Prerequisites

• Lecture: "Biological and Artificial Neural Networks "
• Basic knowledge of the Mathematica environment (otherwise, see basic introduction to Mathematica in the description of Exercise 1 on Genetic Algorithms)

Overview

In this laboratory you will experiment with the class of artificial Neural Networks (NN) known as Self-Organizing Maps (SOM). The laboratory exercises are based on a Mathematica notebook. Download and open the notebook with Mathematica and then follow the instructions given for each exercise.

The Mathematica notebook for the exercise can be downloaded here.

Exercise 1: SOM basics

A detailed description of the exercise can downloaded here.

Exercise 2: The functions and parameters of the algorithm

detailed description of the exercise can downloaded here.

Exercise 3: The geometry of the input and output spaces

detailed description of the exercise can downloaded here.

Exercise 4: The training set

detailed description of the exercise can downloaded here.

Gallery: SOM Animations

LiveGraphics3D animations of the unfolding of a 3D, 2D, and 1D lattice in a 3D input space, with random uniform distribution of points in the input space. To show more clearly the initial ordering phase, the weights are randomly initialized to cover the whole input space, instead of being initially gathered in a small subpart of it.

3D lattice: 5x5x5

2D lattice: 5x20

2D lattice: 10x10

1D lattice: 150x

1D lattice: 100x

1D lattice: 100x