xmeans.__update_clusters() - Code Metrics - Inspection of "#410: [pyclustering.cluster.xmeans] numpy optimiza..." - annoviko/pyclustering - Measure and Improve Code Quality continuously with Scrutinizer

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Push — 0.8.dev ( 0b64b0...837ab1 )

by Andrei

created 2018-02-05 10:10 UTC

xmeans.__update_clusters() C

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"""!

@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 ([email protected])
@date 2014-2018
@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;
# .scrutinizer.yml
before_commands:
    - sudo pip install abc # Python2
    - sudo pip3 install abc # Python3
import random;

from enum import IntEnum;

from math import log;

from pyclustering.cluster.encoder import type_encoding;
from pyclustering.cluster.kmeans import kmeans;

from pyclustering.core.wrapper import ccore_library;

import pyclustering.core.xmeans_wrapper as wrapper;

from pyclustering.utils import euclidean_distance_sqrt, euclidean_distance;
from pyclustering.utils import list_math_addition_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. Method K-Means++ can be used for calculation of initial centers.
             
             CCORE option can be used to use the pyclustering core - C/C++ shared library for processing that significantly increases performance.
             
             CCORE implementation of the algorithm uses thread pool to parallelize the clustering process.
    
    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 centers will be used by the algorithm.
        # let's avoid random initial centers and initialize them using K-Means++ method:
        initial_centers = kmeans_plusplus_initializer(sample, 2).initialize();
        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
    
    @see center_initializer
    
    """
    
    def __init__(self, data, initial_centers = None, kmax = 20, tolerance = 0.025, criterion = splitting_type.BAYESIAN_INFORMATION_CRITERION, ccore = True):
        """!
        @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;
        if (self.__ccore):
            self.__ccore = ccore_library.workable();


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

        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)):
                #if ( (current_cluster_number == len(allocated_centers)) or (len(allocated_centers) > self.__kmax) ):
                    break;
                else:
                    self.__centers = allocated_centers;
            
            self.__clusters, self.__centers = self.__improve_parameters(self.__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.
        
        """

        local_data = self.__pointer_data;
        if (available_indexes):
            local_data = [ self.__pointer_data[i] for i in available_indexes ];
        
        kmeans_instance = kmeans(local_data, centers, tolerance=self.__tolerance, ccore=False);
        kmeans_instance.process();
        
        local_clusters = kmeans_instance.get_clusters();
        local_centers = kmeans_instance.get_centers();
        
        clusters = [];
        if (available_indexes):
            for local_cluster in local_clusters:
                current_cluster = [];
                for index_point in local_cluster:
                    current_cluster.append(available_indexes[index_point]);
                    
                clusters.append(current_cluster);
        else:
            clusters = local_clusters;
        
        return (clusters, local_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 = [];
        amount_free_centers = self.__kmax - len(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) and (amount_free_centers > 0) ):
                    allocated_centers.append(parent_child_centers[0]);
                    allocated_centers.append(parent_child_centers[1]);
                    
                    amount_free_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;


    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;

            # in case of the same points, sigma_sqrt can be zero (issue: #407)
            sigma_multiplier = 0.0;
            if (sigma_sqrt <= 0.0):
                sigma_multiplier = float('-inf');
            else:
                sigma_multiplier = dimension * 0.5 * log(sigma_sqrt);
            
            # splitting criterion    
            for index_cluster in range(0, len(clusters), 1):
                n = len(clusters[index_cluster]);

                L = n * log(n) - n * log(N) - n * 0.5 * log(2.0 * numpy.pi) - n * sigma_multiplier - (n - K) * 0.5;
                
                # BIC calculation
                scores[index_cluster] = L - p * 0.5 * log(N);
                
        return sum(scores);


