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"""!
@brief Cluster analysis algorithm: agglomerative algorithm.
@details Implementation based on paper @cite book::algorithms_for_clustering_data.
@authors Andrei Novikov (pyclustering@yandex.ru)
@date 2014-2020
@copyright BSD-3-Clause
"""
from enum import IntEnum
from pyclustering.cluster.encoder import type_encoding
from pyclustering.utils import euclidean_distance_square
from pyclustering.core.wrapper import ccore_library
import pyclustering.core.agglomerative_wrapper as wrapper
class type_link(IntEnum):
"""!
@brief Enumerator of types of link between clusters.
"""
## Distance between the two nearest objects in clusters is considered as a link, so-called SLINK method (the single-link clustering method).
SINGLE_LINK = 0
## Distance between the farthest objects in clusters is considered as a link, so-called CLINK method (the complete-link clustering method).
COMPLETE_LINK = 1
## Average distance between objects in clusters is considered as a link.
AVERAGE_LINK = 2
## Distance between centers of clusters is considered as a link.
CENTROID_LINK = 3
class agglomerative:
"""!
@brief Class represents agglomerative algorithm for cluster analysis.
@details Agglomerative algorithm considers each data point (object) as a separate cluster at the beginning and
step by step finds the best pair of clusters for merge until required amount of clusters is obtained.
Example of agglomerative algorithm where centroid link is used:
@code
from pyclustering.cluster.agglomerative import agglomerative, type_link
from pyclustering.cluster import cluster_visualizer
from pyclustering.samples.definitions import FCPS_SAMPLES
from pyclustering.utils import read_sample
# Sample for cluster analysis (represented by list)
sample = read_sample(FCPS_SAMPLES.SAMPLE_TARGET)
# Create object that uses python code only
agglomerative_instance = agglomerative(sample, 6, type_link.SINGLE_LINK, ccore=True)
# Cluster analysis
agglomerative_instance.process()
# Obtain results of clustering
clusters = agglomerative_instance.get_clusters()
# Visualize clustering results
visualizer = cluster_visualizer()
visualizer.append_clusters(clusters, sample)
visualizer.show()
@endcode
There is example of clustering 'LSUN' sample:
@code
from pyclustering.cluster.agglomerative import agglomerative, type_link
from pyclustering.cluster import cluster_visualizer
from pyclustering.samples.definitions import FCPS_SAMPLES
from pyclustering.utils import read_sample
# sample Lsun for cluster analysis
lsun_sample = read_sample(FCPS_SAMPLES.SAMPLE_LSUN)
# create instance of the algorithm that will use ccore library (the last argument)
agglomerative_instance = agglomerative(lsun_sample, 3, type_link.SINGLE_LINK, True)
# start processing
agglomerative_instance.process()
# get result and visualize it
lsun_clusters = agglomerative_instance.get_clusters()
visualizer = cluster_visualizer()
visualizer.append_clusters(lsun_clusters, lsun_sample)
visualizer.show()
@endcode
Example of agglomerative clustering using different links:
@image html agglomerative_lsun_clustering_single_link.png
"""
def __init__(self, data, number_clusters, link = None, ccore = True):
"""!
@brief Constructor of agglomerative hierarchical algorithm.
@param[in] data (list): Input data that is presented as a list of points (objects), each point should be represented by list, for example
[[0.1, 0.2], [0.4, 0.5], [1.3, 0.9]].
@param[in] number_clusters (uint): Number of clusters that should be allocated.
@param[in] link (type_link): Link type that is used for calculation similarity between objects and clusters, if it is not specified centroid link will be used by default.
@param[in] ccore (bool): Defines should be CCORE (C++ pyclustering library) used instead of Python code or not (by default it is 'False').
"""
self.__pointer_data = data
self.__number_clusters = number_clusters
self.__similarity = link
self.__verify_arguments()
if self.__similarity is None:
self.__similarity = type_link.CENTROID_LINK
self.__clusters = []
self.__ccore = ccore
if self.__ccore:
self.__ccore = ccore_library.workable()
if self.__similarity == type_link.CENTROID_LINK:
self.__centers = self.__pointer_data.copy() # used in case of usage of centroid links
def process(self):
"""!
@brief Performs cluster analysis in line with rules of agglomerative algorithm and similarity.
@return (agglomerative) Returns itself (Agglomerative instance).
@see get_clusters()
"""
if self.__ccore is True:
self.__clusters = wrapper.agglomerative_algorithm(self.__pointer_data, self.__number_clusters, self.__similarity)
else:
self.__clusters = [[index] for index in range(0, len(self.__pointer_data))]
current_number_clusters = len(self.__clusters)
while current_number_clusters > self.__number_clusters:
self.__merge_similar_clusters()
current_number_clusters = len(self.__clusters)
return self
def get_clusters(self):
"""!
@brief Returns list of allocated clusters, each cluster contains indexes of objects in list of data.
@remark Results of clustering can be obtained using corresponding gets methods.
@return (list) List of allocated clusters, each cluster contains indexes of objects in list of data.
@see process()
"""
return self.__clusters
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 __merge_similar_clusters(self):
"""!
@brief Merges the most similar clusters in line with link type.
"""
if self.__similarity == type_link.AVERAGE_LINK:
self.__merge_by_average_link()
elif self.__similarity == type_link.CENTROID_LINK:
self.__merge_by_centroid_link()
elif self.__similarity == type_link.COMPLETE_LINK:
self.__merge_by_complete_link()
elif self.__similarity == type_link.SINGLE_LINK:
self.__merge_by_signle_link()
else:
raise NameError('Not supported similarity is used')
def __merge_by_average_link(self):
"""!
