An Algorithm for Computing Minimum-Length Irreducible Testors

Abstract

In pattern recognition, the elimination of unnecessary and/or redundant attributes is known as feature selection. Irreducible testors have been used to perform this task. An objective of the Minimum Description Length Principle (MDL) applied to feature selection in pattern recognition and data mining is to select the minimum number of attributes in a data set. Consequently, the MDL principle leads us to consider the subset of irreducible testors of minimum length. Some algorithms that find the whole set of irreducible testors have been reported in the literature. However, none of these algorithms was designed to generate only minimum-length irreducible testors. In this paper, we propose the first algorithm specifically designed to calculate all minimum-length irreducible testors from a training sample. The paper presents some experimental results obtained using synthetic and real data in which the performance of the proposed algorithm is contrasted with other state-of-the-art algorithms that were adapted to generate only irreducible testers of minimum length. INDEX TERMS Feature selection, MDL principle, minimum-length irreducible testors, testor.

An Algorithm for Computing All Rough Set Constructs for Dimensionality Reduction

“…To reduce the search space, Proposition 5 is used to determine a priori if a zero-row prevails after adding any of the remaining attributes to the current attribute subset. This idea was introduced in [22] as a pruning strategy to compute the minimum-length irreducible testor. Similarly, it can be used to prune the search space for computing constructs.…”

RoPM: An Algorithm for Computing Typical Testors Based on Recursive Reductions of the Basic Matrix

“…The experiments were aimed to evaluate its with respect the two fastest algorithms: fast-BR and GCreduct [24]. The comparison with the recent algorithms presented in [27,28] was not performed because they do not deliver the full set of TTs. The tests were conducted on a laptop Alienware, model 17R3, Intel(R) Core (TM) i7-6700HQ CPU @2.60 GHZ (8 CPUs) processor, 16 GB RAM, Windows 10 Pro 64 bits operating system.…”

“…Various strategies have been developed to reach this goal, for example, the application of hardware and software-hardware configurations [25,26]. In addition, several algorithms have been proposed in order to compute only the minimum-length TTs [27,28], not the set of all TTs.…”

“…In particular, GCreduct is an algorithm that allows for the search of reducts (from the rough set theory) and TTs [21,24]. Reducts and TTs are concepts very close related to each other [21,[27][28][29][30].…”