Learning Opposites with Evolving Rules

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.Comment: Accepted for publication in The 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), August 2-5, 2015, Istanbul, Turke

Learning Opposites Using Neural Networks

Many research works have successfully extended algorithms such as evolutionary algorithms, reinforcement agents and neural networks using "opposition-based learning" (OBL). Two types of the "opposites" have been defined in the literature, namely \textit{type-I} and \textit{type-II}. The former are linear in nature and applicable to the variable space, hence easy to calculate. On the other hand, type-II opposites capture the "oppositeness" in the output space. In fact, type-I opposites are considered a special case of type-II opposites where inputs and outputs have a linear relationship. However, in many real-world problems, inputs and outputs do in fact exhibit a nonlinear relationship. Therefore, type-II opposites are expected to be better in capturing the sense of "opposition" in terms of the input-output relation. In the absence of any knowledge about the problem at hand, there seems to be no intuitive way to calculate the type-II opposites. In this paper, we introduce an approach to learn type-II opposites from the given inputs and their outputs using the artificial neural networks (ANNs). We first perform \emph{opposition mining} on the sample data, and then use the mined data to learn the relationship between input $x$ and its opposite $\breve{x}$. We have validated our algorithm using various benchmark functions to compare it against an evolving fuzzy inference approach that has been recently introduced. The results show the better performance of a neural approach to learn the opposites. This will create new possibilities for integrating oppositional schemes within existing algorithms promising a potential increase in convergence speed and/or accuracy.Comment: To appear in proceedings of the 23rd International Conference on Pattern Recognition (ICPR 2016), Cancun, Mexico, December 201