def templateDistanceCalculation(self, cluster1, cluster2, type_measurement):
entry1 = cfentry(len(cluster1), linear_sum(cluster1), square_sum(cluster1));
entry2 = cfentry(len(cluster2), linear_sum(cluster2), square_sum(cluster2));
# check that the same distance from 1 to 2 and from 2 to 1.
distance12 = entry1.get_distance(entry2, type_measurement);
distance21 = entry2.get_distance(entry1, type_measurement);
assert distance12 == distance21;
# check with utils calculation
float_delta = 0.0000001;
if (type_measurement == measurement_type.CENTROID_EUCLIDIAN_DISTANCE):
assert distance12 == euclidean_distance_sqrt(entry1.get_centroid(), entry2.get_centroid());
elif (type_measurement == measurement_type.CENTROID_MANHATTAN_DISTANCE):
assert distance12 == manhattan_distance(entry1.get_centroid(), entry2.get_centroid());
elif (type_measurement == measurement_type.AVERAGE_INTER_CLUSTER_DISTANCE):
assert numpy.isclose(distance12, average_inter_cluster_distance(cluster1, cluster2)) == True;
elif (type_measurement == measurement_type.AVERAGE_INTRA_CLUSTER_DISTANCE):
assert numpy.isclose(distance12, average_intra_cluster_distance(cluster1, cluster2)) == True;
elif (type_measurement == measurement_type.VARIANCE_INCREASE_DISTANCE):
assert numpy.isclose(distance12, variance_increase_distance(cluster1, cluster2)) == True;
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)):
# Find nearest objects
candidate_minimum_distance = float('Inf');
for index_object1 in self.__clusters[index_cluster1]:
for index_object2 in self.__clusters[index_cluster2]:
distance = euclidean_distance_sqrt(self.__pointer_data[index_object1], self.__pointer_data[index_object2]);
if (distance < candidate_minimum_distance):
candidate_minimum_distance = distance;
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 __update_clusters(self):
"""!
@brief Calculate Euclidean distance to each point from the each cluster. Nearest points are captured by according clusters and as a result clusters are updated.
@return (list) updated clusters as list of clusters. Each cluster contains indexes of objects from data.
"""
clusters = [[] for i in range(len(self.__centers))];
for index_point in range(len(self.__pointer_data)):
index_optim = -1;
dist_optim = 0.0;
for index in range(len(self.__centers)):
# dist = euclidean_distance(data[index_point], centers[index]); # Slow solution
dist = euclidean_distance_sqrt(self.__pointer_data[index_point], self.__centers[index]); # Fast solution
if ( (dist < dist_optim) or (index is 0)):
index_optim = index;
dist_optim = dist;
clusters[index_optim].append(index_point);
# If cluster is not able to capture object it should be removed
clusters = [cluster for cluster in clusters if len(cluster) > 0];
return clusters;
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 _ 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 __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 __update_clusters(self, medoids):
"""!
@brief Forms cluster in line with specified medoids by calculation distance from each point to medoids.
"""
self.__belong = [0] * len(self.__pointer_data)
self.__clusters = [[] for i in range(len(medoids))]
for index_point in range(len(self.__pointer_data)):
index_optim = -1
dist_optim = 0.0
for index in range(len(medoids)):
dist = euclidean_distance_sqrt(
self.__pointer_data[index_point],
self.__pointer_data[medoids[index]])
if ((dist < dist_optim) or (index is 0)):
index_optim = index
dist_optim = dist
self.__clusters[index_optim].append(index_point)
self.__belong[index_point] = index_optim
# If cluster is not able to capture object it should be removed
self.__clusters = [
cluster for cluster in self.__clusters if len(cluster) > 0
]
def __update_clusters(self):
"""!
@brief Calculate Manhattan 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 = [[] for i in range(len(self.__medians))]
for index_point in range(len(self.__pointer_data)):
index_optim = -1
dist_optim = 0.0
for index in range(len(self.__medians)):
dist = euclidean_distance_sqrt(
self.__pointer_data[index_point], self.__medians[index])
if ((dist < dist_optim) or (index is 0)):
index_optim = index
dist_optim = dist
clusters[index_optim].append(index_point)
# If cluster is not able to capture object it should be removed
clusters = [cluster for cluster in clusters if len(cluster) > 0]
return clusters
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 __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.__medoids))];
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.__medoids)):
dist = euclidean_distance_sqrt(self.__pointer_data[index_point], self.__medoids[index]);
if ( (dist < dist_optim) or (index is 0)):
index_optim = index;
dist_optim = dist;
clusters[index_optim].append(index_point);
return clusters;
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 get_distance_matrix(self):
"""!