Push — 0.8.dev ( 0b64b0...837ab1 )

xmeans.__update_clusters() C

Complexity

Size

Duplication

Importance

1. Missing Dependencies

2. Missing init.py files

1			"""!
2
3			@brief Cluster analysis algorithm: X-Means
4			@details Based on article description:
5			- D.Pelleg, A.Moore. X-means: Extending K-means with Efficient Estimation of the Number of Clusters. 2000.
6
7			@authors Andrei Novikov ([email protected])
8			@date 2014-2018
9			@copyright GNU Public License
10
11			@cond GNU_PUBLIC_LICENSE
12			PyClustering is free software: you can redistribute it and/or modify
13			it under the terms of the GNU General Public License as published by
14			the Free Software Foundation, either version 3 of the License, or
15			(at your option) any later version.
16
17			PyClustering is distributed in the hope that it will be useful,
18			but WITHOUT ANY WARRANTY; without even the implied warranty of
19			MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20			GNU General Public License for more details.
21
22			You should have received a copy of the GNU General Public License
23			along with this program. If not, see <http://www.gnu.org/licenses/>.
24			@endcond
25
26			"""
27
28
29			import numpy;
			0 ignored issues – show Configuration introduced 2017-08-16 14:12 UTC by Report Bug Copy Issue Report The import `numpy` could not be resolved. This can be caused by one of the following: 1. Missing Dependencies This error could indicate a configuration issue of Pylint. Make sure that your libraries are available by adding the necessary commands. # .scrutinizer.yml before_commands: - sudo pip install abc # Python2 - sudo pip3 install abc # Python3 Tip: We are currently not using virtualenv to run pylint, when installing your modules make sure to use the command for the correct version. 2. Missing __init__.py files This error could also result from missing `__init__.py` files in your module folders. Make sure that you place one file in each sub-folder. Loading history...
30			import random;
31
32			from enum import IntEnum;
33
34			from math import log;
35
36			from pyclustering.cluster.encoder import type_encoding;
37			from pyclustering.cluster.kmeans import kmeans;
38
39			from pyclustering.core.wrapper import ccore_library;
40
41			import pyclustering.core.xmeans_wrapper as wrapper;
42
43			from pyclustering.utils import euclidean_distance_sqrt, euclidean_distance;
44			from pyclustering.utils import list_math_addition_number;
45
46
47			class splitting_type(IntEnum):
48			"""!
49			@brief Enumeration of splitting types that can be used as splitting creation of cluster in X-Means algorithm.
50
51			"""
52
53			## Bayesian information criterion (BIC) to approximate the correct number of clusters.
54			## Kass's formula is used to calculate BIC:
55			## \f[BIC(\theta) = L(D) - \frac{1}{2}pln(N)\f]
56			##
57			## 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:
58			## \f[p = (K - 1) + MK + 1\f]
59			##
60			## The log-likelihood of the data:
61			## \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]
62			##
63			## The maximum likelihood estimate (MLE) for the variance:
64			## \f[\hat{\sigma}^2 = \frac{1}{N - K}\sum\limits_{j}\sum\limits_{i}\|\|x_{ij} - \hat{C}_j\|\|^2\f]
65			BAYESIAN_INFORMATION_CRITERION = 0;
66
67			## Minimum noiseless description length (MNDL) to approximate the correct number of clusters.
68			## Beheshti's formula is used to calculate upper bound:
69			## \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]
70			##
71			## where \f$\alpha\f$ and \f$\beta\f$ represent the parameters for validation probability and confidence probability.
72			##
73			## To improve clustering results some contradiction is introduced:
74			## \f[W = \frac{1}{n_j}\sum\limits_{i}\|\|x_{ij} - \hat{C}_j\|\|\f]
75			## \f[\hat{\sigma}^2 = \frac{1}{N - K}\sum\limits_{j}\sum\limits_{i}\|\|x_{ij} - \hat{C}_j\|\|\f]
76			MINIMUM_NOISELESS_DESCRIPTION_LENGTH = 1;
77
78
79			class xmeans:
80			"""!
81			@brief Class represents clustering algorithm X-Means.
82			@details X-means clustering method starts with the assumption of having a minimum number of clusters,
83			and then dynamically increases them. X-means uses specified splitting criterion to control
84			the process of splitting clusters. Method K-Means++ can be used for calculation of initial centers.
