Classification via Two-Way Comparisons

TL;DR

This paper introduces the first polynomial-time algorithm for constructing minimum-cost decision trees using equality and less-than comparisons for classifying ordered query sets, improving efficiency over lookup tables and traditional search trees.

Contribution

The paper presents the first polynomial-time algorithm for optimal decision tree construction based on two-way comparisons for ordered query sets.

Findings

Algorithm efficiently constructs minimal decision trees

Extends to multiple class options per query

Reduces size and improves speed over lookup tables

Abstract

Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the class to which $q$ belongs. Such a tree can be much smaller than a lookup table, and much faster and smaller than a conventional search tree. We give the first polynomial-time algorithm for the problem. The algorithm extends naturally to the setting where each query has multiple allowed classes.