xmeans

Complexity

Total Complexity

50

Size/Duplication

Total Lines	390
Duplicated Lines	14.36 %

Importance

Changes

0

12 Methods

Rating	Name	Duplication	Size	Complexity
A	get_cluster_encoding()	0	11	1
B	process()	0	28	6
A	get_clusters()	0	12	1
B	__init__()	0	27	3
A	get_centers()	0	12	1
B	__bayesian_information_criterion()	40	42	5
C	__update_clusters()	11	34	7
B	__update_centers()	0	22	4
B	__improve_parameters()	0	28	5
C	__improve_structure()	0	52	8
B	__splitting_criterion()	0	22	4
B	__minimum_noiseless_description_length()	1	50	5

"""!


@brief Cluster analysis algorithm: X-Means

@details Based on article description:

         - D.Pelleg, A.Moore. X-means: Extending K-means with Efficient Estimation of the Number of Clusters. 2000.


@authors Andrei Novikov (pyclustering@yandex.ru)

@date 2014-2017

@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;

The import numpy could not be resolved.

import random;


from enum import IntEnum;


from math import log;


from pyclustering.cluster.encoder import type_encoding;


import pyclustering.core.xmeans_wrapper as wrapper;


from pyclustering.utils import euclidean_distance_sqrt, euclidean_distance;

from pyclustering.utils import list_math_addition_number, list_math_addition, list_math_division_number;



class splitting_type(IntEnum):

    """!

    @brief Enumeration of splitting types that can be used as splitting creation of cluster in X-Means algorithm.

    

    """

    

    ## Bayesian information criterion (BIC) to approximate the correct number of clusters.

    ## Kass's formula is used to calculate BIC:

    ## \f[BIC(\theta) = L(D) - \frac{1}{2}pln(N)\f]

    ##

    ## The number of free parameters \f$p\f$ is simply the sum of \f$K - 1\f$ class probabilities, \f$MK\f$ centroid coordinates, and one variance estimate:

    ## \f[p = (K - 1) + MK + 1\f]

    ##

    ## The log-likelihood of the data:

    ## \f[L(D) = n_jln(n_j) - n_jln(N) - \frac{n_j}{2}ln(2\pi) - \frac{n_jd}{2}ln(\hat{\sigma}^2) - \frac{n_j - K}{2}\f]

    ##

    ## The maximum likelihood estimate (MLE) for the variance:

    ## \f[\hat{\sigma}^2 = \frac{1}{N - K}\sum\limits_{j}\sum\limits_{i}||x_{ij} - \hat{C}_j||^2\f]

    BAYESIAN_INFORMATION_CRITERION = 0;

    

    ## Minimum noiseless description length (MNDL) to approximate the correct number of clusters.

    ## Beheshti's formula is used to calculate upper bound:

    ## \f[Z = \frac{\sigma^2 \sqrt{2K} }{N}(\sqrt{2K} + \beta) + W - \sigma^2 + \frac{2\alpha\sigma}{\sqrt{N}}\sqrt{\frac{\alpha^2\sigma^2}{N} + W - \left(1 - \frac{K}{N}\right)\frac{\sigma^2}{2}} + \frac{2\alpha^2\sigma^2}{N}\f]

    ##

    ## where \f$\alpha\f$ and \f$\beta\f$ represent the parameters for validation probability and confidence probability.

    ##

    ## To improve clustering results some contradiction is introduced:

    ## \f[W = \frac{1}{n_j}\sum\limits_{i}||x_{ij} - \hat{C}_j||\f]

    ## \f[\hat{\sigma}^2 = \frac{1}{N - K}\sum\limits_{j}\sum\limits_{i}||x_{ij} - \hat{C}_j||\f]

    MINIMUM_NOISELESS_DESCRIPTION_LENGTH = 1;



class xmeans:

    """!

    @brief Class represents clustering algorithm X-Means.

    @details X-means clustering method starts with the assumption of having a minimum number of clusters, 

             and then dynamically increases them. X-means uses specified splitting criterion to control 

             the process of splitting clusters.

