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Data Stream Clustering: Introducing Recursively Extendable aggregation functions for Incremental Cluster Fusion Processes

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第3期55卷 1421-1435页

作者： Urio-Larrea, A. Camargo, H. Lucca, G. Asmus, T. Marco-Detchart, C. Schick, L. Lopez-Molina, C. Andreu-Perez, J. Bustince, H. Dimuro, G. P. Univ Publ Navarra Dept Estadist Pamplona 31006 Spain Univ Fed Sao Carlos Dept Computac BR-13565905 Sao Carlos Brazil Univ Catolica Pelotas Ctr Ciencias Sociais & Tecnol BR-96015560 Pelotas Brazil Univ Fed Rio Grande Inst Matemat Estat & Fisisca BR-96203900 Rio Grande Brazil Univ Fed Rio Grande Ctr Ciencias Computacionais BR-96203900 Rio Grande Brazil Univ Essex Sch Comp Sci & Elect Engn Colchester England

In data stream (DS) learning, the system has to extract knowledge from data generated continuously, usually at high speed and in large volumes, making it impossible to store the entire set of data to be processed in batch mode. Hence, machine learning models must be built incrementally by processing the incoming examples, as data arrive, while updating the model to be compatible with the current data. In fuzzy DS clustering, the model can either absorb incoming data into existing clusters or initiate a new cluster. As the volume of data increases, there is a possibility that the clusters will overlap to the point where it is convenient to merge two or more clusters into one. Then, a cluster comparison measure (CM) should be applied, to decide whether such clusters should be combined, also in an incremental manner. This defines an incremental fusion process based on aggregation functions that can aggregate the incoming inputs without storing all the previous inputs. The objective of this article is to solve the fuzzy DS clustering problem of incrementally comparing fuzzy clusters on a formal basis. First, we formalize and operationalize incremental fusion processes of fuzzy clusters by introducing recursively extendable (RE) aggregation functions, studying construction methods and different classes of such functions. Second, we propose two approaches to compare clusters: 1) similarity and 2) overlapping between clusters, based on RE aggregation functions. Finally, we analyze the effect of those incremental CMs on the online and offline phases of the well-known fuzzy clustering algorithm d-FuzzStream, showing that our new approach outperforms the original algorithm and presents better or comparable performance to other state-of-the-art DS clustering algorithms found in the literature.

关键词： aggregation functions data streams (DSs) fuzzy clustering fuzzy clustering overlap indices overlap indices similarity measures similarity measures similarity measures

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Abstract aggregation functions and social choice

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FUZZY SETS AND SYSTEMS 2023年 454卷 190-198页

作者： Candeal, Juan C. Univ Zaragoza Fac Econ & Empresa Dept Anal Econ Gran Via2 Zaragoza 50005 Spain

A characterization of what we call pseudo-projective aggregation functions is shown, thus generalizing existing recent results in the literature. The approach followed is then applied to obtain certain characterizations of projective and pseudo-projective aggregation operators as well as to develop a social choice voting model. (c) 2022 Elsevier B.V. All rights reserved.

关键词： aggregation functions aggregation operators Social choice

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Characterization of homogeneous and quasi-homogeneous binary aggregation functions

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FUZZY SETS AND SYSTEMS 2022年 433卷 96-107页

作者： Su, Yong Zong, Wenwen Mesiar, Radko Suzhou Univ Sci & Technol Sch Math Sci Suzhou 215009 Jiangsu Peoples R China Univ Jinan Sch Math Sci Jinan 250022 Shandong Peoples R China Slovak Univ Technol Bratislava Fac Civil Engn Dept Math & Descript Geometry Bratislava Slovakia Palacky Univ Olomouc Fac Sci Dept Algebra & Geometry 17Listopadu 12 Olomouc 77146 Czech Republic

Homogeneity, which plays an essential role in decision making, economics and image processing, reflects the regularity of aggregation functions with respect to the inputs with the same ratio. Quasi-homogeneity is a relaxed homogeneity that reflects the original output as well as the same ratio. This paper is devoted to the characterization of all homogeneous/quasi-homogeneous binary aggregation functions in terms of single-argument functions. (c) 2021 Elsevier B.V. All rights reserved.

关键词： aggregation functions Homogeneity Regularity Quasi-homogeneity

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Motor-Imagery-Based Brain-Computer Interface Using Signal Derivation and aggregation functions

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第8期52卷 7944-7955页

作者： Fumanal-Idocin, Javier Wang, Yu-Kai Lin, Chin-Teng Fernandez, Javier Antonio Sanz, Jose Bustince, Humberto Univ Publ Navarra Dept Estadist Informat & Matemat Pamplona 31006 Spain Univ Technol Sydney Fac Engn & Informat Technol Australian AI Inst Ultimo NSW 2007 Australia Univ Publ Navarra Inst Smart Cities Pamplona 31006 Spain Univ Publ Navarra Lab Navarrabiomed IdiSNA Hosp Complex Navarre CHN Pamplona 31008 Spain

