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Hyperbox-based machine learning algorithms: a comprehensive survey

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Abstract

With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new information and knowledge from different data sources. Learning algorithms using hyperboxes as fundamental representational and building blocks are a branch of machine learning methods. These algorithms have enormous potential for high scalability and online adaptation of predictors built using hyperbox data representations to the dynamically changing environments and streaming data. This paper aims to give a comprehensive survey of the literature on hyperbox-based machine learning models. In general, according to the architecture and characteristic features of the resulting models, the existing hyperbox-based learning algorithms may be grouped into three major categories: fuzzy min–max neural networks, hyperbox-based hybrid models and other algorithms based on hyperbox representations. Within each of these groups, this paper shows a brief description of the structure of models, associated learning algorithms and an analysis of their advantages and drawbacks. Main applications of these hyperbox-based models to the real-world problems are also described in this paper. Finally, we discuss some open problems and identify potential future research directions in this field.

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Acknowledgements

T.T. Khuat is supported by a FEIT-UTS scholarship for his PhD research.

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Authors and Affiliations

  1. Advanced Analytics Institute, Faculty of Engineering and Information Technology, University of Technology Sydney, Ultimo, NSW, Australia

    Thanh Tung Khuat & Bogdan Gabrys

  2. EBTIC, Khalifa University, Abu Dhabi, UAE

    Dymitr Ruta

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  1. Thanh Tung Khuat
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  2. Dymitr Ruta
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  3. Bogdan Gabrys
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Appendix

Appendix

The key steps to search the relevant literature are presented as follows:

1.1 Formulating search terms and selecting research databases

The main terms used to construct the search strings are hyperbox, fuzzy min max, and classifier. We used Boolean operators to build a search expression as follows:

(hyperbox or “fuzzy min max”) and (classifier or classification or clustering or algorithm)

This search string was employed to seek for research articles, conference papers or book chapters in five popular databases including ScienceDirect (2019), IEEE Xplore (2019), Springer Link (2019), ACM Digital Library (2019), IOS Press (2019). In addition, literature which was cited in the selected ones and was satisfied the inclusion criteria was also considered.

1.2 Publication selection criteria

1.2.1 Inclusion criteria

We applied the following inclusion criteria to choose relevant studies including journal articles and magazines, book chapters, and conference papers:

(I1):

Studies that propose a new machine learning model using hyperbox representations or a significant improvement in the existing hyperbox-based model.

(I2):

Studies that apply the hyperbox-based machine learning models or their variants to deal with the real world problems. These models must illustrate their effectiveness on practical data sets.

(I3):

Papers are peer-reviewed and published either in a specialized proceedings or in a reputable journal.

(I4):

Studies that were not published from year 1992 to year 2018

1.2.2 Exclusion criteria

Exclusion criteria are used to exclude the studies which are irrelevant to this research. We designed these conditions as follows:

  • Papers which are not relevant to the research question.

  • Studies that mention to hyperbox-based machine learning algorithms but not focus on enhancing the existing methods or solving a new real-world issues.

  • Papers that their contents are simple, and the authors do not describe or analyze their novel contribution to the research topic.

  • Studies that do not resolve the classification or clustering problems.

1.2.3 Literature selection strategy

Literature was evaluated through three stages: automatic search, screening, and eligible selection. In the first step, above search strings were put into search engines of five databases to seek for studies of interest. In the next phase, the title and the abstract of the studies obtained in the previous phase were verified whether it satisfies our field of interest in this paper. To select the satisfied papers, we read through all papers in the second steps and assessed the studies based on the satisfactions of inclusion criteria either I1 or I2, and I3 and I4. If the paper meets any exclusion criteria, it would be discarded. The quality of the proposed methods in the literature and their efficiency in comparison with other similar approaches were considered in the choice of final papers as well. In the evaluation process, other publications cited in the papers of the third stages were reviewed, and qualified works closely related to this study were also selected.

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Khuat, T.T., Ruta, D. & Gabrys, B. Hyperbox-based machine learning algorithms: a comprehensive survey. Soft Comput 25, 1325–1363 (2021). https://doi.org/10.1007/s00500-020-05226-7

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