85
86			CCORE option can be used to use the pyclustering core - C/C++ shared library for processing that significantly increases performance.
87
88			CCORE implementation of the algorithm uses thread pool to parallelize the clustering process.
89
90			Example:
91			@code
92			# sample for cluster analysis (represented by list)
93			sample = read_sample(path_to_sample);
94
95			# create object of X-Means algorithm that uses CCORE for processing
96			# initial centers - optional parameter, if it is None, then random centers will be used by the algorithm.
97			# let's avoid random initial centers and initialize them using K-Means++ method:
98			initial_centers = kmeans_plusplus_initializer(sample, 2).initialize();
99			xmeans_instance = xmeans(sample, initial_centers, ccore = True);
100
101			# run cluster analysis
102			xmeans_instance.process();
103
104			# obtain results of clustering
105			clusters = xmeans_instance.get_clusters();
106
107			# display allocated clusters
108			draw_clusters(sample, clusters);
109			@endcode
110
111			@see center_initializer
112
113			"""
114
115			def __init__(self, data, initial_centers = None, kmax = 20, tolerance = 0.025, criterion = splitting_type.BAYESIAN_INFORMATION_CRITERION, ccore = True):
116			"""!
117			@brief Constructor of clustering algorithm X-Means.
118
119			@param[in] data (list): Input data that is presented as list of points (objects), each point should be represented by list or tuple.
120			@param[in] initial_centers (list): Initial coordinates of centers of clusters that are represented by list: [center1, center2, ...],
121			if it is not specified then X-Means starts from the random center.
122			@param[in] kmax (uint): Maximum number of clusters that can be allocated.
123			@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.
124			@param[in] criterion (splitting_type): Type of splitting creation.
125			@param[in] ccore (bool): Defines should be CCORE (C++ pyclustering library) used instead of Python code or not.
126
127			"""
128
129			self.__pointer_data = data;
130			self.__clusters = [];
131
132			if (initial_centers is not None):
133			self.__centers = initial_centers[:];
134			else:
135			self.__centers = [ [random.random() for _ in range(len(data[0])) ] ];
136
137			self.__kmax = kmax;
138			self.__tolerance = tolerance;
139			self.__criterion = criterion;
140
141			self.__ccore = ccore;
142			if (self.__ccore):
143			self.__ccore = ccore_library.workable();
144
145
146			def process(self):
147			"""!
148			@brief Performs cluster analysis in line with rules of X-Means algorithm.
149
150			@remark Results of clustering can be obtained using corresponding gets methods.
151
152			@see get_clusters()
153			@see get_centers()
154
155			"""
156
157			if (self.__ccore is True):
158			self.__clusters, self.__centers = wrapper.xmeans(self.__pointer_data, self.__centers, self.__kmax, self.__tolerance, self.__criterion);
159
160			else:
161			self.__clusters = [];
162			while ( len(self.__centers) <= self.__kmax ):
163			current_cluster_number = len(self.__centers);
164
165			self.__clusters, self.__centers = self.__improve_parameters(self.__centers);
166			allocated_centers = self.__improve_structure(self.__clusters, self.__centers);
167
168			if (current_cluster_number == len(allocated_centers)):
169			#if ( (current_cluster_number == len(allocated_centers)) or (len(allocated_centers) > self.__kmax) ):
170			break;
171			else:
172			self.__centers = allocated_centers;
173
174			self.__clusters, self.__centers = self.__improve_parameters(self.__centers);
175
176
177			def get_clusters(self):
178			"""!
179			@brief Returns list of allocated clusters, each cluster contains indexes of objects in list of data.
180
181			@return (list) List of allocated clusters.
182
183			@see process()
184			@see get_centers()
185
186			"""
187
188			return self.__clusters;
189
190
191			def get_centers(self):
192			"""!
193			@brief Returns list of centers for allocated clusters.
194
195			@return (list) List of centers for allocated clusters.
196
197			@see process()
198			@see get_clusters()
199
200			"""
201
202			return self.__centers;
203
204
205			def get_cluster_encoding(self):
206			"""!