Brain-computer interface (BCI) technologies are popular methods of communication between the human brain and external devices. One of the most popular approaches to BCI is motor imagery (MI). In BCI applications, the electroencephalography (EEG) is a very popular measurement for brain dynamics because of its noninvasive nature. Although there is a high interest in the BCI topic, the performance of existing systems is still far from ideal, due to the difficulty of performing pattern recognition tasks in EEG signals. This difficulty lies in the selection of the correct EEG channels, the signal-to-noise ratio of these signals, and how to discern the redundant information among them. BCI systems are composed of a wide range of components that perform signal preprocessing, feature extraction, and decision making. In this article, we define a new BCI framework, called enhanced fusion framework, where we propose three different ideas to improve the existing MI-based BCI frameworks. First, we include an additional preprocessing step of the signal: a differentiation of the EEG signal that makes it time invariant. Second, we add an additional frequency band as a feature for the system: the sensorimotor rhythm band, and we show its effect on the performance of the system. Finally, we make a profound study of how to make the final decision in the system. We propose the usage of both up to six types of different classifiers and a wide range of aggregation functions (including classical aggregations, Choquet and Sugeno integrals, and their extensions and overlap functions) to fuse the information given by the considered classifiers. We have tested this new system on a dataset of 20 volunteers performing MI-based brain-computer interface experiments. On this dataset, the new system achieved 88.80% accuracy. We also propose an optimized version of our system that is able to obtain up to 90.76%. Furthermore, we find that the pair Choquet/Sugeno integrals and overlap functions are th

关键词： Electroencephalography Feature extraction Decision making Rhythm Data mining Task analysis Smart cities aggregation functions brain-computer-interface (BCI) classification information fusion motor imagery (MI) signal processing

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Positively homogeneous and super-/sub-additive aggregation functions

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FUZZY SETS AND SYSTEMS 2022年 451卷 385-397页

作者： Seliga, Adam Hrinakova, Katarina Seligova, Ivana Slovak Univ Technol Bratislava Fac Civil Engn Dept Math & Descript Geometry Radlinskeho 11 Bratislava 81005 Slovakia Slovak Univ Technol Bratislava Fac Elect Engn & Informat Technol Bratislava Inst Comp Sci & Math Ilkovicova 3 Bratislava 81219 Slovakia Pikes Peak Community Coll Dept Math 5675 S Acad Blvd Colorado Springs CO 80906 USA

In this contribution, we fully characterize one- and two-dimensional positively homogeneous aggregation functions and provide a method of checking non-decreasingness of positively homogeneous functions in higher dimensions. We also examine the interaction of positive homogeneity with super-addivity and sub-additivity of functions and link it to the concavity and convexity, respectively, of their generalized opposite diagonal functions. Some remarks on the computation of a linear super-additive transformation of aggregation functions are added. (c) 2022 Elsevier B.V. All rights reserved.

关键词： aggregation functions Positive homogeneity Generalized opposite diagonal functions Concavity

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aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2021年 137卷 34-50页

作者： Milfont, Thadeu Mezzomo, Ivan Bedregal, Benjamin Mansilla, Edmundo Bustince, Humberto Univ Fed Rural Semiarido UFERSA Dept Ciencias Nat Matemat & Estat DCME Mossoro RN Brazil Univ Fed Rio Grande do Norte UFRN Dept Informat & Matemat Aplicada DIMAp Programa Posgrad Sistemas & Comp Natal RN Brazil Univ Magallanes UMAG Dept Matemat & Fis DMF Punta Arenas Chile Univ Publ Navarra Dept Estadist Informat & Matemat Navarra 31006 Spain

n-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by L-n([0, 1]). This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions concerning an admissible order on the set of n-dimensional intervals and the construction of aggregation functions on L-n([0, 1]) based on the operations of the semi-vector spaces. In particular, extensions of the family of OWA and weighted average aggregation functions are investigated. Finally, we develop a multi-criteria group decision-making method based on n-dimensional aggregation functions with respect to an admissible order and give an illustrative example. (C) 2021 Elsevier Inc. All rights reserved.

关键词： n-Dimensional fuzzy sets Ordered semi-vector spaces Admissible orders aggregation functions Ordered weighted averaging Decision making

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Monotone Fuzzy Rule Interpolation for TSK-FIS-Like n-ary aggregation functions

Monotone Fuzzy Rule Interpolation for TSK-FIS-Like n-ary Agg...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Jong, Chian Haur Tay, Kai Meng Kerk, Yi Wen Lim, Chee Peng Univ Malaysia Sarawak Data Sci Ctr UNIMAS Water Ctr Fac Engn Kota Samarahan Malaysia Univ Kebangsaan Malaysia Ctr Artificial Intelligence Technol Bangi Malaysia Deakin Univ Inst Intelligent Syst Res & Innovat Geelong Vic 3216 Australia

