN:
            return euclidean_distance

        elif self.__type == type_metric.EUCLIDEAN_SQUARE:
            return euclidean_distance_square

        elif self.__type == type_metric.MANHATTAN:
            return manhattan_distance

        elif self.__type == type_metric.CHEBYSHEV:
            return chebyshev_distance

        elif self.__type == type_metric.MINKOWSKI:
            return lambda point1, point2: minkowski_distance(point1, point2, self.__args.get('degree', 2))

        elif self.__type == type_metric.CANBERRA:
            return canberra_distance

        elif self.__type == type_metric.CHI_SQUARE:
            return chi_square_distance

        elif self.__type == type_metric.GOWER:
            max_range = self.__get_gower_max_range()
            return lambda point1, point2: gower_distance(point1, point2, max_range)

        elif self.__type == type_metric.USER_DEFINED:
            return self.__func

        else:
            raise ValueError("Unknown type of metric: '%d'", self.__type)


    def __get_gower_max_range(self):
        """!
        @brief Returns max range for Gower distance using input parameters ('max_range' or 'data').

        @return (numpy.array) Max range for Gower distance.

        """
        max_range = self.__args.get('max_range', None)
        if max_range is None:
            data = self.__args.get('data', None)
            if data is None:
                raise ValueError("Gower distance requires 'data' or 'max_range' argument to construct metric.")

            max_range = numpy.max(data, axis=0) - numpy.min(data, axis=0)
            self.__args['max_range'] = max_range

        return max_range


    def __create_distance_calculator_numpy(self):
        """!
        @brief Creates distance metric calculator that uses numpy.

        @return (callable) Callable object of distance metric calculator.

        """
        if self.__type == type_metric.EUCLIDEAN:
            return euclidean_distance_numpy

        elif self.__type == type_metric.EUCLIDEAN_SQUARE:
            return euclidean_distance_square_numpy

        elif self.__type == type_metric.MANHATTAN:
            return manhattan_distance_numpy

        elif self.__type == type_metric.CHEBYSHEV:
            return chebyshev_distance_numpy

        elif self.__type == type_metric.MINKOWSKI:
            return lambda object1, object2: minkowski_distance_numpy(object1, object2, self.__args.get('degree', 2))

        elif self.__type == type_metric.CANBERRA:
            return canberra_distance_numpy

        elif self.__type == type_metric.CHI_SQUARE:
            return chi_square_distance_numpy

        elif self.__type == type_metric.GOWER:
            max_range = self.__get_gower_max_range()
            return lambda object1, object2: gower_distance_numpy(object1, object2, max_range)

        elif self.__type == type_metric.USER_DEFINED:
            return self.__func

        else:
            raise ValueError("Unknown type of metric: '%d'", self.__type)



def euclidean_distance(point1, point2):
    """!
    @brief Calculate Euclidean distance between two vectors.
    @details The Euclidean between vectors (points) a and b is calculated by following formula:

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

    Where N is a length of each vector.

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

    @return (double) Euclidean distance between two vectors.

    @see euclidean_distance_square, manhattan_distance, chebyshev_distance

    """
    distance = euclidean_distance_square(point1, point2)
    return distance ** 0.5


def euclidean_distance_numpy(object1, object2):
    """!
    @brief Calculate Euclidean distance between two objects using numpy.

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

    @return (double) Euclidean distance between two objects.

    """
    return numpy.sum(numpy.sqrt(numpy.square(object1 - object2)), axis=1).T


def euclidean_distance_square(point1, point2):
    """!
    @brief Calculate square Euclidean distance between two vectors.

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

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

    @return (double) Square Euclidean distance between two vectors.

    @see euclidean_distance, manhattan_distance, chebyshev_distance

    """
    distance = 0.0
    for i in range(len(point1)):
        distance += (point1[i] - point2[i]) ** 2.0

    return distance


def euclidean_distance_square_numpy(object1, object2):
    """!
    @brief Calculate square Euclidean distance between two objects using numpy.

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

    @return (double) Square Euclidean distance between two objects.

    """
    return numpy.sum(numpy.square(object1 - object2), axis=1).T


def manhattan_distance(point1, point2):
    """!
    @brief Calculate Manhattan distance between between two vectors.

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

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

    @return (double) Manhattan distance between two vectors.

    @see euclidean_distance_square, euclidean_distance, chebyshev_distance

    """
    distance = 0.0
    dimension = len(point1)

    for i in range(dimension):
        distance += abs(point1[i] - point2[i])

    return distance


def manhattan_distance_numpy(object1, object2):
    """!
    @brief Calculate Manhattan distance between two objects using numpy.