207			@brief Returns clustering result representation type that indicate how clusters are encoded.
208
209			@return (type_encoding) Clustering result representation.
210
211			@see get_clusters()
212
213			"""
214
215			return type_encoding.CLUSTER_INDEX_LIST_SEPARATION;
216
217
218			def __improve_parameters(self, centers, available_indexes = None):
219			"""!
220			@brief Performs k-means clustering in the specified region.
221
222			@param[in] centers (list): Centers of clusters.
223			@param[in] available_indexes (list): Indexes that defines which points can be used for k-means clustering, if None - then all points are used.
224
225			@return (list) List of allocated clusters, each cluster contains indexes of objects in list of data.
226
227			"""
228
229			local_data = self.__pointer_data;
230			if (available_indexes):
231			local_data = [ self.__pointer_data[i] for i in available_indexes ];
232
233			kmeans_instance = kmeans(local_data, centers, tolerance=self.__tolerance, ccore=False);
234			kmeans_instance.process();
235
236			local_clusters = kmeans_instance.get_clusters();
237			local_centers = kmeans_instance.get_centers();
238
239			clusters = [];
240			if (available_indexes):
241			for local_cluster in local_clusters:
242			current_cluster = [];
243			for index_point in local_cluster:
244			current_cluster.append(available_indexes[index_point]);
245
246			clusters.append(current_cluster);
247			else:
248			clusters = local_clusters;
249
250			return (clusters, local_centers);
251
252
253			def __improve_structure(self, clusters, centers):
254			"""!
255			@brief Check for best structure: divides each cluster into two and checks for best results using splitting criterion.
256
257			@param[in] clusters (list): Clusters that have been allocated (each cluster contains indexes of points from data).
258			@param[in] centers (list): Centers of clusters.
259
260			@return (list) Allocated centers for clustering.
261
262			"""
263
264			difference = 0.001;
265
266			allocated_centers = [];
267			amount_free_centers = self.__kmax - len(centers);
268
269			for index_cluster in range(len(clusters)):
270			# split cluster into two child clusters
271			parent_child_centers = [];
272			parent_child_centers.append(list_math_addition_number(centers[index_cluster], -difference));
273			parent_child_centers.append(list_math_addition_number(centers[index_cluster], difference));
274
275			# solve k-means problem for children where data of parent are used.
276			(parent_child_clusters, parent_child_centers) = self.__improve_parameters(parent_child_centers, clusters[index_cluster]);
277
278			# If it's possible to split current data
279			if (len(parent_child_clusters) > 1):
280			# Calculate splitting criterion
281			parent_scores = self.__splitting_criterion([ clusters[index_cluster] ], [ centers[index_cluster] ]);
282			child_scores = self.__splitting_criterion([ parent_child_clusters[0], parent_child_clusters[1] ], parent_child_centers);
283
284			split_require = False;
285
286			# Reallocate number of centers (clusters) in line with scores
287			if (self.__criterion == splitting_type.BAYESIAN_INFORMATION_CRITERION):
288			if (parent_scores < child_scores): split_require = True;
289
290			elif (self.__criterion == splitting_type.MINIMUM_NOISELESS_DESCRIPTION_LENGTH):
291			# If its score for the split structure with two children is smaller than that for the parent structure,
292			# then representing the data samples with two clusters is more accurate in comparison to a single parent cluster.
293			if (parent_scores > child_scores): split_require = True;
294
295			if ( (split_require is True) and (amount_free_centers > 0) ):
296			allocated_centers.append(parent_child_centers[0]);
297			allocated_centers.append(parent_child_centers[1]);
298
299			amount_free_centers -= 1;
300			else:
301			allocated_centers.append(centers[index_cluster]);
302
303
304			else:
305			allocated_centers.append(centers[index_cluster]);
306
307			return allocated_centers;
308
309
310			def __splitting_criterion(self, clusters, centers):
311			"""!
312			@brief Calculates splitting criterion for input clusters.
313
314			@param[in] clusters (list): Clusters for which splitting criterion should be calculated.
315			@param[in] centers (list): Centers of the clusters.
316
