center_initializer.py

"""!

@brief Collection of center initializers for algorithm that uses initial centers, for example, for K-Means or X-Means.
@details Implementation based on paper @cite article::kmeans++::1.
         
@authors Andrei Novikov, Aleksey Kukushkin (pyclustering@yandex.ru)
@date 2014-2019
@copyright GNU Public License

@see pyclustering.cluster.kmeans
@see puclustering.cluster.xmeans

@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
import random
import warnings


class random_center_initializer:
    """!
    @brief Random center initializer is for generation specified amount of random of centers for specified data.
    
    """

    def __init__(self, data, amount_centers):
        """!
        @brief Creates instance of random center initializer.
        
        @param[in] data (list): List of points where each point is represented by list of coordinates.
        @param[in] amount_centers (unit): Amount of centers that should be initialized.
        
        """
        
        self.__data = data
        self.__amount = amount_centers
        self.__available_indexes = set(list(range(len(self.__data))))

        if self.__amount <= 0:
            raise ValueError("Amount of cluster centers should be at least 1.")

        if self.__amount > len(self.__data):
            raise ValueError("Amount of cluster centers '%d' should be less than data size." % self.__amount)


    def initialize(self, **kwargs):
        """!
        @brief Generates random centers in line with input parameters.

        @param[in] **kwargs: Arbitrary keyword arguments (available arguments: 'return_index').

        <b>Keyword Args:</b><br>
            - return_index (bool): If True then returns indexes of points from input data instead of points itself.

        @return (list) List of initialized initial centers.
                  If argument 'return_index' is False then returns list of points.
                  If argument 'return_index' is True then returns list of indexes.
        
        """
        return_index = kwargs.get('return_index', False)
        if self.__amount == len(self.__data):
            if return_index:
                return list(range(len(self.__data)))
            return self.__data[:]

        return [self.__create_center(return_index) for _ in range(self.__amount)]


    def __create_center(self, return_index):
        """!
        @brief Generates and returns random center.

        @param[in] return_index (bool): If True then returns index of point from input data instead of point itself.
        
        """
        random_index_point = random.randint(0, len(self.__data[0]))
        if random_index_point not in self.__available_indexes:
            random_index_point = self.__available_indexes.pop()
        else:
            self.__available_indexes.remove(random_index_point)

        if return_index:
            return random_index_point
        return self.__data[random_index_point]



class kmeans_plusplus_initializer:
    """!
    @brief K-Means++ is an algorithm for choosing the initial centers for algorithms like K-Means or X-Means.
    @details K-Means++ algorithm guarantees an approximation ratio O(log k). Clustering results are depends on
              initial centers in case of K-Means algorithm and even in case of X-Means. This method is used to find
              out optimal initial centers.

    Algorithm can be divided into three steps. The first center is chosen from input data randomly with
    uniform distribution at the first step. At the second, probability to being center is calculated for each point:
    \f[p_{i}=\frac{D(x_{i})}{\sum_{j=0}^{N}D(x_{j})}\f]
    where \f$D(x_{i})\f$ is a distance from point \f$i\f$ to the closest center. Using this probabilities next center
    is chosen. The last step is repeated until required amount of centers is initialized.

    Pyclustering implementation of the algorithm provides feature to consider several candidates on the second
    step, for example:

    @code
        amount_centers = 4;
        amount_candidates = 3;
        initializer = kmeans_plusplus_initializer(sample, amount_centers, amount_candidates);
    @endcode

    If the farthest points should be used as centers then special constant 'FARTHEST_CENTER_CANDIDATE' should be used
    for that purpose, for example:
    @code
        amount_centers = 4;
        amount_candidates = kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE;
        initializer = kmeans_plusplus_initializer(sample, amount_centers, amount_candidates);
    @endcode

    There is an example of initial centers that were calculated by the K-Means++ method:

    @image html kmeans_plusplus_initializer_results.png
    
    Code example where initial centers are prepared for K-Means algorithm:
    @code
        from pyclustering.cluster.center_initializer import kmeans_plusplus_initializer
        from pyclustering.cluster.kmeans import kmeans
        from pyclustering.cluster import cluster_visualizer
        from pyclustering.utils import read_sample
        from pyclustering.samples.definitions import SIMPLE_SAMPLES

        # Read data 'SampleSimple3' from Simple Sample collection.
        sample = read_sample(SIMPLE_SAMPLES.SAMPLE_SIMPLE3)

        # Calculate initial centers using K-Means++ method.
        centers = kmeans_plusplus_initializer(sample, 4, kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE).initialize()

        # Display initial centers.
        visualizer = cluster_visualizer()
        visualizer.append_cluster(sample)
        visualizer.append_cluster(centers, marker='*', markersize=10)
        visualizer.show()

        # Perform cluster analysis using K-Means algorithm with initial centers.
        kmeans_instance = kmeans(sample, centers)

        # Run clustering process and obtain result.
        kmeans_instance.process()
        clusters = kmeans_instance.get_clusters()
    @endcode
    
    """


    
    FARTHEST_CENTER_CANDIDATE = "farthest"


    def __init__(self, data, amount_centers, amount_candidates=None):
        """!
        @brief Creates K-Means++ center initializer instance.
        