@brief Calculates distance matrix (U-matrix).
@details The U-Matrix visualizes based on the distance in input space between a weight vector and its neighbors on map.
@return (list) Distance matrix (U-matrix).
@see show_distance_matrix()
@see get_density_matrix()
"""
if (self.__ccore_som_pointer is not None):
self._weights = wrapper.som_get_weights(self.__ccore_som_pointer)
if (self._conn_type != type_conn.func_neighbor):
self._neighbors = wrapper.som_get_neighbors(
self.__ccore_som_pointer)
distance_matrix = [[0.0] * self._cols for i in range(self._rows)]
for i in range(self._rows):
for j in range(self._cols):
neuron_index = i * self._cols + j
if (self._conn_type == type_conn.func_neighbor):
self._create_connections(type_conn.grid_eight)
for neighbor_index in self._neighbors[neuron_index]:
distance_matrix[i][j] += euclidean_distance_sqrt(
self._weights[neuron_index],
self._weights[neighbor_index])
distance_matrix[i][j] /= len(self._neighbors[neuron_index])
return distance_matrix
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_sqrt(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 get_distance_matrix(self):
"""!
@brief Calculates distance matrix (U-matrix).
@details The U-Matrix visualizes based on the distance in input space between a weight vector and its neighbors on map.
@return (list) Distance matrix (U-matrix).
@see show_distance_matrix()
@see get_density_matrix()
"""
if (self.__ccore_som_pointer is not None):
self._weights = wrapper.som_get_weights(self.__ccore_som_pointer);
if (self._conn_type != type_conn.func_neighbor):
self._neighbors = wrapper.som_get_neighbors(self.__ccore_som_pointer);
distance_matrix = [ [0.0] * self._cols for i in range(self._rows) ];
for i in range(self._rows):
for j in range(self._cols):
neuron_index = i * self._cols + j;
if (self._conn_type == type_conn.func_neighbor):
self._create_connections(type_conn.grid_eight);
for neighbor_index in self._neighbors[neuron_index]:
distance_matrix[i][j] += euclidean_distance_sqrt(self._weights[neuron_index], self._weights[neighbor_index]);
distance_matrix[i][j] /= len(self._neighbors[neuron_index]);
return distance_matrix;
def __recursive_nearest_nodes(self, point, distance, sqrt_distance, node, best_nodes):
"""!
@brief Returns list of neighbors such as tuple (distance, node) that is located in area that is covered by distance.
@param[in] point (list): Coordinates that is considered as centroind for searching
@param[in] distance (double): Distance from the center where seaching is performed.
@param[in] sqrt_distance (double): Square distance from the center where searching is performed.
@param[in] node (node): Node from that searching is performed.
@param[in|out] best_nodes (list): List of founded nodes.
"""
minimum = node.data[node.disc] - distance;
maximum = node.data[node.disc] + distance;
if (node.right is not None):
if (point[node.disc] >= minimum):
self.__recursive_nearest_nodes(point, distance, sqrt_distance, node.right, best_nodes);
if (node.left is not None):
if (point[node.disc] < maximum):
self.__recursive_nearest_nodes(point, distance, sqrt_distance, node.left, best_nodes);
candidate_distance = euclidean_distance_sqrt(point, node.data);
if (candidate_distance <= sqrt_distance):
best_nodes.append( (candidate_distance, node) );
def process(self):
"""!
@brief Performs cluster analysis in line with rules of K-Means algorithm.
@remark Results of clustering can be obtained using corresponding get methods.
@see get_clusters()
@see get_centers()
"""
if (self.__ccore is True):
self.__clusters = wrapper.kmeans(self.__pointer_data, self.__centers, self.__tolerance);
self.__centers = self.__update_centers();
else:
changes = float('inf');
stop_condition = self.__tolerance * self.__tolerance; # Fast solution
#stop_condition = self.__tolerance; # Slow solution
# Check for dimension
if (len(self.__pointer_data[0]) != len(self.__centers[0])):
raise NameError('Dimension of the input data and dimension of the initial cluster centers must be equal.');
while (changes > stop_condition):
self.__clusters = self.__update_clusters();
updated_centers = self.__update_centers(); # changes should be calculated before asignment
#changes = max([euclidean_distance(self.__centers[index], updated_centers[index]) for index in range(len(self.__centers))]); # Slow solution
changes = max([euclidean_distance_sqrt(self.__centers[index], updated_centers[index]) for index in range(len(updated_centers))]); # Fast solution
self.__centers = updated_centers;
def templateDistanceCalculation(self, cluster1, cluster2, type_measurement):
entry1 = cfentry(len(cluster1), linear_sum(cluster1), square_sum(cluster1));
entry2 = cfentry(len(cluster2), linear_sum(cluster2), square_sum(cluster2));
