Rough Cognitive Networks

Fuzzy-Rough Cognitive Networks: Theoretical Analysis and Simpler Models

Fuzzy-rough cognitive networks (FRCNs) are recurrent neural networks (RNNs) intended for structured classification purposes in which the problem is described by an explicit set of features. The advantage of this granular neural system relies on its transparency and simplicity while being competitive to state-of-the-art classifiers. Despite their relative empirical success in terms of prediction rates, there are limited studies on FRCNs' dynamic properties and how their building blocks contribute to the algorithm's performance. In this article, we theoretically study these issues and conclude that boundary and negative neurons always converge to a unique fixed-point attractor. Moreover, we demonstrate that negative neurons have no impact on the algorithm's performance and that the ranking of positive neurons is invariant. Moved by our theoretical findings, we propose two simpler fuzzy-rough classifiers that overcome the detected issues and maintain the competitive prediction rates of this classifier. Toward the end, we present a case study concerned with image classification, in which a convolutional neural network is coupled with one of the simpler models derived from the theoretical analysis of the FRCN model. The numerical simulations suggest that once the features have been extracted, our granular neural system performs as well as other RNNs.

Dynamics of Fuzzy-Rough Cognitive Networks

Fuzzy-rough cognitive networks (FRCNs) are interpretable recurrent neural networks, primarily designed for solving classification problems. Their structure is simple and transparent, while the performance is comparable to the well-known black-box classifiers. Although there are many applications on fuzzy cognitive maps and recently for FRCNS, only a very limited number of studies discuss the theoretical issues of these models. In this paper, we examine the behaviour of FRCNs viewing them as discrete dynamical systems. It will be shown that their mathematical properties highly depend on the size of the network, i.e., there are structural differences between the long-term behaviour of FRCN models of different size, which may influence the performance of these modelling tools.

Development and Analysis of Neural Networks Realized in the Presence of Granular Data

In this article, we propose a design and evaluation framework of granular neural networks realized in the presence of information granules. Neural networks realized in this manner are able to process both nonnumerical data, such as information granules as well as numerical data. Information granules are meaningful and semantically sound entities formed by organizing existing knowledge and available experimental data. The directional nature of mapping between the input and output data needs to be considered when building information granules. The development of neural networks advocated in this article is realized as a two-phase process. First, a collection of information granules is formed through granulation of numeric data in the input and output spaces. Second, neural networks are constructed on the basis of information granules rather than original (numeric) data. The proposed method leads to the construction of neural networks in a completely new way. In comparison with traditional (numeric) neural networks, the networks developed in the presence of granular data require shorter learning time. They also produce the results (outputs) that are information granules rather than numeric entities. The quality of granular outputs generated by our neural networks is evaluated in terms of the coverage and specificity criteria that are pertinent to the characterization of the information granules.

Short-term cognitive networks, flexible reasoning and nonsynaptic learning

While the machine learning literature dedicated to fully automated reasoning algorithms is abundant, the number of methods enabling the inference process on the basis of previously defined knowledge structures is scanter. Fuzzy Cognitive Maps (FCMs) are recurrent neural networks that can be exploited towards this goal because of their flexibility to handle external knowledge. However, FCMs suffer from a number of issues that range from the limited prediction horizon to the absence of theoretically sound learning algorithms able to produce accurate predictions. In this paper we propose a neural system named Short-term Cognitive Networks that tackle some of these limitations. In our model, used for regression and pattern completion, weights are not constricted and may have a causal nature or not. As a second contribution, we present a nonsynaptic learning algorithm to improve the network performance without modifying the previously defined weight matrix. Besides, we derive a stop condition to prevent the algorithm from iterating without significantly decreasing the global simulation error.