ISBN: (纸本)9798350332285

Fuzzy Rule Interpolation (FRI) is important for fuzzy inference systems modeling pertaining to a sparse fuzzy rule base system. The focus of this paper is on a specific class of FRI, i.e., monotone FRI (MFRI), for modeling monotone Takagi-Sugeno-Kang Fuzzy Inference System (TSK-FIS) in the presence of a monotone sparse fuzzy rule base. On the other hand, a function is denoted as an n-ary aggregation function for a given n-dimensional input space and an output space when both the monotone and boundary properties are satisfied. In this paper, a set of sufficient conditions derived from the principles of Ordered Weighted Averaging (OWA) and the concept of orness for TSK-FIS to obey the monotone property is firstly formulated. We show that it is necessary to have a dense fuzzy rule base, which can be obtained by interpolation of fuzzy rules in a sparse fuzzy rule base, for constructing a monotone TSK-FIS. We then devise a two-stage MFRI for establishing monotone TSK-FIS. The first stage comprises a sufficient condition, inspired from the orness concept, to generate intermediate fuzzy membership functions (FMFs). The second stage deduces the monotone consequent of each intermediate rule from the available sparse fuzzy rules. We further extend our MFRI formulation to form TSK-FIS-like n-ary aggregation functions.

关键词： monotonicity fuzzy rule interpolation Takagi-Sugeno-Kang Fuzzy Inference System Ordered Weighted Average orness aggregation functions

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On the Use of aggregation functions for Semi-Supervised Network Embedding

On the Use of Aggregation Functions for Semi-Supervised Netw...

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International Joint Conference on Neural Networks (IJCNN)

作者： de Moraes Junior, Marcelo Isaias Marcacini, Ricardo Marcondes Univ Sao Paulo Inst Math & Comp Sci Sao Carlos SP Brazil

ISBN: (纸本)9781665488679

Network embedding methods map nodes into vector representations, aiming to preserve important properties of relationships between nodes through similarities in a latent vectorspace model. Graph Neural Networks (GNNs) based on aggregate functions have received significant attention among different network embedding methods. In general, the embeddings of a node are recursively generated by aggregating embeddings from neighboring nodes. aggregation is a crucial step in these methods, and different aggregation functions have been proposed, from simple averaging and max pooling operations to complex functions based on attention mechanisms. However, we note that there is a lack of studies comparing aggregate functions, especially in more practical real-world scenarios involving semi-supervised tasks. This paper introduces a methodology to evaluate different aggregation functions for semi-supervised learning through a model selection strategy guided by a statistical significance analysis framework. We show that Transformers-based aggregation functions are competitive for semi-supervised scenarios and obtain relevant results in different domains. Furthermore, we also discuss scenarios where "less is more", mainly when there are constraints on the availability of computational resources.

关键词： Network Embedding Graph Neural Networks Semi-Supervised Learning aggregation functions

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The effectiveness of aggregation functions used in fuzzy local contrast constructions

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FUZZY SETS AND SYSTEMS 2024年 491卷

作者： Pekala, Barbara Bentkowska, Urszula Kepski, Michal Mrukowicz, Marcin Univ Rzeszow Inst Comp Sci Pigonia 1 PL-35310 Rzeszow Poland Univ Informat Technol & Management Rzeszow Poland

In this paper, we explore the concept of local contrast of a fuzzy relation, which can be perceived as a measure for distinguishing the degrees of membership of elements within a defined region of an image. We introduce four distinct methods for constructing fuzzy local contrast: one uses a similarity measure, the second relies on the aggregation of similarity, the third is based on the aggregation of restricted equivalence, and the fourth utilizes the notion of equivalence. We further divide the constructions using similarity measures into two categories based on the two known definitions of similarity: distance-based similarity and aggregation functionbased similarity. These construction methods also incorporate fuzzy implications and negations. aggregation functions, which can be manipulated to enhance the effectiveness of the constructed fuzzy local contrast, play a significant role in most of our proposed constructions. For each construction method, several examples of fuzzy local contrasts are provided. The usefulness of the new fuzzy local contrasts is examined by applying them in image processing for salient region detection.

关键词： Contrast measures aggregation functions Saliency detection Similarity measures Restricted equivalence

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A survey on the enumeration of classes of logical connectives and aggregation functions defined on a finite chain, with new results

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FUZZY SETS AND SYSTEMS 2024年 490卷

作者： Munar, Marc Couceiro, Miguel Massanet, Sebastia Ruiz-Aguilera, Daniel Univ Balearic Isl Dept Math & Comp Sci Soft Comp Image Proc & Aggregat Scopia Res Grp Palma De Mallorca 07122 Spain Hlth Res Inst Balearic Isl IdISBa Palma De Mallorca 07010 Spain Univ Lorraine CNRS LORIA F-54000 Nancy France Univ Lisbon Inst Super Tecn INESC ID P-1000029 Lisbon Portugal

The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for instance, the ability to anticipate the computational cost required for generating operators with different properties. This is of paramount importance in image processing and decision making scenarios, where the identification of the most optimal operator is essential. Furthermore, it facilitates the examination of how constraining a certain property is in relation to its parent class. As a consequence, this paper aims to compile the main existing formulas and the methodologies with which they have been derived. Additionally, we introduce some novel formulas for the number of smooth discrete aggregation functions with neutral element or absorbing element, idempotent conjunctions, and commutative and idempotent conjunctions.

关键词： Logical connectives aggregation functions Finite chains Enumeration Discrete t-norms Discrete implications

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