# check that the same distance from 1 to 2 and from 2 to 1.
distance12 = entry1.get_distance(entry2, type_measurement);
distance21 = entry2.get_distance(entry1, type_measurement);
assert distance12 == distance21;
# check with utils calculation
float_delta = 0.0000001;
if (type_measurement == measurement_type.CENTROID_EUCLIDIAN_DISTANCE):
assert distance12 == euclidean_distance_sqrt(entry1.get_centroid(), entry2.get_centroid());
elif (type_measurement == measurement_type.CENTROID_MANHATTAN_DISTANCE):
assert distance12 == manhattan_distance(entry1.get_centroid(), entry2.get_centroid());
elif (type_measurement == measurement_type.AVERAGE_INTER_CLUSTER_DISTANCE):
assert numpy.isclose(distance12, average_inter_cluster_distance(cluster1, cluster2)) == True;
elif (type_measurement == measurement_type.AVERAGE_INTRA_CLUSTER_DISTANCE):
assert numpy.isclose(distance12, average_intra_cluster_distance(cluster1, cluster2)) == True;
elif (type_measurement == measurement_type.VARIANCE_INCREASE_DISTANCE):
assert numpy.isclose(distance12, variance_increase_distance(cluster1, cluster2)) == True;
def get_distance(self, entry, type_measurement):
"""!
@brief Calculates distance between two clusters in line with measurement type.
@details In case of usage CENTROID_EUCLIDIAN_DISTANCE square euclidian distance will be returned.
Square root should be taken from the result for obtaining real euclidian distance between
entries.
@param[in] entry (cfentry): Clustering feature to which distance should be obtained.
@param[in] type_measurement (measurement_type): Distance measurement algorithm between two clusters.
@return (double) Distance between two clusters.
"""
if (type_measurement is measurement_type.CENTROID_EUCLIDIAN_DISTANCE):
return euclidean_distance_sqrt(entry.get_centroid(), self.get_centroid());
elif (type_measurement is measurement_type.CENTROID_MANHATTAN_DISTANCE):
return manhattan_distance(entry.get_centroid(), self.get_centroid());
elif (type_measurement is measurement_type.AVERAGE_INTER_CLUSTER_DISTANCE):
return self.__get_average_inter_cluster_distance(entry);
elif (type_measurement is measurement_type.AVERAGE_INTRA_CLUSTER_DISTANCE):
return self.__get_average_intra_cluster_distance(entry);
elif (type_measurement is measurement_type.VARIANCE_INCREASE_DISTANCE):
return self.__get_variance_increase_distance(entry);
else:
assert 0;
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_sqrt(
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])
def __recursive_nearest_nodes(self, point, distance, sqrt_distance,
node_head, best_nodes):
"""!
@brief Returns list of neighbors such as tuple (distance, node) that is located in area that is covered by distance.
@param[in] point (list): Coordinates that is considered as centroind for searching
@param[in] distance (double): Distance from the center where seaching is performed.
@param[in] sqrt_distance (double): Square distance from the center where searching is performed.
@param[in] node_head (node): Node from that searching is performed.
@param[in|out] best_nodes (list): List of founded nodes.
"""
if (node_head.right is not None):
minimum = node_head.data[node_head.disc] - distance
if (point[node_head.disc] >= minimum):
self.__recursive_nearest_nodes(point, distance, sqrt_distance,
node_head.right, best_nodes)
if (node_head.left is not None):
maximum = node_head.data[node_head.disc] + distance
if (point[node_head.disc] < maximum):
self.__recursive_nearest_nodes(point, distance, sqrt_distance,
node_head.left, best_nodes)
candidate_distance = euclidean_distance_sqrt(point, node_head.data)
if (candidate_distance <= sqrt_distance):
best_nodes.append((candidate_distance, node_head))
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)):
# Find nearest objects
candidate_minimum_distance = float('Inf');
for index_object1 in self.__clusters[index_cluster1]:
for index_object2 in self.__clusters[index_cluster2]:
distance = euclidean_distance_sqrt(self.__pointer_data[index_object1], self.__pointer_data[index_object2]);
if (distance < candidate_minimum_distance):
candidate_minimum_distance = distance;
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 __update_clusters(self):
"""!
