documentation for the kmedoid function from pyclustering

doc/doc_kmedoids.py

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+"""!
+
+@brief Cluster analysis algorithm: K-Medoids.
+@details Implementation based on papers @cite book::algorithms_for_clustering_data, @cite book::finding_groups_in_data.
+
+@authors Andrei Novikov (pyclustering@yandex.ru)
+@date 2014-2019
+@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 pyclustering.cluster.encoder import type_encoding
+
+from pyclustering.utils import medoid
+from pyclustering.utils.metric import distance_metric, type_metric
+
+import pyclustering.core.kmedoids_wrapper as wrapper
+
+from pyclustering.core.wrapper import ccore_library
+from pyclustering.core.metric_wrapper import metric_wrapper
+
+
+class kmedoids:
+    """!
+    @brief Class represents clustering algorithm K-Medoids.
+    @details The algorithm is less sensitive to outliers tham K-Means. The principle difference between K-Medoids and K-Medians is that
+             K-Medoids uses existed points from input data space as medoids, but median in K-Medians can be unreal object (not from
+             input data space).
+    
+    Clustering example:
+    @code
+        from pyclustering.cluster.kmedoids import kmedoids
+        from pyclustering.cluster import cluster_visualizer
+        from pyclustering.utils import read_sample
+        from pyclustering.samples.definitions import FCPS_SAMPLES
+
+        # Load list of points for cluster analysis.
+        sample = read_sample(FCPS_SAMPLES.SAMPLE_TWO_DIAMONDS)
+
+        # Set random initial medoids.
+        initial_medoids = [1, 500]
+
+        # Create instance of K-Medoids algorithm.
+        kmedoids_instance = kmedoids(sample, initial_medoids)
+
+        # Run cluster analysis and obtain results.
+        kmedoids_instance.process()
+        clusters = kmedoids_instance.get_clusters()
+
+        # Show allocated clusters.
+        print(clusters)
+
+        # Display clusters.
+        visualizer = cluster_visualizer()
+        visualizer.append_clusters(clusters, sample)
+        visualizer.show()
+    @endcode
+
+    Metric for calculation distance between points can be specified by parameter additional 'metric':
+    @code
+        # create Minkowski distance metric with degree equals to '2'
+        metric = distance_metric(type_metric.MINKOWSKI, degree=2)
+
+        # create K-Medoids algorithm with specific distance metric
+        kmedoids_instance = kmedoids(sample, initial_medoids, metric=metric)
+
+        # run cluster analysis and obtain results
+        kmedoids_instance.process()
+        clusters = kmedoids_instance.get_clusters()
+    @endcode
+
+    Distance matrix can be used instead of sequence of points to increase performance and for that purpose parameter 'data_type' should be used:
+    @code
+        # calculate distance matrix for sample
+        sample = read_sample(path_to_sample)
+        matrix = calculate_distance_matrix(sample)
+
+        # create K-Medoids algorithm for processing distance matrix instead of points
+        kmedoids_instance = kmedoids(matrix, initial_medoids, data_type='distance_matrix')
+
+        # run cluster analysis and obtain results
+        kmedoids_instance.process()
+
+        clusters = kmedoids_instance.get_clusters()
+        medoids = kmedoids_instance.get_medoids()
+    @endcode
+
+    """
+    
+    
+    def __init__(self, data, initial_index_medoids, tolerance=0.001, ccore=True, **kwargs):
+        """!
+        @brief Constructor of clustering algorithm K-Medoids.
+        
+        @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_index_medoids (list): Indexes of intial medoids (indexes of points in input data).
+        @param[in] tolerance (double): Stop condition: if maximum value of distance change of medoids of clusters is less than tolerance than algorithm will stop processing.
+        @param[in] ccore (bool): If specified than CCORE library (C++ pyclustering library) is used for clustering instead of Python code.
+        @param[in] **kwargs: Arbitrary keyword arguments (available arguments: 'metric', 'data_type', 'itermax').
+
+        <b>Keyword Args:</b><br>
+            - metric (distance_metric): Metric that is used for distance calculation between two points.
+            - data_type (string): Data type of input sample 'data' that is processed by the algorithm ('points', 'distance_matrix').
+            - itermax (uint): Maximum number of iteration for cluster analysis.
+
+        """
+        self.__pointer_data = data
+        self.__clusters = []
+        self.__medoid_indexes = initial_index_medoids
+        self.__tolerance = tolerance
+
+        self.__metric = kwargs.get('metric', distance_metric(type_metric.EUCLIDEAN_SQUARE))
+        self.__data_type = kwargs.get('data_type', 'points')
+        self.__itermax = kwargs.get('itermax', 200)
+
+        self.__distance_calculator = self.__create_distance_calculator()
+
+        self.__ccore = ccore and self.__metric.get_type() != type_metric.USER_DEFINED
+        if self.__ccore:
+            self.__ccore = ccore_library.workable()
+
+        #self.__verify_instance()
+
+
+    def process(self):
+        """!
+        @brief Performs cluster analysis in line with rules of K-Medoids algorithm.
+
+        @return (kmedoids) Returns itself (K-Medoids instance).
+
+        @remark Results of clustering can be obtained using corresponding get methods.
