# Mapping one feature space to another for prediction purposes?

I have a historical data set which comes with two sets of features, (X,Y,Z) and (A,B,C).

The task is to see how similar a new data point is to the points in my historical data set in the space (X,Y,Z), except that for new incoming data points, I only have values in (A,B,C) not (X,Y,Z).

How do I map the distances in (A,B,C) to distances in (X,Y,Z) ?

Should I simply regress X,Y, and Z each against (A,B,C)?

• Can you clarify what this historical data set looks like? Are there rows of points and each point has six features: X, Y, Z, A, B, and C? Or are the points with X, Y, Z features in no way related (at least as far as you know) to the points with A, B, C features? And do you know if there is a 1:1 relationship between A-X, B-Y, and C-Z values (e.g., an A value always maps to the same single X value) and if there is a monotonic relationship between the two (meaning that as A increases, X also increases)? If there isn't, performing a linear regression may not be very helpful. – AlexK May 5 '19 at 7:55