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"""!
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@brief Chaotic Neural Network
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@details Based on article description:
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- E.N.Benderskaya, S.V.Zhukova. Large-dimension image clustering by means of fragmentary synchronization in chaotic systems. 2007.
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- E.N.Benderskaya, S.V.Zhukova. Clustering by Chaotic Neural Networks with Mean Field Calculated Via Delaunay Triangulation. 2008.
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@authors Andrei Novikov ([email protected])
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@date 2014-2016
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@copyright GNU Public License
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@cond GNU_PUBLIC_LICENSE
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PyClustering is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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PyClustering is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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@endcond
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"""
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import matplotlib.pyplot as plt;
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import matplotlib.animation as animation;
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from matplotlib import rcParams;
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from matplotlib.font_manager import FontProperties;
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import math;
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import numpy;
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import random;
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from enum import IntEnum;
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from scipy.spatial import Delaunay;
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from pyclustering.utils import euclidean_distance_sqrt, average_neighbor_distance, heaviside, draw_dynamics;
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class type_conn(IntEnum):
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"""!
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@brief Enumeration of connection types for Chaotic Neural Network.
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@see cnn_network
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"""
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## All oscillators have connection with each other.
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ALL_TO_ALL = 0,
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## Connections between oscillators are created in line with Delaunay triangulation.
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TRIANGULATION_DELAUNAY = 1,
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class cnn_dynamic:
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"""!
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@brief Container of output dynamic of the chaotic neural network where states of each neuron during simulation are stored.
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@see cnn_network
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"""
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def __init__(self, output = [], time = []):
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"""!
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@brief Costructor of the chaotic neural network output dynamic.
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@param[in] phase (list): Dynamic of oscillators on each step of simulation.
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@param[in] time (list): Simulation time.
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"""
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## Output value of each neuron on each iteration.
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self.output = output;
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## Sequence of simulation steps of the network.
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self.time = time;
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def __len__(self):
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"""!
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@brief (uint) Returns amount of simulation steps that are stored.
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"""
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return len(self.output);
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View Code Duplication |
def allocate_observation_matrix(self):
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"""!
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@brief Allocates observation matrix in line with output dynamic of the network.
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@details Matrix where state of each neuron is denoted by zero/one in line with Heaviside function on each iteration.
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@return (list) Observation matrix of the network dynamic.
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"""
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number_neurons = len(self.output[0]);
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observation_matrix = [];
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for iteration in range(len(self.output)):
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obervation_column = [];
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for index_neuron in range(number_neurons):
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obervation_column.append(heaviside(self.output[iteration][index_neuron]));
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observation_matrix.append(obervation_column);
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return observation_matrix;
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View Code Duplication |
def __allocate_neuron_patterns(self, start_iteration, stop_iteration):
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"""!
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@brief Allocates observation transposed matrix of neurons that is limited by specified periods of simulation.
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@details Matrix where state of each neuron is denoted by zero/one in line with Heaviside function on each iteration.
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@return (list) Transposed observation matrix that is limited by specified periods of simulation.
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"""
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pattern_matrix = [];
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for index_neuron in range(len(self.output[0])):
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pattern_neuron = [];
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for iteration in range(start_iteration, stop_iteration):
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pattern_neuron.append(heaviside(self.output[iteration][index_neuron]))
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pattern_matrix.append(pattern_neuron);
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return pattern_matrix;
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def allocate_sync_ensembles(self, steps):
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"""!
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@brief Allocate clusters in line with ensembles of synchronous neurons where each synchronous ensemble corresponds to only one cluster.
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@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
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otherwise inccorect results are allocated.
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@return (list) Grours (lists) of indexes of synchronous oscillators.
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For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].
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"""
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iterations = steps;
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if (iterations >= len(self.output)):
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iterations = len(self.output);
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ensembles = [];
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start_iteration = len(self.output) - iterations;
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end_iteration = len(self.output);
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pattern_matrix = self.__allocate_neuron_patterns(start_iteration, end_iteration);
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ensembles.append( [0] );
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for index_neuron in range(1, len(self.output[0])):
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neuron_pattern = pattern_matrix[index_neuron][:];
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neuron_assigned = False;
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for ensemble in ensembles:
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ensemble_pattern = pattern_matrix[ensemble[0]][:];
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if (neuron_pattern == ensemble_pattern):
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ensemble.append(index_neuron);
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neuron_assigned = True;
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break;
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if (neuron_assigned is False):
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ensembles.append( [index_neuron] );
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return ensembles;
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class cnn_visualizer:
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"""!