@brief Calculate Manhattan 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 = [[] for i in range(len(self.__medians))];
for index_point in range(len(self.__pointer_data)):
index_optim = -1;
dist_optim = 0.0;
for index in range(len(self.__medians)):
dist = euclidean_distance_sqrt(self.__pointer_data[index_point], self.__medians[index]);
if ( (dist < dist_optim) or (index is 0)):
index_optim = index;
dist_optim = dist;
clusters[index_optim].append(index_point);
# If cluster is not able to capture object it should be removed
clusters = [cluster for cluster in clusters if len(cluster) > 0];
return clusters;
def get_distance(self, entry, type_measurement):
"""!
@brief Calculates distance between two clusters in line with measurement type.
@param[in] entry (cfentry): Clustering feature to which distance should be obtained.
@param[in] type_measurement (measurement_type): Distance measurement algorithm between two clusters.
@return (double) Distance between two clusters.
"""
if (type_measurement is measurement_type.CENTROID_EUCLIDIAN_DISTANCE):
return euclidean_distance_sqrt(entry.get_centroid(), self.get_centroid());
elif (type_measurement is measurement_type.CENTROID_MANHATTAN_DISTANCE):
return manhattan_distance(entry.get_centroid(), self.get_centroid());
elif (type_measurement is measurement_type.AVERAGE_INTER_CLUSTER_DISTANCE):
return self.__get_average_inter_cluster_distance(entry);
elif (type_measurement is measurement_type.AVERAGE_INTRA_CLUSTER_DISTANCE):
return self.__get_average_intra_cluster_distance(entry);
elif (type_measurement is measurement_type.VARIANCE_INCREASE_DISTANCE):
return self.__get_variance_increase_distance(entry);
else:
assert 0;
def process(self):
"""!
@brief Performs cluster analysis in line with rules of K-Medoids algorithm.
@remark Results of clustering can be obtained using corresponding get methods.
@see get_clusters()
@see get_medoids()
"""
if (self.__ccore is True):
self.__clusters = wrapper.kmedoids(self.__pointer_data, self.__medoid_indexes, self.__tolerance);
self.__medoids, self.__medoid_indexes = self.__update_medoids();
else:
changes = float('inf');
stop_condition = self.__tolerance * self.__tolerance; # Fast solution
#stop_condition = self.__tolerance; # Slow solution
while (changes > stop_condition):
self.__clusters = self.__update_clusters();
updated_medoids, update_medoid_indexes = self.__update_medoids(); # changes should be calculated before asignment
changes = max([euclidean_distance_sqrt(self.__medoids[index], updated_medoids[index]) for index in range(len(updated_medoids))]); # Fast solution
self.__medoids = updated_medoids;
self.__medoid_indexes = update_medoid_indexes;
def process(self):
"""!
@brief Performs cluster analysis in line with rules of K-Medians algorithm.
@remark Results of clustering can be obtained using corresponding get methods.
@see get_clusters()
@see get_medians()
"""
changes = float('inf');
stop_condition = self.__tolerance * self.__tolerance; # Fast solution
#stop_condition = self.__tolerance; # Slow solution
# Check for dimension
if (len(self.__pointer_data[0]) != len(self.__medians[0])):
raise NameError('Dimension of the input data and dimension of the initial cluster medians must be equal.');
while (changes > stop_condition):
self.__clusters = self.__update_clusters();
updated_centers = self.__update_medians(); # changes should be calculated before asignment
changes = max([euclidean_distance_sqrt(self.__medians[index], updated_centers[index]) for index in range(len(updated_centers))]); # Fast solution
self.__medians = updated_centers;
def __init__(self, rows, cols, conn_type = type_conn.grid_eight, parameters = None, ccore = False):
"""!
@brief Constructor of self-organized map.
@param[in] rows (uint): Number of neurons in the column (number of rows).
@param[in] cols (uint): Number of neurons in the row (number of columns).
@param[in] conn_type (type_conn): Type of connection between oscillators in the network (grid four, grid eight, honeycomb, function neighbour).
@param[in] parameters (som_parameters): Other specific parameters.
@param[in] ccore (bool): If True simulation is performed by CCORE library (C++ implementation of pyclustering).
