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Discrimant analysis with multiple categories/groups, via linear optimization.
The problem:
We want to predict a categorical outcome/variable, e.g.,
DryWell vs. OilOnly vs. GasOnly vs. OilGas,
based on one or more explanatory variables,
given a set of observations.
Basic approach: For each item(or observation) i,
compute a score for each category or group c, c = 1, 2, ....
We classify item i to that category c that has
the highest score over all categories.
If xobs(i,j) is the value of item i for feature/variable j,
score(i,c) = beta(c,0) + beta(c,1)*xobs(i,1) + beta(c,2)*xobs(i,2)+...;
! Ref: Gochet, W., A. Stam, V. Srinivasan, and S. Chen (1997),
"Multigroup Discriminant Analysis Using Linear Programming".
Operations Research, vol. 45, no. 2, pp. 213-225;