Bi-Criteria Optimization of Decision Trees with Applications to Data Analysis

This paper is devoted to the study of bi-criteria optimization problems for decision trees. We consider different cost functions such as depth, average depth, and number of nodes. We design algorithms that allow us to construct the set of Pareto optimal points (POPs) for a given decision table and the corresponding bi-criteria optimization problem. These algorithms are suitable for investigation of medium-sized decision tables. We discuss three examples of applications of the created tools: the study of relationships among depth, average depth and number of nodes for decision trees for corner point detection (such trees are used in computer vision for object tracking), study of systems of decision rules derived from decision trees, and comparison of different greedy algorithms for decision tree construction as single- and bi-criteria optimization algorithms.