    

    Example:

    @code

        # sample for cluster analysis (represented by list)

        sample = read_sample(path_to_sample);

        

        # create object of X-Means algorithm that uses CCORE for processing

        # initial centers - optional parameter, if it is None, then random center will be used by the algorithm

        initial_centers = [ [0.0, 0.5] ];

        xmeans_instance = xmeans(sample, initial_centers, ccore = True);

        

        # run cluster analysis

        xmeans_instance.process();

        

        # obtain results of clustering

        clusters = xmeans_instance.get_clusters();

        

        # display allocated clusters

        draw_clusters(sample, clusters);

    @endcode

    

    """

    

    def __init__(self, data, initial_centers = None, kmax = 20, tolerance = 0.025, criterion = splitting_type.BAYESIAN_INFORMATION_CRITERION, ccore = False):

        """!

        @brief Constructor of clustering algorithm X-Means.

        

        @param[in] data (list): Input data that is presented as list of points (objects), each point should be represented by list or tuple.

        @param[in] initial_centers (list): Initial coordinates of centers of clusters that are represented by list: [center1, center2, ...], 

                    if it is not specified then X-Means starts from the random center.

        @param[in] kmax (uint): Maximum number of clusters that can be allocated.

        @param[in] tolerance (double): Stop condition for each iteration: if maximum value of change of centers of clusters is less than tolerance than algorithm will stop processing.

        @param[in] criterion (splitting_type): Type of splitting creation.

        @param[in] ccore (bool): Defines should be CCORE (C++ pyclustering library) used instead of Python code or not.

        

        """

           

        self.__pointer_data = data;

        self.__clusters = [];

        

        if (initial_centers is not None):

            self.__centers = initial_centers[:];

        else:

            self.__centers = [ [random.random() for _ in range(len(data[0])) ] ];

        

        self.__kmax = kmax;

        self.__tolerance = tolerance;

        self.__criterion = criterion;

         

        self.__ccore = ccore;

         

    def process(self):

        """!

        @brief Performs cluster analysis in line with rules of X-Means algorithm.

        

        @remark Results of clustering can be obtained using corresponding gets methods.

        

        @see get_clusters()

        @see get_centers()

        

        """

        

        if (self.__ccore is True):

            self.__clusters = wrapper.xmeans(self.__pointer_data, self.__centers, self.__kmax, self.__tolerance, self.__criterion);

            self.__clusters = [ cluster for cluster in self.__clusters if len(cluster) > 0 ]; 

            

            self.__centers = self.__update_centers(self.__clusters);

        else:

            self.__clusters = [];

            while ( len(self.__centers) < self.__kmax ):

                current_cluster_number = len(self.__centers);

                 

                (self.__clusters, self.__centers) = self.__improve_parameters(self.__centers);

                allocated_centers = self.__improve_structure(self.__clusters, self.__centers);

                

                if ( (current_cluster_number == len(allocated_centers)) ):

                    break;

                else:

                    self.__centers = allocated_centers;

                    

     

    def get_clusters(self):

        """!

        @brief Returns list of allocated clusters, each cluster contains indexes of objects in list of data.

        

        @return (list) List of allocated clusters.

        

        @see process()

        @see get_centers()

        

        """

         

        return self.__clusters;

     

     

    def get_centers(self):

        """!

        @brief Returns list of centers for allocated clusters.

        

        @return (list) List of centers for allocated clusters.

        

        @see process()

        @see get_clusters()

        

        """

         

        return self.__centers;



    def get_cluster_encoding(self):

        """!

        @brief Returns clustering result representation type that indicate how clusters are encoded.

        

        @return (type_encoding) Clustering result representation.

        

        @see get_clusters()

        

        """

        

        return type_encoding.CLUSTER_INDEX_LIST_SEPARATION;



    def __improve_parameters(self, centers, available_indexes = None):

        """!

        @brief Performs k-means clustering in the specified region.

        

        @param[in] centers (list): Centers of clusters.

        @param[in] available_indexes (list): Indexes that defines which points can be used for k-means clustering, if None - then all points are used.

        

        @return (list) List of allocated clusters, each cluster contains indexes of objects in list of data.

        

        """


        changes = numpy.Inf;


        stop_condition = self.__tolerance * self.__tolerance; # Fast solution


        clusters = [];


        while (changes > stop_condition):

            clusters = self.__update_clusters(centers, available_indexes);

            clusters = [ cluster for cluster in clusters if len(cluster) > 0 ]; 

            

            updated_centers = self.__update_centers(clusters);

          

            changes = max([euclidean_distance_sqrt(centers[index], updated_centers[index]) for index in range(len(updated_centers))]);    # Fast solution

              

            centers = updated_centers;

          

        return (clusters, centers);

     

     

    def __improve_structure(self, clusters, centers):

        """!

