I'm trying to solve a classification problem using a random forest in R. The training data is a particle's charge at 30 different time instances. However, I need to convert this 30 dimensional data into a single value. I've tried using the sum of the charge across the 30 time bins and I've tried using the variable importance to calculate a weighted sum. To clarify, I fitted a random forest to the 30 dimensional training data and then used the resulting variable importance values to assign a weighting to each time interval for the weighted sum.
Then I trained a random forest on the one dimensional data using the sum and the variable importance weighted sum values. However, the random forest performed better when I wasn't using a weighted sum.
I've tried this with the standard randomForest package and the cforest package and I get the same results.
Could anybody explain why the weighted sum doesn't perform better? In principle should using a weighted sum work better?