"""
# some of these parameters are required despite core implementation, for example, for network demonstration.
self._cols = cols;
self._rows = rows;
self._size = cols * rows;
self._conn_type = conn_type;
if (parameters is not None):
self._params = parameters;
else:
self._params = som_parameters();
if (self._params.init_radius is None):
if ((cols + rows) / 4.0 > 1.0):
self._params.init_radius = 2.0;
elif ( (cols > 1) and (rows > 1) ):
self._params.init_radius = 1.5;
else:
self._params.init_radius = 1.0;
if (ccore is True):
self.__ccore_som_pointer = wrapper.som_create(rows, cols, conn_type, self._params);
else:
# location
self._location = list();
for i in range(self._rows):
for j in range(self._cols):
self._location.append([float(i), float(j)]);
# awards
self._award = [0] * self._size;
self._capture_objects = [ [] for i in range(self._size) ];
# distances
self._sqrt_distances = [ [ [] for i in range(self._size) ] for j in range(self._size) ];
for i in range(self._size):
for j in range(i, self._size, 1):
dist = euclidean_distance_sqrt(self._location[i], self._location[j]);
self._sqrt_distances[i][j] = dist;
self._sqrt_distances[j][i] = dist;
# connections
if (conn_type != type_conn.func_neighbor):
self._create_connections(conn_type);
def _competition(self, x):
"""!
@brief Calculates neuron winner (distance, neuron index).
@param[in] x (list): Input pattern from the input data set, for example it can be coordinates of point.
@return (uint) Returns index of neuron that is winner.
"""
index = 0;
minimum = euclidean_distance_sqrt(self._weights[0], x);
for i in range(1, self._size, 1):
candidate = euclidean_distance_sqrt(self._weights[i], x);
if (candidate < minimum):
index = i;
minimum = candidate;
return index;
def _competition(self, x):
"""!
@brief Calculates neuron winner (distance, neuron index).
@param[in] x (list): Input pattern from the input data set, for example it can be coordinates of point.
@return (uint) Returns index of neuron that is winner.
"""
index = 0
minimum = euclidean_distance_sqrt(self._weights[0], x)
for i in range(1, self._size, 1):
candidate = euclidean_distance_sqrt(self._weights[i], x)
if (candidate < minimum):
index = i
minimum = candidate
return index
def __neighbor_indexes(self, point):
"""!
@brief Return list of indexes of neighbors of specified point for the data.
@param[in] point (list): An index of a point for which potential neighbors should be returned in line with connectivity radius.
@return (list) Return list of indexes of neighbors in line the connectivity radius.
"""
# return [i for i in range(0, len(data)) if euclidean_distance(data[point], data[i]) <= eps and data[i] != data[point]]; # Slow mode
return [i for i in range(0, len(self.__pointer_data)) if euclidean_distance_sqrt(self.__pointer_data[point], self.__pointer_data[i]) <= self.__sqrt_eps and self.__pointer_data[i] != self.__pointer_data[point]]; # Fast mode
def __calculate_weight(self, stimulus1, stimulus2):
"""!
@brief Calculate weight between neurons that have external stimulus1 and stimulus2.
@param[in] stimulus1 (list): External stimulus of the first neuron.
@param[in] stimulus2 (list): External stimulus of the second neuron.
@return (double) Weight between neurons that are under specified stimulus.
"""
distance = euclidean_distance_sqrt(stimulus1, stimulus2)
return math.exp(-distance / (2.0 * self.__average_distance))
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)
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 = 0.0
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])
Wi = 0.0
for index_object in clusters[index_cluster]:
Wi += euclidean_distance_sqrt(
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 __calculate_estimation(self):
"""!
@brief Calculates estimation (cost) of the current clusters. The lower the estimation,
the more optimally configuration of clusters.
@return (double) estimation of current clusters.
"""
estimation = 0.0;
for index_cluster in range(0, len(self.__clusters)):
cluster = self.__clusters[index_cluster];
index_medoid = self.__current[index_cluster];
for index_point in cluster:
estimation += euclidean_distance_sqrt(self.__pointer_data[index_point], self.__pointer_data[index_medoid]);
return estimation;
def __calculate_estimation(self):
"""!
@brief Calculates estimation (cost) of the current clusters. The lower the estimation,
the more optimally configuration of clusters.
@return (double) estimation of current clusters.