        @brief Check for best structure: divides each cluster into two and checks for best results using splitting criterion.

        

        @param[in] clusters (list): Clusters that have been allocated (each cluster contains indexes of points from data).

        @param[in] centers (list): Centers of clusters.

        

        @return (list) Allocated centers for clustering.

        

        """

         

        difference = 0.001;

          

        allocated_centers = [];

          

        for index_cluster in range(len(clusters)):

            # split cluster into two child clusters

            parent_child_centers = [];

            parent_child_centers.append(list_math_addition_number(centers[index_cluster], -difference));

            parent_child_centers.append(list_math_addition_number(centers[index_cluster], difference));

          

            # solve k-means problem for children where data of parent are used.

            (parent_child_clusters, parent_child_centers) = self.__improve_parameters(parent_child_centers, clusters[index_cluster]);

              

            # If it's possible to split current data

            if (len(parent_child_clusters) > 1):

                # Calculate splitting criterion

                parent_scores = self.__splitting_criterion([ clusters[index_cluster] ], [ centers[index_cluster] ]);

                child_scores = self.__splitting_criterion([ parent_child_clusters[0], parent_child_clusters[1] ], parent_child_centers);

              

                split_require = False;

                

                # Reallocate number of centers (clusters) in line with scores

                if (self.__criterion == splitting_type.BAYESIAN_INFORMATION_CRITERION):

                    if (parent_scores < child_scores): split_require = True;

                    

                elif (self.__criterion == splitting_type.MINIMUM_NOISELESS_DESCRIPTION_LENGTH):

                    # If its score for the split structure with two children is smaller than that for the parent structure, 

                    # then representing the data samples with two clusters is more accurate in comparison to a single parent cluster.

                    if (parent_scores > child_scores): split_require = True;

                

                if (split_require is True):

                    allocated_centers.append(parent_child_centers[0]);

                    allocated_centers.append(parent_child_centers[1]);

                else:

                    allocated_centers.append(centers[index_cluster]);


                    

            else:

                allocated_centers.append(centers[index_cluster]);

          

        return allocated_centers;

     

     

    def __splitting_criterion(self, clusters, centers):

        """!

        @brief Calculates splitting criterion for input clusters.

        

        @param[in] clusters (list): Clusters for which splitting criterion should be calculated.

        @param[in] centers (list): Centers of the clusters.

        

        @return (double) Returns splitting criterion. High value of splitting cretion means that current structure is much better.

        

        @see __bayesian_information_criterion(clusters, centers)

        @see __minimum_noiseless_description_length(clusters, centers)

        

        """

        

        if (self.__criterion == splitting_type.BAYESIAN_INFORMATION_CRITERION):

            return self.__bayesian_information_criterion(clusters, centers);

        

        elif (self.__criterion == splitting_type.MINIMUM_NOISELESS_DESCRIPTION_LENGTH):

            return self.__minimum_noiseless_description_length(clusters, centers);

        

        else:

            assert 0;



    def __minimum_noiseless_description_length(self, clusters, centers):

        """!

        @brief Calculates splitting criterion for input clusters using minimum noiseless description length criterion.

        

        @param[in] clusters (list): Clusters for which splitting criterion should be calculated.

        @param[in] centers (list): Centers of the clusters.

        

        @return (double) Returns splitting criterion in line with bayesian information criterion. 

                Low value of splitting cretion means that current structure is much better.

        

        @see __bayesian_information_criterion(clusters, centers)

        

        """

        

        scores = float('inf');

        

        W = 0.0;

        K = len(clusters);

        N = 0.0;


        sigma_sqrt = 0.0;

        

        alpha = 0.9;

        betta = 0.9;

        

        for index_cluster in range(0, len(clusters), 1):

            Ni = len(clusters[index_cluster]);

            if (Ni == 0): 

                return float('inf');

            

            Wi = 0.0;

            for index_object in clusters[index_cluster]:

                # euclidean_distance_sqrt should be used in line with paper, but in this case results are

                # very poor, therefore square root is used to improved.

                Wi += euclidean_distance(self.__pointer_data[index_object], centers[index_cluster]);