@brief Merges the most similar clusters in line with average link type.
"""
minimum_average_distance = float('Inf')
for index_cluster1 in range(0, len(self.__clusters)):
for index_cluster2 in range(index_cluster1 + 1, len(self.__clusters)):
# Find farthest objects
candidate_average_distance = 0.0
for index_object1 in self.__clusters[index_cluster1]:
for index_object2 in self.__clusters[index_cluster2]:
candidate_average_distance += euclidean_distance_square(self.__pointer_data[index_object1], self.__pointer_data[index_object2])
candidate_average_distance /= (len(self.__clusters[index_cluster1]) + len(self.__clusters[index_cluster2]))
if candidate_average_distance < minimum_average_distance:
minimum_average_distance = candidate_average_distance
indexes = [index_cluster1, index_cluster2]
self.__clusters[indexes[0]] += self.__clusters[indexes[1]]
self.__clusters.pop(indexes[1]) # remove merged cluster.
def __merge_by_centroid_link(self):
"""!
@brief Merges the most similar clusters in line with centroid link type.
"""
minimum_centroid_distance = float('Inf')
indexes = None
for index1 in range(0, len(self.__centers)):
for index2 in range(index1 + 1, len(self.__centers)):
distance = euclidean_distance_square(self.__centers[index1], self.__centers[index2])
if distance < minimum_centroid_distance:
minimum_centroid_distance = distance
indexes = [index1, index2]
self.__clusters[indexes[0]] += self.__clusters[indexes[1]]
self.__centers[indexes[0]] = self.__calculate_center(self.__clusters[indexes[0]])
self.__clusters.pop(indexes[1]) # remove merged cluster.
self.__centers.pop(indexes[1]) # remove merged center.
def __merge_by_complete_link(self):
"""!
@brief Merges the most similar clusters in line with complete link type.
"""
minimum_complete_distance = float('Inf')
indexes = None
for index_cluster1 in range(0, len(self.__clusters)):
for index_cluster2 in range(index_cluster1 + 1, len(self.__clusters)):
candidate_maximum_distance = self.__calculate_farthest_distance(index_cluster1, index_cluster2)
if candidate_maximum_distance < minimum_complete_distance:
minimum_complete_distance = candidate_maximum_distance
indexes = [index_cluster1, index_cluster2]
self.__clusters[indexes[0]] += self.__clusters[indexes[1]]
self.__clusters.pop(indexes[1]) # remove merged cluster.
def __calculate_farthest_distance(self, index_cluster1, index_cluster2):
"""!
@brief Finds two farthest objects in two specified clusters in terms and returns distance between them.
@param[in] (uint) Index of the first cluster.
@param[in] (uint) Index of the second cluster.
@return The farthest euclidean distance between two clusters.
"""
candidate_maximum_distance = 0.0
for index_object1 in self.__clusters[index_cluster1]:
for index_object2 in self.__clusters[index_cluster2]:
distance = euclidean_distance_square(self.__pointer_data[index_object1], self.__pointer_data[index_object2])
if distance > candidate_maximum_distance:
candidate_maximum_distance = distance
return candidate_maximum_distance
def __merge_by_signle_link(self):
"""!
@brief Merges the most similar clusters in line with single link type.
"""
minimum_single_distance = float('Inf')
indexes = None
for index_cluster1 in range(0, len(self.__clusters)):
for index_cluster2 in range(index_cluster1 + 1, len(self.__clusters)):
candidate_minimum_distance = self.__calculate_nearest_distance(index_cluster1, index_cluster2)
if candidate_minimum_distance < minimum_single_distance:
minimum_single_distance = candidate_minimum_distance
indexes = [index_cluster1, index_cluster2]
self.__clusters[indexes[0]] += self.__clusters[indexes[1]]
self.__clusters.pop(indexes[1]) # remove merged cluster.
def __calculate_nearest_distance(self, index_cluster1, index_cluster2):
"""!
@brief Finds two nearest objects in two specified clusters and returns distance between them.
@param[in] (uint) Index of the first cluster.
@param[in] (uint) Index of the second cluster.
@return The nearest euclidean distance between two clusters.
"""
candidate_minimum_distance = float('Inf')
for index_object1 in self.__clusters[index_cluster1]:
for index_object2 in self.__clusters[index_cluster2]:
distance = euclidean_distance_square(self.__pointer_data[index_object1], self.__pointer_data[index_object2])
if distance < candidate_minimum_distance:
candidate_minimum_distance = distance
return candidate_minimum_distance
def __calculate_center(self, cluster):
"""!
@brief Calculates new center.
@return (list) New value of the center of the specified cluster.
"""
dimension = len(self.__pointer_data[cluster[0]])
center = [0] * dimension
for index_point in cluster:
for index_dimension in range(0, dimension):
center[index_dimension] += self.__pointer_data[index_point][index_dimension]
for index_dimension in range(0, dimension):
center[index_dimension] /= len(cluster)
return center
def __verify_arguments(self):
"""!
@brief Verify input parameters for the algorithm and throw exception in case of incorrectness.
"""
if len(self.__pointer_data) == 0:
raise ValueError("Input data is empty (size: '%d')." % len(self.__pointer_data))
if self.__number_clusters <= 0:
raise ValueError("Amount of cluster (current value: '%d') for allocation should be greater than 0." %
self.__number_clusters)
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