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"""!
@brief Chaotic Neural Network
@details Implementation based on paper @cite article::nnet::cnn::1, @cite inproceedings::nnet::cnn::1.
@authors Andrei Novikov (pyclustering@yandex.ru)
@date 2014-2020
@copyright BSD-3-Clause
"""
import math
import numpy
import random
import matplotlib.pyplot as plt
from matplotlib import rcParams
from matplotlib.font_manager import FontProperties
from enum import IntEnum
from scipy.spatial import Delaunay
from pyclustering.utils import euclidean_distance_square, average_neighbor_distance, heaviside, draw_dynamics
class type_conn(IntEnum):
"""!
@brief Enumeration of connection types for Chaotic Neural Network.
@see cnn_network
"""
## All oscillators have connection with each other.
ALL_TO_ALL = 0,
## Connections between oscillators are created in line with Delaunay triangulation.
TRIANGULATION_DELAUNAY = 1,
class cnn_dynamic:
"""!
@brief Container of output dynamic of the chaotic neural network where states of each neuron during simulation are stored.
@see cnn_network
"""
def __init__(self, output=None, time=None):
"""!
@brief Costructor of the chaotic neural network output dynamic.
@param[in] output (list): Dynamic of oscillators on each step of simulation.
@param[in] time (list): Simulation time.
"""
## Output value of each neuron on each iteration.
self.output = output or []
## Sequence of simulation steps of the network.
self.time = time or []
def __len__(self):
"""!
@brief (uint) Returns amount of simulation steps that are stored.
"""
return len(self.output)
def allocate_observation_matrix(self):
"""!
@brief Allocates observation matrix in line with output dynamic of the network.
@details Matrix where state of each neuron is denoted by zero/one in line with Heaviside function on each iteration.
@return (list) Observation matrix of the network dynamic.
"""
number_neurons = len(self.output[0])
observation_matrix = []
for iteration in range(len(self.output)):
obervation_column = []
for index_neuron in range(number_neurons):
obervation_column.append(heaviside(self.output[iteration][index_neuron]))
observation_matrix.append(obervation_column)
return observation_matrix
def __allocate_neuron_patterns(self, start_iteration, stop_iteration):
"""!
@brief Allocates observation transposed matrix of neurons that is limited by specified periods of simulation.
@details Matrix where state of each neuron is denoted by zero/one in line with Heaviside function on each iteration.
@return (list) Transposed observation matrix that is limited by specified periods of simulation.
"""
pattern_matrix = []
for index_neuron in range(len(self.output[0])):
pattern_neuron = []
for iteration in range(start_iteration, stop_iteration):
pattern_neuron.append(heaviside(self.output[iteration][index_neuron]))
pattern_matrix.append(pattern_neuron)
return pattern_matrix
def allocate_sync_ensembles(self, steps):
"""!
@brief Allocate clusters in line with ensembles of synchronous neurons where each synchronous ensemble corresponds to only one cluster.
@param[in] steps (double): Amount of steps from the end that is used for analysis. During specified period chaotic neural network should have stable output
otherwise inccorect results are allocated.
@return (list) Grours (lists) of indexes of synchronous oscillators.
For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].
"""
iterations = steps
if iterations >= len(self.output):
iterations = len(self.output)
ensembles = []
start_iteration = len(self.output) - iterations
end_iteration = len(self.output)
pattern_matrix = self.__allocate_neuron_patterns(start_iteration, end_iteration)
ensembles.append( [0] )
for index_neuron in range(1, len(self.output[0])):
neuron_pattern = pattern_matrix[index_neuron][:]
neuron_assigned = False
for ensemble in ensembles:
ensemble_pattern = pattern_matrix[ensemble[0]][:]
if neuron_pattern == ensemble_pattern:
ensemble.append(index_neuron)
neuron_assigned = True
break
if neuron_assigned is False:
ensembles.append( [index_neuron] )
return ensembles
class cnn_visualizer:
"""!
@brief Visualizer of output dynamic of chaotic neural network (CNN).
"""
@staticmethod
def show_output_dynamic(cnn_output_dynamic):
"""!
@brief Shows output dynamic (output of each neuron) during simulation.
@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
@see show_dynamic_matrix
@see show_observation_matrix
"""
draw_dynamics(cnn_output_dynamic.time, cnn_output_dynamic.output, x_title="t", y_title="x")
@staticmethod
def show_dynamic_matrix(cnn_output_dynamic):
"""!
