The U-curve optimization problem: improvements on the original algorithm and time complexity analysis

TL;DR

This paper introduces the UCS algorithm, an optimal solution for the U-curve optimization problem, improving upon the original U-Curve algorithm and demonstrating superior performance in feature selection tasks.

Contribution

The paper presents the UCS algorithm, proving its optimality, and compares its performance with existing algorithms, showing significant improvements.

Findings

UCS outperforms UBB and SFFS in experiments

UCS is proven to be an optimal algorithm for the U-curve problem

Proposed improvements could further enhance UCS performance

Abstract

The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning. Recently, the U-Curve algorithm was proposed to give optimal solutions to the U-curve problem. In this article, we point out that the U-Curve algorithm is in fact suboptimal, and introduce the U-Curve-Search (UCS) algorithm, which is actually optimal. We also present the results of optimal and suboptimal experiments, in which UCS is compared with the UBB optimal branch-and-bound algorithm and the SFFS heuristic, respectively. We show that, in both experiments, $\proc{UCS}$ had a better performance than its competitor. Finally, we analyze the obtained results and point out improvements on UCS that might enhance the performance of this algorithm.