# Predicting Co-Ordinate Data

This is on a prediction model we were trying out among a bunch of us trying out ML for the first time. Basically I have a training data set of network user ID's with their location (latitude and longitude). Also tracked are a couple of features such as the time of their first post, second post etc and a few details on their friends. My goal is to use these features to predict the location (latitude/ longitude) for a test set of data. Any ideas on what kind of model to use here and what ML technique to try out? At the moment we are using basic multiple regression to predict the latitude and longitude separately using independent models. But I was hoping to see if it is possible to approach the problem differently.

Any thoughts?

• Were unable to find a working R package for anything similar like the Curds and Whey algorithm. – Klite Jun 22 '15 at 6:52
• see Kriging maybe – Antoine Jun 22 '15 at 9:32
• Currently we are doing basic multiple regression using the given predictors and predicting the latitude separately and the longitude separately. My belief is that there must be a better option available where i can predict both the lat and long in pairs using one unified model. Or some other approach to the problem all together. I did google a bit on current research in "Multivariate mutiple regression" as this seems to be an appropriate description of the problem, but I'm unable to find any effective solutions. – Klite Jun 22 '15 at 11:55

For example, rather than running linear regression on each coordinate separately, you could formulate your regression differently : treat your vector $(y_1,y_2)$of coordinates as a vector response $Y$, and if your variables are a vector $X$, your parameters, instead of being a vector, could now be a matrix $A$ such that
$$Y = AX + \epsilon$$
Where $\epsilon$ follows a hypothesis of your choice. If you make both components of $\epsilon$ independent, you'll fall back to independent regressions. But you may also choose the components to be indentical. You could also impose relations on $A$, forcing to look for correlations between both coordinates. A detailed account can be found here.