@brief Shows output dynamic as matrix in grey colors.
@details This type of visualization is convenient for observing allocated clusters.
@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
@see show_output_dynamic
@see show_observation_matrix
"""
network_dynamic = numpy.array(cnn_output_dynamic.output)
plt.imshow(network_dynamic.T, cmap=plt.get_cmap('gray'), interpolation='None', vmin=0.0, vmax=1.0)
plt.show()
@staticmethod
def show_observation_matrix(cnn_output_dynamic):
"""!
@brief Shows observation matrix as black/white blocks.
@details This type of visualization is convenient for observing allocated clusters.
@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
@see show_output_dynamic
@see show_dynamic_matrix
"""
observation_matrix = numpy.array(cnn_output_dynamic.allocate_observation_matrix())
plt.imshow(observation_matrix.T, cmap = plt.get_cmap('gray'), interpolation='None', vmin = 0.0, vmax = 1.0)
plt.show()
class cnn_network:
"""!
@brief Chaotic neural network based on system of logistic map where clustering phenomenon can be observed.
@details Here is an example how to perform cluster analysis using chaotic neural network:
@code
from pyclustering.cluster import cluster_visualizer
from pyclustering.samples.definitions import SIMPLE_SAMPLES
from pyclustering.utils import read_sample
from pyclustering.nnet.cnn import cnn_network, cnn_visualizer
# Load stimulus from file.
stimulus = read_sample(SIMPLE_SAMPLES.SAMPLE_SIMPLE3)
# Create chaotic neural network, amount of neurons should be equal to amount of stimulus.
network_instance = cnn_network(len(stimulus))
# Perform simulation during 100 steps.
steps = 100
output_dynamic = network_instance.simulate(steps, stimulus)
# Display output dynamic of the network.
cnn_visualizer.show_output_dynamic(output_dynamic)
# Display dynamic matrix and observation matrix to show clustering phenomenon.
cnn_visualizer.show_dynamic_matrix(output_dynamic)
cnn_visualizer.show_observation_matrix(output_dynamic)
# Visualize clustering results.
clusters = output_dynamic.allocate_sync_ensembles(10)
visualizer = cluster_visualizer()
visualizer.append_clusters(clusters, stimulus)
visualizer.show()
@endcode
"""
def __init__(self, num_osc, conn_type = type_conn.ALL_TO_ALL, amount_neighbors = 3):
"""!
@brief Constructor of chaotic neural network.
@param[in] num_osc (uint): Amount of neurons in the chaotic neural network.
@param[in] conn_type (type_conn): CNN type connection for the network.
@param[in] amount_neighbors (uint): k-nearest neighbors for calculation scaling constant of weights.
"""
self.__num_osc = num_osc
self.__conn_type = conn_type
self.__amount_neighbors = amount_neighbors
self.__average_distance = 0.0
self.__weights = None
self.__weights_summary = None
self.__location = None # just for network visualization
random.seed()
self.__output = [ random.random() for _ in range(num_osc) ]
def __len__(self):
"""!
@brief Returns size of the chaotic neural network that is defined by amount of neurons.
"""
return self.__num_osc
def simulate(self, steps, stimulus):
"""!
@brief Simulates chaotic neural network with extrnal stimulus during specified steps.
@details Stimulus are considered as a coordinates of neurons and in line with that weights
are initialized.
@param[in] steps (uint): Amount of steps for simulation.
@param[in] stimulus (list): Stimulus that are used for simulation.
@return (cnn_dynamic) Output dynamic of the chaotic neural network.
"""
self.__create_weights(stimulus)
self.__location = stimulus
dynamic = cnn_dynamic([], [])
dynamic.output.append(self.__output)
dynamic.time.append(0)
for step in range(1, steps, 1):
self.__output = self.__calculate_states()
dynamic.output.append(self.__output)
dynamic.time.append(step)
return dynamic
def __calculate_states(self):
"""!
@brief Calculates new state of each neuron.
@detail There is no any assignment.
@return (list) Returns new states (output).
"""
output = [ 0.0 for _ in range(self.__num_osc) ]
for i in range(self.__num_osc):
output[i] = self.__neuron_evolution(i)
return output
def __neuron_evolution(self, index):
"""!
@brief Calculates state of the neuron with specified index.