+        
+        @see get_clusters()
+        @see get_medoids()
+        
+        """
+        
+        if self.__ccore is True:
+            ccore_metric = metric_wrapper.create_instance(self.__metric)
+            self.__clusters, self.__medoid_indexes = wrapper.kmedoids(self.__pointer_data, self.__medoid_indexes, self.__tolerance, self.__itermax, ccore_metric.get_pointer(), self.__data_type)
+        
+        else:
+            changes = float('inf')
+            iterations = 0
+
+            while changes > self.__tolerance and iterations < self.__itermax:
+                self.__clusters = self.__update_clusters()
+                update_medoid_indexes = self.__update_medoids()
+
+                changes = max([self.__distance_calculator(self.__medoid_indexes[index], update_medoid_indexes[index]) for index in range(len(update_medoid_indexes))])
+
+                self.__medoid_indexes = update_medoid_indexes
+
+                iterations += 1
+
+        return self
+
+
+    def predict(self, points):
+        """!
+        @brief Calculates the closest cluster to each point.
+
+        @param[in] points (array_like): Points for which closest clusters are calculated.
+
+        @return (list) List of closest clusters for each point. Each cluster is denoted by index. Return empty
+                 collection if 'process()' method was not called.
+
+        An example how to calculate (or predict) the closest cluster to specified points.
+        @code
+            from pyclustering.cluster.kmedoids import kmedoids
+            from pyclustering.samples.definitions import SIMPLE_SAMPLES
+            from pyclustering.utils import read_sample
+
+            # Load list of points for cluster analysis.
+            sample = read_sample(SIMPLE_SAMPLES.SAMPLE_SIMPLE3)
+
+            # Initial medoids for sample 'Simple3'.
+            initial_medoids = [4, 12, 25, 37]
+
+            # Create instance of K-Medoids algorithm with prepared centers.
+            kmedoids_instance = kmedoids(sample, initial_medoids)
+
+            # Run cluster analysis.
+            kmedoids_instance.process()
+
+            # Calculate the closest cluster to following two points.
+            points = [[0.35, 0.5], [2.5, 2.0]]
+            closest_clusters = kmedoids_instance.predict(points)
+            print(closest_clusters)
+        @endcode
+
+        """
+
+        if len(self.__clusters) == 0:
+            return []
+
+        medoids = [ self.__pointer_data[index] for index in self.__medoid_indexes ]
+        differences = numpy.zeros((len(points), len(medoids)))
+        for index_point in range(len(points)):
+            differences[index_point] = [ self.__metric(points[index_point], center) for center in medoids ]
+
+        return numpy.argmin(differences, axis=1)
+
+
+    def get_clusters(self):
+        """!
+        @brief Returns list of allocated clusters, each cluster contains indexes of objects in list of data.
+        
+        @see process()
+        @see get_medoids()
+        
+        """
+        
+        return self.__clusters
+    
+    
+    def get_medoids(self):
+        """!
+        @brief Returns list of medoids of allocated clusters represented by indexes from the input data.
+        
+        @see process()
+        @see get_clusters()
+        
+        """
+
+        return self.__medoid_indexes
+
+
+    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 __verify_instance(self):
+        pass
+
+
+    def __create_distance_calculator(self):
+        """!
+        @brief Creates distance calculator in line with algorithms parameters.
+
+        @return (callable) Distance calculator.
+
+        """
+        if self.__data_type == 'points':
+            return lambda index1, index2: self.__metric(self.__pointer_data[index1], self.__pointer_data[index2])
+
+        elif self.__data_type == 'distance_matrix':
+            if isinstance(self.__pointer_data, numpy.matrix):
+                return lambda index1, index2: self.__pointer_data.item((index1, index2))
+
+            return lambda index1, index2: self.__pointer_data[index1][index2]
+
+        else:
+            raise TypeError("Unknown type of data is specified '%s'" % self.__data_type)
+
+
+    def __update_clusters(self):
+        """!
+        @brief Calculate distance to each point from the each cluster. 
+        @details Nearest points are captured by according clusters and as a result clusters are updated.
+        
+        @return (list) updated clusters as list of clusters where each cluster contains indexes of objects from data.
+        
+        """
+        
+        clusters = [[self.__medoid_indexes[i]] for i in range(len(self.__medoid_indexes))]
+        for index_point in range(len(self.__pointer_data)):
+            if index_point in self.__medoid_indexes:
+                continue
+
+            index_optim = -1
+            dist_optim = float('Inf')
+            
+            for index in range(len(self.__medoid_indexes)):
+                dist = self.__distance_calculator(index_point, self.__medoid_indexes[index])
+                
+                if dist < dist_optim:
+                    index_optim = index
+                    dist_optim = dist
+            
+            clusters[index_optim].append(index_point)
+        
+        return clusters
+    
+    
+    def __update_medoids(self):
+        """!
+        @brief Find medoids of clusters in line with contained objects.
+        
+        @return (list) list of medoids for current number of clusters.
+        
+        """
+
+        medoid_indexes = [-1] * len(self.__clusters)
+        
+        for index in range(len(self.__clusters)):
+            medoid_index = medoid(self.__pointer_data, self.__clusters[index], metric=self.__metric, data_type=self.__data_type)
+            medoid_indexes[index] = medoid_index
+             
+        return medoid_indexes