How is the SOM working?

Question

I know the basic working of self organizing maps but I am having a hard time visualizing them. Let's say I have a 2*2 grid an I have mapped a data of 200*1000 on it. Can I access the 200 data points in my training set again using my grid?If so then how is it possible?If the answer is no then what is the use of this maps as my original data cannot be retrieved from the compressed data?

Answer 1

I'm not sure what you mean, are you saying that you have mapped 200 high-dimensional data points onto a 2D grid? If so it should only be a matter of finding the closest 2D-coordinate for each data point and then map it to this position. In other words, each coordinate on the grid has a weight of the same dimension as the input data and if trained correctly you can loop through the grid and find the weight which has the lowest euclidian distance from each sample in your input data, called the bmu (best matching unit). The corresponding 2D-coordinate is then mapped to the given input, from there you can plot it or whatever you like.

SOM is mostly used for visualisation and exploration of high-d data, your original data is not 'retrievable' from it, but it can give you some intuition of how the data is distributed.