Hyperrectangles Selection for Monotonic Classification by Using Evolutionary Algorithms

Abstract

In supervised learning, some real problems require the response attribute to represent ordinal values that should increase with some of the explaining attributes. They are called classification problems with monotonicity constraints. Hyperrectangles can be viewed as storing objects in R n which can be used to learn concepts combining instance-based classification with the axis-parallel rectangle mainly used in rule induction systems. This hybrid paradigm is known as nested generalized exemplar learning. In this paper, we propose the selection of the most effective hyperrectangles by means of evolutionary algorithms to tackle monotonic classification. The model proposed is compared through an exhaustive experimental analysis involving a large number of data sets coming from real classification and regression problems. The results reported show that our evolutionary proposal outperforms other instance-based and rule learning models, such as OLM, OSDL, k-NN and MID; in accuracy and mean absolute error, requiring a fewer number of hyperrectangles.

Monotonic classification: An overview on algorithms, performance measures and data sets

“…• Monotonic Accuracy (MAcc [44] • Monotonicity Compliance (MCC [46]), defined as the proportion of the input space where the requested monotonicity constraints are not violated, weighted by the joint probability distribution of the input space.…”

“…• Monotonic Accuracy (MAcc [44]), computed as standard Accuracy, but only considering those examples that completely fulfill the monotonicity constraints in the test set. In other words, non-monotonic examples do not take part in the calculation of MAcc.…”

“…• Monotonic Mean Absolute Error (MMAE [44]), calculated as standard MAE, but only considering those examples that completely fulfill the monotonicity constraints in the test set.…”

Fuzzy k-Nearest Neighbors with monotonicity constraints: Moving towards the robustness of monotonic noise

“…Instance-based learning has proven to be a good approach for monotonic classification [2,15,31,18]. However, some of these methods, such as Monotonic k-Nearest Neighbors [15] (MkNN), need to learn from a fully monotonic set to ensure monotonic predictions.…”

Label noise filtering techniques to improve monotonic classification

“…Several monotonic classification approaches have been proposed in the specialized literature. They include classification trees and rule induction [9,10,11,12,13,14], neural networks [15,16], instance-based learning [4,17,18] and hybridizations [19,20]. Some of them require the training set to be purely monotone to work correctly, such as the MKNN classifier [18].…”