Prerequisite: ANN | Self Organizing Neural Network (SONN) Learning Algorithm
To implement a SONN, here are some essential consideration-
- Construct a Self Organizing Neural Network (SONN) or Kohonen Network with 100 neurons arranged in a 2-dimensional matrix with 10 rows and 10 columns
- Train the network with 1500 2-dimensional input vectors randomly generated in the interval between -1 and +1
- Select initial synaptic weights randomly in the same interval -1 and +1
- Assign learning rate parameter
is equal to 0.1
- Objective is to classify 2-dimensional input vectors such that each neuron in the network should respond only to the input vectors occurring in its region
- Test the performance of the self organizing neurons using the following Input vectors:
is equal to 0.1![\[$\mathbf{X}_{1}=\left[\begin{array}{ll}0.1 & 0.8\end{array}\right]^{\mathrm{T}}, \mathbf{X}_{2}=[0.5-0.2]^{\mathrm{T}}, \\ \mathbf{X}_{3}=[-0.8-0.9]^{\mathrm{T}}, \mathbf{X}_{4}=\left[\begin{array}{lll}-0.0 .6 & 0.9\end{array}\right]^{\mathrm{T}}$\]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-83f6cb0144757ceb3eae2c40a20c5218_l3-1.png "Rendered by QuickLaTeX.com")
Python Implementation of SONN:
# Importing Libraries import math from tqdm.notebook import tqdm import matplotlib.pyplot as plt import numpy as np # Generating Data : using uniform random number generator data_ = np.random.uniform(-1, 1, (1500, 2)) # print(data_.shape) # Hyperparameter Initialization x, y = 10, 10 # dimensions of Map sigma = 1. # spread of neighborhood learning_rate = 0.5 # learning rate epochs = 50000 # no of iterations decay_parameter = epochs / 2 # decay parameter # Activation map and Assigning Weights # using random number generation activation_map = np.zeros((x, y)) weights = 2 * (np.random.ranf((x, y, data_.shape[1])) - 0.5) # print(weights.shape) # Define Neighborhood Region neighbour_x = np.arange(x) neighbour_y = np.arange(y) # Function: decay_learning_rate_sigma def decay_learning_rate_sigma(iteration): learning_rate_ = learning_rate/(1 + iteration / decay_parameter) sigma_ = sigma / (1 + iteration / decay_parameter) return learning_rate_, sigma_ # Function: to get winner neuron def get_winner_neuron(x): s = np.subtract(x, weights) # x - w it = np.nditer(activation_map, flags =['multi_index']) while not it.finished: # || x - w || activation_map[it.multi_index] = np.linalg.norm(s[it.multi_index]) it.iternext() return np.unravel_index(activation_map.argmin(), activation_map.shape) # Update weights def update_weights(win_neuron, inputx, iteration): # decay learning rate and sigma learning_rate_, sigma_ = decay_learning_rate_sigma(iteration) # get neighborhood about winning neuron (Mexican hat function) d = 2 * np.pi * (sigma_**2) ax = np.exp(-1 * np.square(neighbour_x - win_neuron[0]) / d) ay = np.exp(-1 * np.square(neighbour_y - win_neuron[1]) / d) neighborhood = np.outer(ax, ay) it = np.nditer(neighborhood, flags = ['multi_index']) while not it.finished: weights[it.multi_index] += learning_rate_ * neighborhood[it.multi_index] * (inputx - weights[it.multi_index]) it.iternext() # Training model: Learning Phase for epoch in tqdm(range(1, epochs + 1)): np.random.shuffle(data_) idx = np.random.randint(0, data_.shape[0]) win_neuron = get_winner_neuron(data_[idx]) update_weights(win_neuron, data_[idx], epoch) if epoch == 1 or epoch == 100 == 0 or epoch == 1000 or epoch == 10000 or epoch == 50000: plot_x = [] plot_y = [] for i in range(weights.shape[0]): for j in range(weights.shape[1]): plot_x.append(weights[i][j][0]) plot_y.append(weights[i][j][1]) plt.title('After ' + str(epoch) + ' iterations') plt.scatter(plot_x, plot_y, c = 'r') plt.show() plt.close() |
Output:
# Testing the model performance test_inputs = np.array([[0.1, 0.8], [0.5, -0.2], [-0.8, -0.9], [-0.6, 0.9]]) # print(test_inputs.shape) # The plots below depict the working of this Kohonen Network on # given test inputs [0.1, 0.8], [0.5, -0.2], [-0.8, -0.9], [-0.6, 0.9] for i in range(test_inputs.shape[0]): test_input = test_inputs[i, :] win_neuron = get_winner_neuron(test_input) plot_x = np.arange(-1, 1, 0.1) plot_y = np.arange(-1, 1, 0.1) xx, yy = np.meshgrid(plot_x, plot_y) coordx, coordy = weights[win_neuron[0]][win_neuron[1]][0], weights[win_neuron[0]][win_neuron[1]][1] dist = math.sqrt((coordx-test_input[0])**2 + (coordy - test_input[1])**2) coordx = round(coordx, 1) coordy = round(coordy, 1) plt.figure(figsize =(20, 20)) plt.title("Distance between activated neuron and input = " + str(dist), fontsize = 30) plt.scatter(xx, yy, c = 'g') plt.scatter(coordx, coordy, c = 'r') plt.show() plt.close() |
Output:
All the 10×10 neurons are represented by green color. The nearest neuron which is activated by the test input is shown with red color. Here, the euclidean distances between activated neurons and test inputs are also shown in these plots. Respective neuron will respond for each of the test input vector samples.