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@brief Visualizer of output dynamic of chaotic neural network (CNN).
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"""
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@staticmethod
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def show_output_dynamic(cnn_output_dynamic):
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"""!
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@brief Shows output dynamic (output of each neuron) during simulation.
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@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
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@see show_dynamic_matrix
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@see show_observation_matrix
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"""
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draw_dynamics(cnn_output_dynamic.time, cnn_output_dynamic.output, x_title = "t", y_title = "x");
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@staticmethod
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def show_dynamic_matrix(cnn_output_dynamic):
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"""!
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@brief Shows output dynamic as matrix in grey colors.
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@details This type of visualization is convenient for observing allocated clusters.
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@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
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@see show_output_dynamic
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@see show_observation_matrix
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"""
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network_dynamic = numpy.array(cnn_output_dynamic.output);
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plt.imshow(network_dynamic.T, cmap = plt.get_cmap('gray'), interpolation='None', vmin = 0.0, vmax = 1.0);
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plt.show();
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@staticmethod
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def show_observation_matrix(cnn_output_dynamic):
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"""!
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@brief Shows observation matrix as black/white blocks.
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@details This type of visualization is convenient for observing allocated clusters.
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@param[in] cnn_output_dynamic (cnn_dynamic): Output dynamic of the chaotic neural network.
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@see show_output_dynamic
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@see show_dynamic_matrix
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"""
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observation_matrix = numpy.array(cnn_output_dynamic.allocate_observation_matrix());
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plt.imshow(observation_matrix.T, cmap = plt.get_cmap('gray'), interpolation='None', vmin = 0.0, vmax = 1.0);
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plt.show();
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class cnn_network:
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"""!
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@brief Chaotic neural network based on system of logistic map where clustering phenomenon can be observed.
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Example:
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@code
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# load stimulus from file
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stimulus = read_sample(SIMPLE_SAMPLES.SAMPLE_SIMPLE1);
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# create chaotic neural network, amount of neurons should be equal to amout of stimulus
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network_instance = cnn_network(len(stimulus));
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# simulate it during 100 steps
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output_dynamic = network_instance.simulate(steps, stimulus);
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# display output dynamic of the network
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cnn_visualizer.show_output_dynamic(output_dynamic);
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# dysplay dynamic matrix and observation matrix to show clustering
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# phenomenon.
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cnn_visualizer.show_dynamic_matrix(output_dynamic);
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cnn_visualizer.show_observation_matrix(output_dynamic);
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@endcode
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"""
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def __init__(self, num_osc, conn_type = type_conn.ALL_TO_ALL, amount_neighbors = 3):
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"""!
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@brief Constructor of chaotic neural network.
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@param[in] num_osc (uint): Amount of neurons in the chaotic neural network.
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@param[in] conn_type (type_conn): CNN type connection for the network.
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@param[in] amount_neighbors (uint): k-nearest neighbors for calculation scaling constant of weights.
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"""
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self.__num_osc = num_osc;
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self.__conn_type = conn_type;
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self.__amount_neighbors = amount_neighbors;
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self.__average_distance = 0.0;
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self.__weights = None;
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self.__weights_summary = None;
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self.__location = None; # just for network visualization
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random.seed();
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self.__output = [ random.random() for _ in range(num_osc) ];
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def __len__(self):
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"""!
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@brief Returns size of the chaotic neural network that is defined by amount of neurons.
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"""
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return self.__num_osc;
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def simulate(self, steps, stimulus):
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"""!
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@brief Simulates chaotic neural network with extrnal stimulus during specified steps.
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@details Stimulus are considered as a coordinates of neurons and in line with that weights
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are initialized.
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@param[in] steps (uint): Amount of steps for simulation.
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@param[in] stimulus (list): Stimulus that are used for simulation.
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303
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@return (cnn_dynamic) Output dynamic of the chaotic neural network.
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305
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"""
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self.__create_weights(stimulus);
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self.__location = stimulus;
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dynamic = cnn_dynamic([], []);
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dynamic.output.append(self.__output);
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312
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dynamic.time.append(0);
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314
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for step in range(1, steps, 1):
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self.__output = self.__calculate_states();
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dynamic.output.append(self.__output);
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dynamic.time.append(step);
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return dynamic;
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def __calculate_states(self):
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"""!
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325
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@brief Calculates new state of each neuron.
