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**What are Self Organizing Maps ?**

A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique for creating a low-dimensional (usually two-dimensional) representation of a higher-dimensional data set while maintaining the data's topological structure. A data set containing p variables recorded in n observations, for example, could be represented as clusters of observations with comparable variable values. These clusters might then be represented as a two-dimensional "map," with proximate cluster observations having more similar values than distal cluster observations. This can make it easier to see and evaluate high-dimensional data. This is a type of artificial neural network but is trained using competitive learning rather than the error-correction learning used by other neural networks.

Self-organizing maps operate in two modes: training and mapping just like other artificial neural networks. First part is training in generating lower dimensional representation from the input data. Second is mapping classifies additional input data using the generated map.

The purpose of training is to convert a p-dimensional input space into a two-dimensional map space. An input space with p variables is described as having p dimensions. A map space is made up of "nodes" or "neurons," which are placed in a two-dimensional hexagonal or rectangular grid. The number of nodes and their arrangement are selected based on the overall objectives of the data analysis and exploration.

Each node in the map space has a "weight" vector that represents the node's position in the input space. Training consists of moving weight vectors toward the input data without distorting the topology produced by the map space, while nodes in the map space remain fixed. After training, the map can be used to classify further input space observations by identifying the node with the shortest distance metric to the input space vector.

**The stages of the SOM algorithm that achieves this can be summarised as follows: **

**Initialization â€“**Choose random values for the initial weight vectors wj .**Sampling â€“**Draw a sample training input vector x from the input space.**Matching â€“**Find the winning neuron I(x) that has weight vector closest to the input vector, i.e. the minimum value of

** 4. Updating â€“** Apply the weight update equation

** where **

is a Gaussian neighbourhood and Î·(t) is the learning rate.

**5. Continuation â€“** keep returning to step 2 until the feature map stops changing.

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