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

    @return (double) Manhattan distance between two objects.

    """
    return numpy.sum(numpy.absolute(object1 - object2), axis=1).T


def chebyshev_distance(point1, point2):
    """!
    @brief Calculate Chebyshev distance (maximum metric) between between two vectors.
    @details 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.

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

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

    @return (double) Chebyshev distance between two vectors.

    @see euclidean_distance_square, euclidean_distance, minkowski_distance

    """
    distance = 0.0
    dimension = len(point1)

    for i in range(dimension):
        distance = max(distance, abs(point1[i] - point2[i]))

    return distance


def chebyshev_distance_numpy(object1, object2):
    """!
    @brief Calculate Chebyshev distance between two objects using numpy.

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

    @return (double) Chebyshev distance between two objects.

    """
    return numpy.max(numpy.absolute(object1 - object2), axis=1).T


def minkowski_distance(point1, point2, degree=2):
    """!
    @brief Calculate Minkowski distance between two vectors.

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

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

    @return (double) Minkowski distance between two vectors.

    @see euclidean_distance

    """
    distance = 0.0
    for i in range(len(point1)):
        distance += (point1[i] - point2[i]) ** degree

    return distance ** (1.0 / degree)


def minkowski_distance_numpy(object1, object2, degree=2):
    """!
    @brief Calculate Minkowski distance between objects using numpy.

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

    @return (double) Minkowski distance between two object.

    """
    return numpy.sum(numpy.power(numpy.power(object1 - object2, degree), 1/degree), axis=1).T


def canberra_distance(point1, point2):
    """!
    @brief Calculate Canberra distance between two vectors.

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

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

    @return (float) Canberra distance between two objects.

    """
    distance = 0.0
    for i in range(len(point1)):
        divider = abs(point1[i]) + abs(point2[i])
        if divider == 0.0:
            continue

        distance += abs(point1[i] - point2[i]) / divider

    return distance


def canberra_distance_numpy(object1, object2):
    """!
    @brief Calculate Canberra distance between two objects using numpy.

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

    @return (float) Canberra distance between two objects.

    """
    with numpy.errstate(divide='ignore', invalid='ignore'):
        result = numpy.divide(numpy.abs(object1 - object2), numpy.abs(object1) + numpy.abs(object2))

    if len(result.shape) > 1:
        return numpy.sum(numpy.nan_to_num(result), axis=1).T
    else:
        return numpy.sum(numpy.nan_to_num(result))


def chi_square_distance(point1, point2):
    """!
    @brief Calculate Chi square distance between two vectors.

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

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

    @return (float) Chi square distance between two objects.

    """
    distance = 0.0
    for i in range(len(point1)):
        divider = abs(point1[i]) + abs(point2[i])
        if divider != 0.0:
            distance += ((point1[i] - point2[i]) ** 2.0) / divider

    return distance


def chi_square_distance_numpy(object1, object2):
    """!
    @brief Calculate Chi square distance between two vectors using numpy.

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

    @return (float) Chi square distance between two objects.

    """
    with numpy.errstate(divide='ignore', invalid='ignore'):
        result = numpy.divide(numpy.power(object1 - object2, 2), numpy.abs(object1) + numpy.abs(object2))

    if len(result.shape) > 1:
        return numpy.sum(numpy.nan_to_num(result), axis=1).T
    else:
        return numpy.sum(numpy.nan_to_num(result))


def gower_distance(point1, point2, max_range):
    """!
    @brief Calculate Gower distance between two vectors.
    @details Implementation is based on the paper @cite article::utils::metric::gower. Gower distance is calculate
              using following formula:
    \f[
    dist\left ( a, b \right )=\frac{1}{p}\sum_{i=0}^{p}\frac{\left | a_{i} - b_{i} \right |}{R_{i}},
    \f]

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

    \f[
    R=max\left ( X \right )-min\left ( X \right )
    \f]

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

    @return (float) Gower distance between two objects.

    """
    distance = 0.0
    dimensions = len(point1)
    for i in range(dimensions):
        if max_range[i] != 0.0:
            distance += abs(point1[i] - point2[i]) / max_range[i]

    return distance / dimensions


def gower_distance_numpy(point1, point2, max_range):
    """!
    @brief Calculate Gower distance between two vectors using numpy.

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

    @return (float) Gower distance between two objects.

    """
    with numpy.errstate(divide='ignore', invalid='ignore'):
        result = numpy.divide(numpy.abs(point1 - point2), max_range)

    if len(result.shape) > 1:
        return numpy.sum(numpy.nan_to_num(result), axis=1).T / len(point1)
    else:
        return numpy.sum(numpy.nan_to_num(result)) / len(point1)