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@detail There is no any assignment.
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327
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328
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@return (list) Returns new states (output).
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330
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"""
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332
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output = [ 0.0 for _ in range(self.__num_osc) ];
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334
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for i in range(self.__num_osc):
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output[i] = self.__neuron_evolution(i);
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337
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return output;
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340
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def __neuron_evolution(self, index):
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341
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"""!
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342
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@brief Calculates state of the neuron with specified index.
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344
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@param[in] index (uint): Index of neuron in the network.
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345
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346
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@return (double) New output of the specified neuron.
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347
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348
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"""
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349
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value = 0.0;
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350
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351
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for index_neighbor in range(self.__num_osc):
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352
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value += self.__weights[index][index_neighbor] * (1.0 - 2.0 * (self.__output[index_neighbor] ** 2));
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353
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354
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return value / self.__weights_summary[index];
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355
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356
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357
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def __create_weights(self, stimulus):
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358
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"""!
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359
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@brief Create weights between neurons in line with stimulus.
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360
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361
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@param[in] stimulus (list): External stimulus for the chaotic neural network.
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362
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363
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"""
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364
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365
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self.__average_distance = average_neighbor_distance(stimulus, self.__amount_neighbors);
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366
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367
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self.__weights = [ [ 0.0 for _ in range(len(stimulus)) ] for _ in range(len(stimulus)) ];
|
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368
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self.__weights_summary = [ 0.0 for _ in range(self.__num_osc) ];
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369
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370
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if (self.__conn_type == type_conn.ALL_TO_ALL):
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371
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self.__create_weights_all_to_all(stimulus);
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372
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|
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373
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|
|
elif (self.__conn_type == type_conn.TRIANGULATION_DELAUNAY):
|
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374
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self.__create_weights_delaunay_triangulation(stimulus);
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375
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376
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377
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def __create_weights_all_to_all(self, stimulus):
|
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378
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"""!
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|
379
|
|
|
@brief Create weight all-to-all structure between neurons in line with stimulus.
|
|
380
|
|
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|
|
381
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|
|
@param[in] stimulus (list): External stimulus for the chaotic neural network.
|
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382
|
|
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|
|
383
|
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|
"""
|
|
384
|
|
|
|
|
385
|
|
|
for i in range(len(stimulus)):
|
|
386
|
|
|
for j in range(i + 1, len(stimulus)):
|
|
387
|
|
|
weight = self.__calculate_weight(stimulus[i], stimulus[j]);
|
|
388
|
|
|
|
|
389
|
|
|
self.__weights[i][j] = weight;
|
|
390
|
|
|
self.__weights[j][i] = weight;
|
|
391
|
|
|
|
|
392
|
|
|
self.__weights_summary[i] += weight;
|
|
393
|
|
|
self.__weights_summary[j] += weight;
|
|
394
|
|
|
|
|
395
|
|
|
|
|
396
|
|
|
def __create_weights_delaunay_triangulation(self, stimulus):
|
|
397
|
|
|
"""!
|
|
398
|
|
|
@brief Create weight Denlauny triangulation structure between neurons in line with stimulus.
|
|
399
|
|
|
|
|
400
|
|
|
@param[in] stimulus (list): External stimulus for the chaotic neural network.
|
|
401
|
|
|
|
|
402
|
|
|
"""
|
|
403
|
|
|
|
|
404
|
|
|
points = numpy.array(stimulus);
|
|
405
|
|
|
triangulation = Delaunay(points);
|
|
406
|
|
View Code Duplication |
|
|
|
|
|
|
|
407
|
|
|
for triangle in triangulation.simplices:
|
|
408
|
|
|
for index_tri_point1 in range(len(triangle)):
|
|
409
|
|
|
for index_tri_point2 in range(index_tri_point1 + 1, len(triangle)):
|
|
410
|
|
|
index_point1 = triangle[index_tri_point1];
|
|
411
|
|
|
index_point2 = triangle[index_tri_point2];
|
|
412
|
|
|
|
|
413
|
|
|
weight = self.__calculate_weight(stimulus[index_point1], stimulus[index_point2]);
|
|
414
|
|
|
|
|
415
|
|
|
self.__weights[index_point1][index_point2] = weight;
|
|
416
|
|
|
self.__weights[index_point2][index_point1] = weight;
|
|
417
|
|
|
|
|
418
|
|
|
self.__weights_summary[index_point1] += weight;
|
|
419
|
|
|
self.__weights_summary[index_point2] += weight;
|
|
420
|
|
|
|
|
421
|
|
|
|
|
422
|
|
|
def __calculate_weight(self, stimulus1, stimulus2):
|
|
423
|
|
|
"""!
