Granular-Balls based Fuzzy Twin Support Vector Machine for Classification
School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；School of Information Science and Technology, Nantong University（南通大学信息科学与技术学院）；Department of Computer Science and Technology, Tongji University（同济大学计算机科学与技术系）
Lixi Zhao, Weiping Ding, Duoqian Miao, Guangming Lang
The twin support vector machine (TWSVM) classifier has attracted increasing attention because of its low computational complexity. However, its performance tends to degrade when samples are affected by noise. The granular-ball fuzzy support vector machine (GBFSVM) classifier partly alleviates the adverse effects of noise, but it relies solely on the distance between the granular-ball's center and the class center to design the granular-ball membership function. In this paper, we first introduce the granular-ball twin support vector machine (GBTWSVM) classifier, which integrates granular-ball computing (GBC) with the twin support vector machine (TWSVM) classifier. By replacing traditional point inputs with granular-balls, we demonstrate how to derive a pair of non-parallel hyperplanes for the GBTWSVM classifier by solving a quadratic programming problem. Subsequently, we design the membership and non-membership functions of granular-balls using Pythagorean fuzzy sets to differentiate the contributions of granular-balls in various regions. Additionally, we develop the granular-ball fuzzy twin support vector machine (GBFTSVM) classifier by incorporating GBC with the fuzzy twin support vector machine (FTSVM) classifier. We demonstrate how to derive a pair of non-parallel hyperplanes for the GBFTSVM classifier by solving a quadratic programming problem. We also design algorithms for the GBTSVM classifier and the GBFTSVM classifier. Finally, the superior classification performance of the GBTWSVM classifier and the GBFTSVM classifier on 20 benchmark datasets underscores their scalability, efficiency, and robustness in tackling classification tasks.
Chongqing University of Telecommunications and Posts（重庆邮电大学）
Most existing fuzzy set methods use points as their input, which is the finest granularity from the perspective of granular computing. Consequently, these methods are neither efficient nor robust to label noise. Therefore, we propose a frame-work called granular-ball fuzzy set by introducing granular-ball computing into fuzzy set. The computational framework is based on the granular-balls input rather than points; therefore, it is more efficient and robust than traditional fuzzy methods, and can be used in various fields of fuzzy data processing according to its extensibility. Furthermore, the…
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for clusters with a large number of different sample sizes are not accurate and efficient. In this paper, starting from the strategy of large-scale priority, the data is fuzzy iterated using granular-balls, and the membership degree of data only considers the two granular-balls where it is located, thus improving the efficiency of iteration. The formed fuzzy granu…
Ghent University（根特大学）；University of Catania（卡塔尼亚大学）；University of Portsmouth（朴茨茅斯大学）；Poznań University of Technology（波兹南理工大学）；Polish Academy of Sciences（波兰科学院）
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute s…
Support vector machines (SVMs) are powerful supervised learning tools developed to solve classification problems. However, SVMs are likely to perform poorly in the classification of imbalanced data. The rough set theory presents a mathematical tool for inference in nondeterministic cases that provides methods for removing irrelevant information from data. In this work, we propose an approach that efficiently used fuzzy rough set theory in weighted least squares twin support vector machine called FRLSTSVM for classification of imbalanced data. The first innovation is introducing a new fuzzy rou…
University of Kashan（卡尚大学）；Aalto University（阿尔托大学）；Isfahan University of Technology (IUT)（伊斯法罕理工大学（IUT））
Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in rea…
École de Technologie Supérieure - Université du Québec（魁北克大学高等技术学院）；University of Santa Catarina（圣卡塔琳娜大学）；SENAI Innovation Institute of Embedded Systems（巴西服务于工业的国家服务机构嵌入式系统创新研究所）
In this paper we present an incremental variant of the Twin Support Vector Machine (TWSVM) called Fuzzy Bounded Twin Support Vector Machine (FBTWSVM) to deal with large datasets and learning from data streams. We combine the TWSVM with a fuzzy membership function, so that each input has a different contribution to each hyperplane in a binary classifier. To solve the pair of quadratic programming problems (QPPs) we use a dual coordinate descent algorithm with a shrinking strategy, and to obtain a robust classification with a fast training we propose the use of a Fourier Gaussian approximation f…
Politecnico di Milano（米兰理工大学）；Beihang University（北京航空航天大学）
Online damage quantification suffers from insufficient labeled data that weakens its accuracy. In this context, adopting the domain adaptation on historical labeled data from similar structures/damages or simulated digital twin data to assist the current diagnosis task would be beneficial. However, most domain adaptation methods are designed for classification and cannot efficiently address damage quantification, a regression problem with continuous real-valued labels. This study first proposes a novel domain adaptation method, the Online Fuzzy-set-based Joint Distribution Adaptation for Regre…
Advanced Analytics Institute, Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程与信息技术学院高级分析研究所）；Data Science Centre, Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程与信息技术学院数据科学中心）
Motivated by the practical demands for simplification of data towards being consistent with human thinking and problem solving as well as tolerance of uncertainty, information granules are becoming important entities in data processing at different levels of data abstraction. This paper proposes a method to construct classifiers from multi-resolution hierarchical granular representations (MRHGRC) using hyperbox fuzzy sets. The proposed approach forms a series of granular inferences hierarchically through many levels of abstraction. An attractive characteristic of our classifier is that it can …
Fuzzy Granule Density-Based Outlier Detection with Multi-Scale Granular Balls
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）；National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University（深圳大学大数据系统计算技术国家工程实验室）；School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机科学学院）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Department of Electrical and Computer Engineering, King Abdulaziz University（阿卜杜勒阿齐兹大学电气与计算机工程系）；Department of Computer Engineering, Istinye University（伊斯提尼耶大学计算机工程系）
Federal University of Lavras (UFLA)（拉夫拉斯联邦大学（UFLA））
Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a …
University of Bologna（博洛尼亚大学）；INFN（意大利国家核物理研究所）；Federal University of Lavras（拉夫拉斯联邦大学）；INFN-CNAF（意大利国家核物理研究所国家核物理计算中心）
Log-based predictive maintenance of computing centers is a main concern regarding the worldwide computing grid that supports the CERN (European Organization for Nuclear Research) physics experiments. A log, as event-oriented adhoc information, is quite often given as unstructured big data. Log data processing is a time-consuming computational task. The goal is to grab essential information from a continuously changeable grid environment to construct a classification model. Evolving granular classifiers are suited to learn from time-varying log streams and, therefore, perform online classificat…
Towards scientific machine learning for granular material simulations -- challenges and opportunities
Deltares（代尔夫特三角洲研究中心）；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）；Saxion University of Applied Sciences（萨克森应用科学大学）；University of Pretoria（比勒陀利亚大学）；University of the Witwatersrand（金山大学）；Emmi AI GmbH（Emmi AI有限责任公司）；Edinburgh Napier University（爱丁堡龙比亚大学）；Delft University of Technology（代尔夫特理工大学）；Lund University（隆德大学）；University of Twente（特温特大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Edinburgh（爱丁堡大学）；Netherlands eScience Center（荷兰eScience中心）；Hong Kong University of Science and Technology（香港科技大学）；Tokyo City University（东京城市大学）；Columbia University（哥伦比亚大学）
