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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.

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