|
|
424
|
|
|
@brief Calculate weight between neurons that have external stimulus1 and stimulus2.
|
|
425
|
|
|
|
|
426
|
|
|
@param[in] stimulus1 (list): External stimulus of the first neuron.
|
|
427
|
|
|
@param[in] stimulus2 (list): External stimulus of the second neuron.
|
|
428
|
|
|
|
|
429
|
|
|
@return (double) Weight between neurons that are under specified stimulus.
|
|
430
|
|
|
|
|
431
|
|
|
"""
|
|
432
|
|
|
|
|
433
|
|
|
distance = euclidean_distance_sqrt(stimulus1, stimulus2);
|
|
434
|
|
|
return math.exp(-distance / (2.0 * self.__average_distance));
|
|
435
|
|
|
|
|
436
|
|
|
|
|
437
|
|
|
def show_network(self):
|
|
438
|
|
|
"""!
|
|
439
|
|
|
@brief Shows structure of the network: neurons and connections between them.
|
|
440
|
|
|
|
|
441
|
|
|
"""
|
|
442
|
|
|
|
|
443
|
|
|
dimension = len(self.__location[0]);
|
|
444
|
|
|
if ( (dimension != 3) and (dimension != 2) ):
|
|
445
|
|
|
raise NameError('Network that is located in different from 2-d and 3-d dimensions can not be represented');
|
|
446
|
|
|
|
|
447
|
|
|
(fig, axes) = self.__create_surface(dimension);
|
|
|
|
|
|
|
448
|
|
|
|
|
449
|
|
|
for i in range(0, self.__num_osc, 1):
|
|
450
|
|
|
if (dimension == 2):
|
|
451
|
|
|
axes.plot(self.__location[i][0], self.__location[i][1], 'bo');
|
|
452
|
|
|
for j in range(i, self.__num_osc, 1): # draw connection between two points only one time
|
|
453
|
|
|
if (self.__weights[i][j] > 0.0):
|
|
454
|
|
|
axes.plot([self.__location[i][0], self.__location[j][0]], [self.__location[i][1], self.__location[j][1]], 'b-', linewidth = 0.5);
|
|
455
|
|
|
|
|
456
|
|
|
elif (dimension == 3):
|
|
457
|
|
|
axes.scatter(self.__location[i][0], self.__location[i][1], self.__location[i][2], c = 'b', marker = 'o');
|
|
458
|
|
|
|
|
459
|
|
|
for j in range(i, self._num_osc, 1): # draw connection between two points only one time
|
|
|
|
|
|
|
460
|
|
|
if (self.__weights[i][j] > 0.0):
|
|
461
|
|
|
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);
|
|
462
|
|
|
|
|
463
|
|
|
plt.grid();
|
|
464
|
|
|
plt.show();
|
|
465
|
|
|
|
|
466
|
|
|
|
|
467
|
|
|
def __create_surface(self, dimension):
|
|
468
|
|
|
"""!
|
|
469
|
|
|
@brief Prepares surface for showing network structure in line with specified dimension.
|
|
470
|
|
|
|
|
471
|
|
|
@param[in] dimension (uint): Dimension of processed data (external stimulus).
|
|
472
|
|
|
|
|
473
|
|
|
@return (tuple) Description of surface for drawing network structure.
|
|
474
|
|
|
|
|
475
|
|
|
"""
|
|
476
|
|
|
|
|
477
|
|
|
rcParams['font.sans-serif'] = ['Arial'];
|
|
478
|
|
|
rcParams['font.size'] = 12;
|
|
479
|
|
|
|
|
480
|
|
|
fig = plt.figure();
|
|
481
|
|
|
axes = None;
|
|
482
|
|
|
if (dimension == 2):
|
|
483
|
|
|
axes = fig.add_subplot(111);
|
|
484
|
|
|
elif (dimension == 3):
|
|
485
|
|
|
axes = fig.gca(projection='3d');
|
|
486
|
|
|
|
|
487
|
|
|
surface_font = FontProperties();
|
|
488
|
|
|
surface_font.set_name('Arial');
|
|
489
|
|
|
surface_font.set_size('12');
|
|
490
|
|
|
|
|
491
|
|
|
return (fig, axes); |
annoviko /
pyclustering
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