Applying d-XChoquet integrals in classification problems

Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.Supported by Navarra de Servicios y Tecnologías, S.A. (NASERTIC), CNPq (301618/2019-4, 305805/2021-5), FAPERGS (19/2551-0001660-3), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019- 108392GB I00 (MCIN/AEI/10.13039/501100011033)

Neuro-inspired edge feature fusion using Choquet integrals

It is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.The authors gratefully acknowledge the financial support of the Spanish Ministry of Science and Technology (project PID2019-108392GB-I00 (AEI/10.13039/501100011033), the Research Services of Universidad Pública de Navarra, CNPq (307781/2016-0, 301618/2019-4), FAPERGS (19/2551-0001660) and PNPD/CAPES (464880/2019-00)

Replacing pooling functions in Convolutional Neural Networks by linear combinations of increasing functions

Traditionally, Convolutional Neural Networks make use of the maximum or arithmetic mean in order to reduce the features extracted by convolutional layers in a downsampling process known as pooling. However, there is no strong argument to settle upon one of the two functions and, in practice, this selection turns to be problem dependent. Further, both of these options ignore possible dependencies among the data. We believe that a combination of both of these functions, as well as of additional ones which may retain different information, can benefit the feature extraction process. In this work, we replace traditional pooling by several alternative functions. In particular, we consider linear combinations of order statistics and generalizations of the Sugeno integral, extending the latter’s domain to the whole real line and setting the theoretical base for their application. We present an alternative pooling layer based on this strategy which we name ‘‘CombPool’’ layer. We replace the pooling layers of three different architectures of increasing complexity by CombPool layers, and empirically prove over multiple datasets that linear combinations outperform traditional pooling functions in most cases. Further, combinations with either the Sugeno integral or one of its generalizations usually yield the best results, proving a strong candidate to apply in most architectures.Tracasa Instrumental (iTRACASA), SpainGobierno de Navarra-Departamento de Universidad, Innovacion y Transformacion Digital, SpainSpanish Ministry of Science, Spain PID2019-108392GB-I00Andalusian Excellence project, Spain PID2019-108392GB-I00Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) PC095-096Fundacao de Amparo a Ciencia e Tecnologia do Estado do Rio Grande do Sul (FAPERGS) P18-FR-4961 301618/2019-4 19/2551-000 1279-