# Self Organizing Map (SOM)

October 23, 2017

### What is Self Organizing Map (SOM)

A neural network is called a mapping network if it is able to compute some functional relationship between its input and its output. For example if the input to a network is the value of an angle and the output is the cosine of that angle, the network perform the mapping θ =cos (θ). For such a simple function, we do not need a Neural Network. However we might want to perform a complicated mapping where does not know how to describe the functional relationship in advance, but we do know of examples of the correct mapping. In this situation, Neural Network is applicable to discover its own algorithms which is extremely useful.

### Self Organizing Map: Overview

The SOM algorithm is based on unsupervised, competitive learning. It provides a topology preserving mapping from the high dimensional space to map units. Map units, or neurons, usually form a two-dimensional lattice and thus the mapping is a mapping from high dimensional space onto a plane. The property of topology preserving means that the mapping preserves the relative distance between the points. Points that are near each other in the input space are mapped to nearby map units in the SOM. The SOM can thus serve as a cluster analyzing tool of high-dimensional data. Also, the SOM has the capability to generalize. Generalization capability means that the network can recognize or characterize inputs it has never encountered before. A new input is assimilated with the map unit it is mapped to.

The Self-Organizing Map is one of the most popular neural network models. It belongs to the category of competitive learning networks. The Self-Organizing Map is based on unsupervised learning, which means that no human intervention is needed during the learning and that little need to be known about the characteristics of the input data. We could, for example, use the SOM for clustering data without knowing the class memberships of the input data. The SOM can be used to detect features inherent to the problem and thus has also been called SOFM, the Self-Organizing Feature Map.

The Self-organizing map (SOM) invented by Teuvo Kohonen, uses a form of Unsupervised Learning. A set of artificial neurons learns to map points in an input space to coordinates in an output space. The input space can have different dimensions and topology from the output space, and the SOM will attempt to preserve these.

### Self Organizing Map :Basic Principle

A SOM is single layer neural network. The name neural network, or more correctly artificial neural network, is due to the historical fact that they were originally inspired by the way biological neurons were believed to work. Although this analogy is, generally speaking, still valid, developments in artificial neural networks and in our knowledge of how biological neurons actually work have led many researchers to refer to the basic computing units of artificial neural networks not as “neurons,” but as “units.” In this paper, to stress the difference between the mathematical model of a biological neuron and our computational units, we will follow the more recent conventions, and refer to them simply as “units.”

Figure 1 Self Organizing Map

There are also many terms used to designate the data that are used to train the network, or later to use it. In this paper, we will follow the term most used in the pattern recognition community, which is simply “pattern” or “data pattern.” Different communities will call it “sample,” “instance,” “point,” or “entity.”

In a SOM, the units are set along an n-dimensional grid. In most applications, this grid is two-dimensional and rectangular, though many applications use hexagonal grids, and one, three, or more dimensional spaces. In this grid, we can define neighborhoods in what we call the output space, as opposed to the input space of the data patterns.

### References

[1] Kohonen T., “Correlation matrix memories”, IEEE Transection Computers, 21:353- 358, 1972.

[2] Lobo, Victor JAS, “Application of self-organizing maps to the maritime environment”, Information Fusion and Geographic Information Systems, Springer Berlin Heidelberg, 2009, 19-36.

[3] “Self-Organizing Map (SOM)”, online available at: http://users.ics.aalto.fi/jhollmen/dippa/node9.html

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