317			@return (double) Returns splitting criterion. High value of splitting cretion means that current structure is much better.
318
319			@see __bayesian_information_criterion(clusters, centers)
320			@see __minimum_noiseless_description_length(clusters, centers)
321
322			"""
323
324			if (self.__criterion == splitting_type.BAYESIAN_INFORMATION_CRITERION):
325			return self.__bayesian_information_criterion(clusters, centers);
326
327			elif (self.__criterion == splitting_type.MINIMUM_NOISELESS_DESCRIPTION_LENGTH):
328			return self.__minimum_noiseless_description_length(clusters, centers);
329
330			else:
331			assert 0;
332
333
334			def __minimum_noiseless_description_length(self, clusters, centers):
335			"""!
336			@brief Calculates splitting criterion for input clusters using minimum noiseless description length criterion.
337
338			@param[in] clusters (list): Clusters for which splitting criterion should be calculated.
339			@param[in] centers (list): Centers of the clusters.
340
341			@return (double) Returns splitting criterion in line with bayesian information criterion.
342			Low value of splitting cretion means that current structure is much better.
343
344			@see __bayesian_information_criterion(clusters, centers)
345
346			"""
347
348			scores = float('inf');
349
350			W = 0.0;
351			K = len(clusters);
352			N = 0.0;
353
354			sigma_sqrt = 0.0;
355
356			alpha = 0.9;
357			betta = 0.9;
358
359			for index_cluster in range(0, len(clusters), 1):
360			Ni = len(clusters[index_cluster]);
361			if (Ni == 0):
362			return float('inf');
363
364			Wi = 0.0;
365			for index_object in clusters[index_cluster]:
366			# euclidean_distance_sqrt should be used in line with paper, but in this case results are
367			# very poor, therefore square root is used to improved.
368			Wi += euclidean_distance(self.__pointer_data[index_object], centers[index_cluster]);
369
370			sigma_sqrt += Wi;
371			W += Wi / Ni;
372			N += Ni;
373
374			if (N - K > 0):
375			sigma_sqrt /= (N - K);
376			sigma = sigma_sqrt ** 0.5;
377
378			Kw = (1.0 - K / N) * sigma_sqrt;
379			Ks = ( 2.0 * alpha * sigma / (N ** 0.5) ) * ( (alpha ** 2.0) * sigma_sqrt / N + W - Kw / 2.0 ) ** 0.5;
380
381			scores = sigma_sqrt * (2 * K)*0.5 ((2 * K)*0.5 + betta) / N + W - sigma_sqrt + Ks + 2 alpha*0.5 sigma_sqrt / N
382
383			return scores;
384
385
386			def __bayesian_information_criterion(self, clusters, centers):
387			"""!
388			@brief Calculates splitting criterion for input clusters using bayesian information criterion.
389
390			@param[in] clusters (list): Clusters for which splitting criterion should be calculated.
391			@param[in] centers (list): Centers of the clusters.
392
393			@return (double) Splitting criterion in line with bayesian information criterion.
394			High value of splitting criterion means that current structure is much better.
395
396			@see __minimum_noiseless_description_length(clusters, centers)
397
398			"""
399
400			scores = [float('inf')] * len(clusters) # splitting criterion
401			dimension = len(self.__pointer_data[0]);
402
403			# estimation of the noise variance in the data set
404			sigma_sqrt = 0.0;
405			K = len(clusters);
406			N = 0.0;
407
408			for index_cluster in range(0, len(clusters), 1):
409			for index_object in clusters[index_cluster]:
410			sigma_sqrt += euclidean_distance_sqrt(self.__pointer_data[index_object], centers[index_cluster]);
411
412			N += len(clusters[index_cluster]);
413
414			if (N - K > 0):
415			sigma_sqrt /= (N - K);
416			p = (K - 1) + dimension * K + 1;
417
418			# in case of the same points, sigma_sqrt can be zero (issue: #407)
419			sigma_multiplier = 0.0;
420			if (sigma_sqrt <= 0.0):
421			sigma_multiplier = float('-inf');
422			else:
423			sigma_multiplier = dimension * 0.5 * log(sigma_sqrt);
424
425			# splitting criterion
426			for index_cluster in range(0, len(clusters), 1):
427			n = len(clusters[index_cluster]);
428
429			L = n * log(n) - n * log(N) - n * 0.5 * log(2.0 * numpy.pi) - n * sigma_multiplier - (n - K) * 0.5;
430
431			# BIC calculation
432			scores[index_cluster] = L - p * 0.5 * log(N);
433
434			return sum(scores);
435

annoviko / pyclustering

Push — 0.8.dev ( 0b64b0...837ab1 )

xmeans.__update_clusters() C

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