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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 .
+@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').
+
+ Keyword Args:
+ - 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