Giovanni Bortolan and Witold Pedrycz
This paper sets out to design hyperbox classifiers of high interpretation capabilities. They are based on a collection of hyperboxes – generic and highly interpretable geometric…
Abstract
Purpose
This paper sets out to design hyperbox classifiers of high interpretation capabilities. They are based on a collection of hyperboxes – generic and highly interpretable geometric descriptors of data belonging to a certain class. Such hyperboxes directly translate into conditional statements (rules) taking on the well‐known format “if feature1 assumes values in [a,b] and feature2 assumes values in [d,f] and … and featuren assumes values in [w,z] then class ω” where the intervals ([a,b],…[w,z]) are the respective edges (features) of the corresponding hyperbox.
Design/methodology/approach
The proposed design process of hyperboxes consists of two main phases. In the first phase, a collection of “seeds” of the hyperboxes is constructed through data clustering being realized by means of the fuzzy C‐means algorithm. During the second phase, the hyperboxes are “grown” (expanded) by applying mechanisms of genetic optimization (and genetic algorithm, in particular).
Findings
It is demonstrated how the underlying geometry of the hyperboxes supports an immediate interpretation of arrhythmia data by linking the ranges of the features (parameters of the ECG signal) forming the edges of the hyperboxes with the two classes of the signals (normal – abnormal). A collection of comprehensive experiments offers an interesting insight into the geometry of the individual categories of the ECG signals and discusses how the resulting hyperbox classifiers link their geometric properties with the obtained classification rates.
Research limitations/implications
The structure of the classifier is essential to enhance interpretation capabilities of the architecture and generate a collection of “if‐then” classification rules.
Originality/value
The study addresses an issue of design of highly interpretable, granular classifiers with the use of the technology of computational intelligence and evolutionary optimization, in particular.
Details
Keywords
Giovanni Bortolan and Witold Pedrycz
Radial basis function (RBF) neural networks form an essential category of architectures of neurocomputing. They exhibit interesting and useful properties of stable and fast…
Abstract
Radial basis function (RBF) neural networks form an essential category of architectures of neurocomputing. They exhibit interesting and useful properties of stable and fast learning associated with significant generalization capabilities. This successful performance of RBF neural networks can be attributed to the use of a collection of properly selected RBFs. In this way this category of the networks strongly relies on some domain knowledge about a classification problem at hand. Following this vein, this study introduces fuzzy clustering, and fussy isodata, in particular, as an efficient tool aimed at constructing receptive fields of RBF neural networks. It is shown that the functions describing these fields are completely derived as a by‐product of fuzzy clustering and do not require any further tedious refinements. The efficiency of the design is illustrated with the use of synthetic two‐dimensional data as well as real‐world highly dimensional ECG patterns. The classification of the latter data set clearly points out advantages of RBF neural networks in pattern recognition problems.