"""
estimation = 0.0;
for index_cluster in range(0, len(self.__clusters)):
cluster = self.__clusters[index_cluster];
index_medoid = self.__current[index_cluster];
for index_point in cluster:
estimation += euclidean_distance_sqrt(self.__pointer_data[index_point], self.__pointer_data[index_medoid]);
return estimation;
def __neighbor_indexes(self, point):
"""!
@brief Return list of indexes of neighbors of specified point for the data.
@param[in] point (list): An index of a point for which potential neighbors should be returned in line with connectivity radius.
@return (list) Return list of indexes of neighbors in line the connectivity radius.
"""
# return [i for i in range(0, len(data)) if euclidean_distance(data[point], data[i]) <= eps and data[i] != data[point]]; # Slow mode
return [
i for i in range(0, len(self.__pointer_data))
if euclidean_distance_sqrt(self.__pointer_data[point], self.
__pointer_data[i]) <= self.__sqrt_eps
and (i != point)
]
def __initialize_distances(self, size, location):
"""!
@brief Initialize distance matrix in SOM grid.
@param[in] size (uint): Amount of neurons in the network.
@param[in] location (list): List of coordinates of each neuron in the network.
@return (list) Distance matrix between neurons in the network.
"""
sqrt_distances = [[[] for i in range(size)] for j in range(size)]
for i in range(size):
for j in range(i, size, 1):
dist = euclidean_distance_sqrt(location[i], location[j])
sqrt_distances[i][j] = dist
sqrt_distances[j][i] = dist
return sqrt_distances
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_sqrt(self.__pointer_data[index_object1], self.__pointer_data[index_object2]);
if (distance < candidate_minimum_distance):
candidate_minimum_distance = distance;
return candidate_minimum_distance;
def __find_another_nearest_medoid(self, point_index, current_medoid_index):
"""!
@brief Finds the another nearest medoid for the specified point that is differ from the specified medoid.
@param[in] point_index: index of point in dataspace for that searching of medoid in current list of medoids is perfomed.
@param[in] current_medoid_index: index of medoid that shouldn't be considered as a nearest.
@return (uint) index of the another nearest medoid for the point.
"""
other_medoid_index = -1;
other_distance_nearest = float('inf');
for index_medoid in self.__current:
if (index_medoid != current_medoid_index):
other_distance_candidate = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[current_medoid_index]);
if (other_distance_candidate < other_distance_nearest):
other_distance_nearest = other_distance_candidate;
other_medoid_index = index_medoid;
return other_medoid_index;
def __has_object_connection(self, oscillator_index1, oscillator_index2):
"""!
@brief Searches for pair of objects that are encoded by specified neurons and that are connected in line with connectivity radius.
@param[in] oscillator_index1 (uint): Index of the first oscillator in the second layer.
@param[in] oscillator_index2 (uint): Index of the second oscillator in the second layer.
@return (bool) True - if there is pair of connected objects encoded by specified oscillators.
"""
som_neuron_index1 = self._som_osc_table[oscillator_index1]
som_neuron_index2 = self._som_osc_table[oscillator_index2]
for index_object1 in self._som.capture_objects[som_neuron_index1]:
for index_object2 in self._som.capture_objects[som_neuron_index2]:
distance = euclidean_distance_sqrt(self._data[index_object1],
self._data[index_object2])
if (distance <= self._radius):
return True
return False
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_sqrt(
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_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_sqrt(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 __find_another_nearest_medoid(self, point_index, current_medoid_index):
"""!
@brief Finds the another nearest medoid for the specified point that is differ from the specified medoid.
@param[in] point_index: index of point in dataspace for that searching of medoid in current list of medoids is perfomed.
@param[in] current_medoid_index: index of medoid that shouldn't be considered as a nearest.
@return (uint) index of the another nearest medoid for the point.
"""
other_medoid_index = -1;
other_distance_nearest = float('inf');
for index_medoid in self.__current:
if (index_medoid != current_medoid_index):
other_distance_candidate = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[current_medoid_index]);
if (other_distance_candidate < other_distance_nearest):
other_distance_nearest = other_distance_candidate;
other_medoid_index = index_medoid;
return other_medoid_index;
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_sqrt(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 __calculate_initial_clusters(self, centers):
"""!
@brief Calculate Euclidean distance to each point from the each cluster.
@brief Nearest points are captured by according clusters and as a result clusters are updated.
@return (list) updated clusters as list of clusters. Each cluster contains indexes of objects from data.
