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A Partitioning Algorithm with Application in Pattern Classification and the Optimization of Decision Trees

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2 Author(s)
Meisel, William S. ; Technology Service Corporation, Santa Monica, Calif. 90401, and the Department-of Electrical Engineering and Computer Science, University of Southern California ; Michalopoulos, D.A.

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.

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Computers, IEEE Transactions on  (Volume:C-22 ,  Issue: 1 )