# How do SOMs make visualization of high-dimension data possible?

Self Organizing Map is credited to be a very effective tool for exploratory data analysis as it aids in visualization of high-dimensional data.

However, the part where the dimensionality reduction is happening is not clear to me. From this article, I understand that the information is essentially embedded in the weight vectors of neurons which are of the same dimensions as of the original patterns. The same weight vectors are supposed to be used for visualization (if I follow from the highly popular colors example).

If this is true, I do not understand how SOM is performing dimensionality reduction and how it is making visualization of high-dimensional data simpler.

Could someone explain (if possible with an example of >3 dimensional data) how SOM performs dimension reduction and makes visualization possible?

Consider a data set of 1000 patterns, each with 100 features. It is impossible to plot this data. When this data is run through SOM, the network learns the weights such that each of the neurons summarizes a subset of the vectors. After the training is complete, similar patterns get mapped to neighborhood neurons and farther apart neurons represent dissimilar patterns. Visualizing this mapping tells which patterns lie where, in a 2D space.

For example, in the world poverty map[1][2], each pattern is a vector of length 39 and represents one country. When this data set is run through SOM, the countries(patterns) are mapped to nearest neurons and it can be seen that the countries are arranged together based on their economic wellness.

After SOM is run until the stopping criterion is met, each pattern/input vector is mapped to the best matching unit. Hence, for example, Belgium (BEL) is closest to the weight vector of the first node in the map (top-right corner) and hence, mapped to it.

Each node is colored based on the average distance of its weight vector with the weight vectors of its neighbors (U-matrix).

However, it is still not clear how dimensionality reduction is achieved.

• I think the reduction in dimensions is referring to the 2D coordinates of your SOM. You're effectively mapping your high dimensional data into a two dimensional space. I have seen some people create a SOM where the 2D grid corresponds to the coordinates in the space spanned by the first two principal components. Commented Mar 23, 2018 at 0:35

Dimensionality reduction can be explained very easy: Consider you have a huge matrix, all countries are listed on the horizontal and all possible features on the vertical and for each feature and each country there is a flag set in the matrix. A lot of the features share similarities from the patterns in which they appear, so that those features can be combined into groups of features. What we are doing now is just a simple matrix factorization from our huge matrix at the beginning, into a small matrix of grouped features on the vertical and countries on the horizontal and another small matrix of all the original features on the one and all the grouped features on the other. This is all the magick, just a simple matrix factorization.