"""
clusters = [[] for _ in range(len(centers))];
for index_point in range(len(self.__sample)):
index_optim, dist_optim = -1, 0.0;
for index in range(len(centers)):
dist = euclidean_distance_sqrt(self.__sample[index_point], centers[index]);
if ( (dist < dist_optim) or (index is 0)):
index_optim, dist_optim = index, dist;
clusters[index_optim].append(index_point);
return clusters;
def __update_clusters(self, medoids):
"""!
@brief Forms cluster in line with specified medoids by calculation distance from each point to medoids.
"""
self.__belong = [0] * len(self.__pointer_data);
self.__clusters = [[] for i in range(len(medoids))];
for index_point in range(len(self.__pointer_data)):
index_optim = -1;
dist_optim = 0.0;
for index in range(len(medoids)):
dist = euclidean_distance_sqrt(self.__pointer_data[index_point], self.__pointer_data[medoids[index]]);
if ( (dist < dist_optim) or (index is 0)):
index_optim = index;
dist_optim = dist;
self.__clusters[index_optim].append(index_point);
self.__belong[index_point] = index_optim;
# If cluster is not able to capture object it should be removed
self.__clusters = [cluster for cluster in self.__clusters if len(cluster) > 0];
def process(self):
"""!
@brief Performs cluster analysis in line with rules of K-Medoids algorithm.
@remark Results of clustering can be obtained using corresponding get methods.
@see get_clusters()
@see get_medoids()
"""
changes = float('inf')
stop_condition = self.__tolerance * self.__tolerance
# Fast solution
#stop_condition = self.__tolerance; # Slow solution
# Check for dimension
if (len(self.__pointer_data[0]) != len(self.__medoids[0])):
raise NameError(
'Dimension of the input data and dimension of the initial cluster medians must be equal.'
)
while (changes > stop_condition):
self.__clusters = self.__update_clusters()
updated_medoids = self.__update_medoids()
# changes should be calculated before asignment
changes = max([
euclidean_distance_sqrt(self.__medoids[index],
updated_medoids[index])
for index in range(len(updated_medoids))
])
# Fast solution
self.__medoids = updated_medoids
def __optimize_configuration(self):
"""!
@brief Finds quasi-optimal medoids and updates in line with them clusters in line with algorithm's rules.
"""
index_neighbor = 0;
while (index_neighbor < self.__maxneighbor):
# get random current medoid that is to be replaced
current_medoid_index = self.__current[random.randint(0, self.__number_clusters - 1)];
current_medoid_cluster_index = self.__belong[current_medoid_index];
# get new candidate to be medoid
candidate_medoid_index = random.randint(0, len(self.__pointer_data) - 1);
candidate_medoid_cluster_index = self.__belong[candidate_medoid_index];
while (candidate_medoid_index in self.__current):
candidate_medoid_index = random.randint(0, len(self.__pointer_data) - 1);
candidate_cost = 0.0;
for point_index in range(0, len(self.__pointer_data)):
if (point_index not in self.__current):
# get non-medoid point and its medoid
point_cluster_index = self.__belong[point_index];
point_medoid_index = self.__current[point_cluster_index];
# get other medoid that is nearest to the point (except current and candidate)
other_medoid_index = self.__find_another_nearest_medoid(point_index, current_medoid_index);
other_medoid_cluster_index = self.__belong[other_medoid_index];
# for optimization calculate all required distances
# from the point to current medoid
distance_current = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[current_medoid_index]);
# from the point to candidate median
distance_candidate = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[candidate_medoid_index]);
# from the point to nearest (own) medoid
distance_nearest = float('inf');
if ( (point_medoid_index != candidate_medoid_index) and (point_medoid_index != current_medoid_cluster_index) ):
distance_nearest = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[point_medoid_index]);
# apply rules for cost calculation
if (point_cluster_index == current_medoid_cluster_index):
# case 1:
if (distance_candidate >= distance_nearest):
candidate_cost += distance_nearest - distance_current;
# case 2:
else:
candidate_cost += distance_candidate - distance_current;
elif (point_cluster_index == other_medoid_cluster_index):
# case 3 ('nearest medoid' is the representative object of that cluster and object is more similar to 'nearest' than to 'candidate'):
if (distance_candidate > distance_nearest):
pass;
# case 4:
else:
candidate_cost += distance_candidate - distance_nearest;
if (candidate_cost < 0):
# set candidate that has won
self.__current[current_medoid_cluster_index] = candidate_medoid_index;
# recalculate clusters
self.__update_clusters(self.__current);
# reset iterations and starts investigation from the begining
index_neighbor = 0;
else:
index_neighbor += 1;
def __init__(self,
rows,
cols,
conn_type=type_conn.grid_eight,
parameters=None,
ccore=False):
"""!
