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Self Organizing Maps


Published on Nov 21, 2015

Abstract

These notes provide an introduction to unsupervised neural networks, in particular Kohonen self-organizing maps; together with some fundamental background material on statistical pattern recognition.

One question which seems to puzzle many of those who encounter unsupervised learning for the first time is how can anything useful be achieved when input information is simply poured into a black box with no provision of any rules as to how this information should be stored, or examples of the various groups into which this information can be placed. If the information is sorted on the basis of how similar one input is with another, then we will have accomplished an important step in condensing the available information by developing a more compact representation.

We can represent this information, and any subsequent information, in a much reduced fashion. We will know which information is more likely. This black box will certainly have learned. It may permit us to perceive some order in what otherwise was a mass of unrelated information to see the wood for the trees.

In any learning system, we need to make full use of the all the available data and to impose any constrains that we feel are justified. If we know that what groups the information must fall into, that certain combinations of inputs preclude others, or that certain rules underlie the production of the information then we must use them. Often, we do not possess such additional information. Consider two examples of experiments. One designed to test a particular hypothesis, say, to determine the effects of alcohol on driving; the second to investigate any possible connection between car accidents and the driver's lifestyle.

In the first experiment, we could arrange a laboratory-based experiment where volunteers took measured amounts of alcohol and then attempted some motor-skill activity (e.g., following a moving light on a computer screen by moving the mouse). We could collect the data (i.e., amount of alcohol vs. error rate on the computer test), conduct the customary statistical test and, finally, draw our conclusions. Our hypothesis may that the more alcohol consumed the greater the error rate we can confirm this on the basis of this experiment. Note, that we cannot prove the relationship only state that we are 99% certain (or whatever level we set ourselves) that the result is not due purely to chance.

The second experiment is much more open-ended (indeed, it could be argued that it is not really an experiment).Data is collected from a large number of drives those that have been involved in accidents and those that have not. This data could include the driver's age, occupation, health details, drinking habits, etc. From this mass of information, we can attempt to discover any possible connections. A number of conventional statistical tools exist to support this (e.g., factor analysis).

We may discover possible relationships including one between accidents and drinking but perhaps many others as well. There could be a number of leads that need following up. Both approaches are valid in searching for causes underlying road accidents. This second experiment can be considered as an example of unsupervised learning.

The next section provides some introductory background material on statistical pattern recognition. The terms and concepts will be useful in understanding the later material on unsupervised neural networks.

As the approach underlying unsupervised networks is the measurement of how similar (or different) various inputs are, we need to consider how the distances between these inputs are measured. This forms the basis Section Three, together with a brief description of non-neural approaches to unsupervised learning. Section Four discusses the background to and basic algorithm of Kohonen self-organizing maps. The next section details some of the properties of these maps and introduces several useful practical points. The final section provides pointers to further information on unsupervised neural networks.














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