            

            sigma_sqrt += Wi;

            W += Wi / Ni;

            N += Ni;

        

        if (N - K > 0):

            sigma_sqrt /= (N - K);

            sigma = sigma_sqrt ** 0.5;

            

            Kw = (1.0 - K / N) * sigma_sqrt;

            Ks = ( 2.0 * alpha * sigma / (N ** 0.5) ) * ( (alpha ** 2.0) * sigma_sqrt / N + W - Kw / 2.0 ) ** 0.5;

            

            scores = sigma_sqrt * (2 * K)**0.5 * ((2 * K)**0.5 + betta) / N + W - sigma_sqrt + Ks + 2 * alpha**0.5 * sigma_sqrt / N

        

        return scores;

This code seems to be duplicated in your project.

    def __bayesian_information_criterion(self, clusters, centers):

        """!

        @brief Calculates splitting criterion for input clusters using bayesian information criterion.

        

        @param[in] clusters (list): Clusters for which splitting criterion should be calculated.

        @param[in] centers (list): Centers of the clusters.

        

        @return (double) Splitting criterion in line with bayesian information criterion.

                High value of splitting criterion means that current structure is much better.

                

        @see __minimum_noiseless_description_length(clusters, centers)

        

        """


        scores = [float('inf')] * len(clusters)     # splitting criterion

        dimension = len(self.__pointer_data[0]);

          

        # estimation of the noise variance in the data set

        sigma_sqrt = 0.0;

        K = len(clusters);

        N = 0.0;

          

        for index_cluster in range(0, len(clusters), 1):

            for index_object in clusters[index_cluster]:

                sigma_sqrt += euclidean_distance_sqrt(self.__pointer_data[index_object], centers[index_cluster]);


            N += len(clusters[index_cluster]);

      

        if (N - K > 0):

            sigma_sqrt /= (N - K);

            p = (K - 1) + dimension * K + 1;

            

            # splitting criterion    

            for index_cluster in range(0, len(clusters), 1):

This code seems to be duplicated in your project.

                n = len(clusters[index_cluster]);

                

                L = n * log(n) - n * log(N) - n * 0.5 * log(2.0 * numpy.pi) - n * dimension * 0.5 * log(sigma_sqrt) - (n - K) * 0.5;

                

                # BIC calculation

                scores[index_cluster] = L - p * 0.5 * log(N);

                

        return sum(scores);

 

 

    def __update_clusters(self, centers, available_indexes = None):

        """!

        @brief Calculates Euclidean distance to each point from the each cluster.

               Nearest points are captured by according clusters and as a result clusters are updated.

               

        @param[in] centers (list): Coordinates of centers of clusters that are represented by list: [center1, center2, ...].

        @param[in] available_indexes (list): Indexes that defines which points can be used from imput data, if None - then all points are used.

        

        @return (list) Updated clusters.

        

        """

            

        bypass = None;

        if (available_indexes is None):

            bypass = range(len(self.__pointer_data));

        else:

            bypass = available_indexes;

          

        clusters = [[] for i in range(len(centers))];

        for index_point in bypass:

            index_optim = -1;

            dist_optim = 0.0;

              

            for index in range(len(centers)):

                # dist = euclidean_distance(data[index_point], centers[index]);         # Slow solution

                dist = euclidean_distance_sqrt(self.__pointer_data[index_point], centers[index]);      # Fast solution

                  

                if ( (dist < dist_optim) or (index is 0)):

                    index_optim = index;

                    dist_optim = dist;

              

            clusters[index_optim].append(index_point);

              

        return clusters;

             

     

    def __update_centers(self, clusters):

        """!

        @brief Updates centers of clusters in line with contained objects.

        

        @param[in] clusters (list): Clusters that contain indexes of objects from data.

        

        @return (list) Updated centers.

        

        """

         

        centers = [[] for i in range(len(clusters))];

        dimension = len(self.__pointer_data[0])

          

        for index in range(len(clusters)):

            point_sum = [0.0] * dimension;

              

            for index_point in clusters[index]:

                point_sum = list_math_addition(point_sum, self.__pointer_data[index_point]);

            

            centers[index] = list_math_division_number(point_sum, len(clusters[index]));

              

        return centers;