What would be a reason to use the Root Mean Square Error (RMSE) to combine data? In this machine learning tutorial by Google they use the Root Mean Square to create a similarity measure between two shoes.
They first calculate the difference between the size of two shoes and then do the same for their price. Finally with those two values they compute Root Mean Square Error (RMSE) however they don't explain why it's appropriate to do so.
Could someone explain why would you use RMSE or in what case does it apply?

As far as I see, this tutorial is mostly interested in presenting how to do clustering with a manually created similarity measure, and use RMSE as a natural choice for coming up with a similarity measure. So, it's not because the Euclidean distance (a scaled version of it to be precise) is the best choice for shoe + price feature pair. They also finish with saying

In general, your similarity measure must directly correspond to the actual similarity.

Noting that the choice of similarity which suits best to your data and problem's needs is left to you.