@param[in] index (uint): Index of neuron in the network.
@return (double) New output of the specified neuron.
"""
value = 0.0
for index_neighbor in range(self.__num_osc):
value += self.__weights[index][index_neighbor] * (1.0 - 2.0 * (self.__output[index_neighbor] ** 2))
return value / self.__weights_summary[index]
def __create_weights(self, stimulus):
"""!
@brief Create weights between neurons in line with stimulus.
@param[in] stimulus (list): External stimulus for the chaotic neural network.
"""
self.__average_distance = average_neighbor_distance(stimulus, self.__amount_neighbors)
self.__weights = [ [ 0.0 for _ in range(len(stimulus)) ] for _ in range(len(stimulus)) ]
self.__weights_summary = [ 0.0 for _ in range(self.__num_osc) ]
if self.__conn_type == type_conn.ALL_TO_ALL:
self.__create_weights_all_to_all(stimulus)
elif self.__conn_type == type_conn.TRIANGULATION_DELAUNAY:
self.__create_weights_delaunay_triangulation(stimulus)
def __create_weights_all_to_all(self, stimulus):
"""!
@brief Create weight all-to-all structure between neurons in line with stimulus.
@param[in] stimulus (list): External stimulus for the chaotic neural network.
"""
for i in range(len(stimulus)):
for j in range(i + 1, len(stimulus)):
weight = self.__calculate_weight(stimulus[i], stimulus[j])
self.__weights[i][j] = weight
self.__weights[j][i] = weight
self.__weights_summary[i] += weight
self.__weights_summary[j] += weight
def __create_weights_delaunay_triangulation(self, stimulus):
"""!
@brief Create weight Denlauny triangulation structure between neurons in line with stimulus.
@param[in] stimulus (list): External stimulus for the chaotic neural network.
"""
points = numpy.array(stimulus)
triangulation = Delaunay(points)
for triangle in triangulation.simplices:
for index_tri_point1 in range(len(triangle)):
for index_tri_point2 in range(index_tri_point1 + 1, len(triangle)):
index_point1 = triangle[index_tri_point1]
index_point2 = triangle[index_tri_point2]
weight = self.__calculate_weight(stimulus[index_point1], stimulus[index_point2])
self.__weights[index_point1][index_point2] = weight
self.__weights[index_point2][index_point1] = weight
self.__weights_summary[index_point1] += weight
self.__weights_summary[index_point2] += weight
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_square(stimulus1, stimulus2)
return math.exp(-distance / (2.0 * self.__average_distance))
def show_network(self):
"""!
@brief Shows structure of the network: neurons and connections between them.
"""
dimension = len(self.__location[0])
if (dimension != 3) and (dimension != 2):
raise NameError('Network that is located in different from 2-d and 3-d dimensions can not be represented')
(fig, axes) = self.__create_surface(dimension)
for i in range(0, self.__num_osc, 1):
if dimension == 2:
axes.plot(self.__location[i][0], self.__location[i][1], 'bo')
for j in range(i, self.__num_osc, 1): # draw connection between two points only one time
if self.__weights[i][j] > 0.0:
axes.plot([self.__location[i][0], self.__location[j][0]], [self.__location[i][1], self.__location[j][1]], 'b-', linewidth = 0.5)
elif dimension == 3:
axes.scatter(self.__location[i][0], self.__location[i][1], self.__location[i][2], c = 'b', marker = 'o')
for j in range(i, self.__num_osc, 1): # draw connection between two points only one time
if self.__weights[i][j] > 0.0:
axes.plot([self.__location[i][0], self.__location[j][0]], [self.__location[i][1], self.__location[j][1]], [self.__location[i][2], self.__location[j][2]], 'b-', linewidth = 0.5)
plt.grid()
plt.show()
def __create_surface(self, dimension):
"""!
@brief Prepares surface for showing network structure in line with specified dimension.
@param[in] dimension (uint): Dimension of processed data (external stimulus).
@return (tuple) Description of surface for drawing network structure.
"""
rcParams['font.sans-serif'] = ['Arial']
rcParams['font.size'] = 12
fig = plt.figure()
axes = None
if dimension == 2:
axes = fig.add_subplot(111)
elif dimension == 3:
axes = fig.gca(projection='3d')
surface_font = FontProperties()
surface_font.set_name('Arial')
surface_font.set_size('12')
return (fig, axes)
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