A Partitioning Algorithm with Application in Pattern Classification and the Optimization of Decision Trees
Issue No. 01 - January (1973 vol. 22)
W.S. Meisel , Technology Service Corporation, Santa Monica, Calif. 90401, and the Department-of Electrical Engineering and Computer Science, University of Southern California
The efficient partitioning of a finite-dimensional space by a decision tree, each node of which corresponds to a comparison involving a single variable, is a problem occurring in pattern classification, piecewise-constant approximation, and in the efficient programming of decision trees. A two-stage algorithm is proposed. The first stage obtains a sufficient partition suboptimally, either by methods suggested in the paper or developed elsewhere; the second stage optimizes the results of the first stage through a dynamic programming approach. In pattern classification, the resulting decision rule yields the minimum average number of calculations to reach a decision. In approximation, arbitrary accuracy for a finite number of unique samples is possible. In programming decision trees, the expected number of computations to reach a decision is minimized.
Decision rules, decision trees, dynamic programming, invariant imbedding, pattern classification, piecewise-constant approximation.
D.A. Michalopoulos, W.S. Meisel, "A Partitioning Algorithm with Application in Pattern Classification and the Optimization of Decision Trees", IEEE Transactions on Computers, vol. 22, no. , pp. 93-103, January 1973, doi:10.1109/T-C.1973.223603