Abstract
Multi-dimensional classification is a cutting-edge problem, in which the values of multiple class variables have to be simultaneously assigned to a given example. It is an extension of the well known multi-label subproblem, in which the class variables are all binary. In this article, we review and expand the set of performance evaluation measures suitable for assessing multi-dimensional classifiers. We focus on multi-dimensional Bayesian network classifiers, which directly cope with multi-dimensional classification and consider dependencies among class variables. A comprehensive survey of this state-of-the-art classification model is offered by covering aspects related to their learning and inference process complexities. We also describe algorithms for structural learning, provide real-world applications where they have been used, and compile a collection of related software.
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Notes
This is a simplification taken from Read et al. (2013) to facilitate discussion of the problem complexity. Actually, we will see later that each class variable can take a different number of values.
A graph is said to be maximal connected if there is a path between every pair of vertices in its undirected version (Bielza et al. 2011).
Note that we have modified the term \(r_s = \sum _{j=1}^{d} |\Omega _{C_j}|\) of Fernandes et al. (2013) by d in the denominator of the equation in order to correctly normalize the score to lie between 0 and 1.
The popular approach to handle concept drifts named ensemble learning consists of combining the predictions of a set of individual classifiers, the so-called ensemble, in order to predict new incoming examples. A comprehensive review of ensemble approaches for data stream analysis was conducted by Krawczyk et al. (2017).
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Acknowledgements
This work has been partially supported by the Spanish Ministry of Science and Innovation through the PID2019-109247GB-IOO project. Santiago Gil-Begue has been supported by the predoctoral grant FPU17/04341 from the Spanish Ministry of Science, Innovation and Universities.
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Gil-Begue, S., Bielza, C. & Larrañaga, P. Multi-dimensional Bayesian network classifiers: A survey. Artif Intell Rev 54, 519–559 (2021). https://doi.org/10.1007/s10462-020-09858-x
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DOI: https://doi.org/10.1007/s10462-020-09858-x