        @param[in] data (array_like): List of points where each point is represented by list of coordinates.
        @param[in] amount_centers (uint): Amount of centers that should be initialized.
        @param[in] amount_candidates (uint): Amount of candidates that is considered as a center, if the farthest points
                    (with the highest probability) should be considered as centers then special constant should be used
                    'FARTHEST_CENTER_CANDIDATE'.

        @see FARTHEST_CENTER_CANDIDATE

        """
        
        self.__data = numpy.array(data)
        self.__amount = amount_centers
        self.__free_indexes = set(range(len(self.__data)))

        if amount_candidates is None:
            self.__candidates = 3
            if self.__candidates > len(self.__data):
                self.__candidates = len(self.__data)
        else:
            self.__candidates = amount_candidates

        self.__check_parameters()

        random.seed()


    def __check_parameters(self):
        """!
        @brief Checks input parameters of the algorithm and if something wrong then corresponding exception is thrown.

        """
        if (self.__amount <= 0) or (self.__amount > len(self.__data)):
            raise ValueError("Amount of cluster centers '" + str(self.__amount) + "' should be at least 1 and "
                             "should be less or equal to amount of points in data.")

        if self.__candidates != kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE:
            if (self.__candidates <= 0) or (self.__candidates > len(self.__data)):
                raise ValueError("Amount of center candidates '" + str(self.__candidates) + "' should be at least 1 "
                                 "and should be less or equal to amount of points in data.")

        if len(self.__data) == 0:
            raise ValueError("Data is empty.")


    def __calculate_shortest_distances(self, data, centers):
        """!
        @brief Calculates distance from each data point to nearest center.
        
        @param[in] data (numpy.array): Array of points for that initialization is performed.
        @param[in] centers (numpy.array): Array of indexes that represents centers.
        
        @return (numpy.array) List of distances to closest center for each data point.
        
        """

        dataset_differences = numpy.zeros((len(centers), len(data)))
        for index_center in range(len(centers)):
            center = data[centers[index_center]]

            dataset_differences[index_center] = numpy.sum(numpy.square(data - center), axis=1).T

        with warnings.catch_warnings():
            numpy.warnings.filterwarnings('ignore', r'All-NaN (slice|axis) encountered')
            shortest_distances = numpy.nanmin(dataset_differences, axis=0)

        return shortest_distances


    def __get_next_center(self, centers):
        """!
        @brief Calculates the next center for the data.

        @param[in] centers (array_like): Current initialized centers represented by indexes.

        @return (array_like) Next initialized center.<br>
                (uint) Index of next initialized center if return_index is True.

        """

        distances = self.__calculate_shortest_distances(self.__data, centers)

        if self.__candidates == kmeans_plusplus_initializer.FARTHEST_CENTER_CANDIDATE:
            for index_point in centers:
                distances[index_point] = numpy.nan
            center_index = numpy.nanargmax(distances)
        else:
            probabilities = self.__calculate_probabilities(distances)
            center_index = self.__get_probable_center(distances, probabilities)

        return center_index


    def __get_initial_center(self, return_index):
        """!
        @brief Choose randomly first center.

        @param[in] return_index (bool): If True then return center's index instead of point.

        @return (array_like) First center.<br>
                (uint) Index of first center.

        """

        index_center = random.randint(0, len(self.__data) - 1)
        if return_index:
            return index_center

        return self.__data[index_center]


    def __calculate_probabilities(self, distances):
        """!
        @brief Calculates cumulative probabilities of being center of each point.

        @param[in] distances (array_like): Distances from each point to closest center.

        @return (array_like) Cumulative probabilities of being center of each point.

        """

        total_distance = numpy.sum(distances)
        if total_distance != 0.0:
            probabilities = distances / total_distance
            return numpy.cumsum(probabilities)
        else:
            return numpy.zeros(len(distances))


    def __get_probable_center(self, distances, probabilities):
        """!
        @brief Calculates the next probable center considering amount candidates.

        @param[in] distances (array_like): Distances from each point to closest center.
        @param[in] probabilities (array_like): Cumulative probabilities of being center of each point.

        @return (uint) Index point that is next initialized center.

        """

        index_best_candidate = 0
        for i in range(self.__candidates):
            candidate_probability = random.random()
            index_candidate = -1

            for index_object in range(len(probabilities)):
                if candidate_probability < probabilities[index_object]:
                    index_candidate = index_object
                    break

            if index_candidate == -1:
                index_best_candidate = next(iter(self.__free_indexes))
            elif distances[index_best_candidate] < distances[index_candidate]:
                index_best_candidate = index_candidate

        return index_best_candidate


    def initialize(self, **kwargs):
        """!
        @brief Calculates initial centers using K-Means++ method.

        @param[in] **kwargs: Arbitrary keyword arguments (available arguments: 'return_index').

        <b>Keyword Args:</b><br>
            - return_index (bool): If True then returns indexes of points from input data instead of points itself.

        @return (list) List of initialized initial centers.
                  If argument 'return_index' is False then returns list of points.
                  If argument 'return_index' is True then returns list of indexes.
        
        """

        return_index = kwargs.get('return_index', False)

        index_point = self.__get_initial_center(True)
        centers = [index_point]
        self.__free_indexes.remove(index_point)

        # For each next center
        for _ in range(1, self.__amount):
            index_point = self.__get_next_center(centers)
            centers.append(index_point)
            self.__free_indexes.remove(index_point)

        if not return_index:
            centers = [self.__data[index] for index in centers]

        return centers