@brief Constructor of self-organized map.
@param[in] rows (uint): Number of neurons in the column (number of rows).
@param[in] cols (uint): Number of neurons in the row (number of columns).
@param[in] conn_type (type_conn): Type of connection between oscillators in the network (grid four, grid eight, honeycomb, function neighbour).
@param[in] parameters (som_parameters): Other specific parameters.
@param[in] ccore (bool): If True simulation is performed by CCORE library (C++ implementation of pyclustering).
"""
# some of these parameters are required despite core implementation, for example, for network demonstration.
self._cols = cols
self._rows = rows
self._size = cols * rows
self._conn_type = conn_type
if (parameters is not None):
self._params = parameters
else:
self._params = som_parameters()
if (self._params.init_radius is None):
if ((cols + rows) / 4.0 > 1.0):
self._params.init_radius = 2.0
elif ((cols > 1) and (rows > 1)):
self._params.init_radius = 1.5
else:
self._params.init_radius = 1.0
if (ccore is True):
self.__ccore_som_pointer = wrapper.som_create(
rows, cols, conn_type, self._params)
else:
# location
self._location = list()
for i in range(self._rows):
for j in range(self._cols):
self._location.append([float(i), float(j)])
# awards
self._award = [0] * self._size
self._capture_objects = [[] for i in range(self._size)]
# distances
self._sqrt_distances = [[[] for i in range(self._size)]
for j in range(self._size)]
for i in range(self._size):
for j in range(i, self._size, 1):
dist = euclidean_distance_sqrt(self._location[i],
self._location[j])
self._sqrt_distances[i][j] = dist
self._sqrt_distances[j][i] = dist
# connections
if (conn_type != type_conn.func_neighbor):
self._create_connections(conn_type)
def __optimize_configuration(self):
"""!
@brief Finds quasi-optimal medoids and updates in line with them clusters in line with algorithm's rules.
"""
index_neighbor = 0;
while (index_neighbor < self.__maxneighbor):
# get random current medoid that is to be replaced
current_medoid_index = self.__current[random.randint(0, self.__number_clusters - 1)];
current_medoid_cluster_index = self.__belong[current_medoid_index];
# get new candidate to be medoid
candidate_medoid_index = random.randint(0, len(self.__pointer_data) - 1);
while (candidate_medoid_index in self.__current):
candidate_medoid_index = random.randint(0, len(self.__pointer_data) - 1);
candidate_cost = 0.0;
for point_index in range(0, len(self.__pointer_data)):
if (point_index not in self.__current):
# get non-medoid point and its medoid
point_cluster_index = self.__belong[point_index];
point_medoid_index = self.__current[point_cluster_index];
# get other medoid that is nearest to the point (except current and candidate)
other_medoid_index = self.__find_another_nearest_medoid(point_index, current_medoid_index);
other_medoid_cluster_index = self.__belong[other_medoid_index];
# for optimization calculate all required distances
# from the point to current medoid
distance_current = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[current_medoid_index]);
# from the point to candidate median
distance_candidate = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[candidate_medoid_index]);
# from the point to nearest (own) medoid
distance_nearest = float('inf');
if ( (point_medoid_index != candidate_medoid_index) and (point_medoid_index != current_medoid_cluster_index) ):
distance_nearest = euclidean_distance_sqrt(self.__pointer_data[point_index], self.__pointer_data[point_medoid_index]);
# apply rules for cost calculation
if (point_cluster_index == current_medoid_cluster_index):
# case 1:
if (distance_candidate >= distance_nearest):
candidate_cost += distance_nearest - distance_current;
# case 2:
else:
candidate_cost += distance_candidate - distance_current;
elif (point_cluster_index == other_medoid_cluster_index):
# case 3 ('nearest medoid' is the representative object of that cluster and object is more similar to 'nearest' than to 'candidate'):
if (distance_candidate > distance_nearest):
pass;
# case 4:
else:
candidate_cost += distance_candidate - distance_nearest;
if (candidate_cost < 0):
# set candidate that has won
self.__current[current_medoid_cluster_index] = candidate_medoid_index;
# recalculate clusters
self.__update_clusters(self.__current);
# reset iterations and starts investigation from the begining
index_neighbor = 0;
else:
index_neighbor += 1;