A note on multiplying Boolean matrices
Communications of the ACM
A Nonparametric Partitioning Procedure for Pattern Classification
IEEE Transactions on Computers
Potential Functions in Mathematical Pattern Recognition
IEEE Transactions on Computers
A "Logical pattern" recognition program
IBM Journal of Research and Development
Mining optimal decision trees from itemset lattices
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
A Recursive Partitioning Decision Rule for Nonparametric Classification
IEEE Transactions on Computers
An Algorithm for Constructing Optimal Binary Decision Trees
IEEE Transactions on Computers
Optimal constraint-based decision tree induction from itemset lattices
Data Mining and Knowledge Discovery
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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.