# Self Organizing Maps - Mapping a single vs more layers

Suppose we train a Self Organizing Map (SOM) with two input layers, meaning we have the following situation:

We have a vector $$x=(x_1,...,x_n)\in\mathbb{R}^n$$ which could represent biometric properties. A health value $$y\in\{1,2,3\}$$ is then assigned to each state $$x$$. Now in principle we could just concatenate those two $$z=(x,y)\in\mathbb{R}^n\times \{1,2,3\}$$ and input this into the SOM algorithm.

Now, there is a second alternative, which is used in the kohonen R package, using the function xyf. This function basically does the same, but this time the distance of an object to a unit is the sum of the distances of $$X$$ and $$Y$$ spaces in contrast to having just one distance defined on $$Z$$. Note that these two are in general different!

The prediction is done in the xyf-function using only $$x$$.

I cannot explain why one would do this if one has the complete element $$z=(x,y)$$. Why would you not use the information stored in $$y$$? If it is of any help, the kohonen clusters are then used in conjunction with a markov chain.