This paper proposes a method to accelerate the training process of a general fuzzy min-max neural network. The purpose is to reduce the unsuitable hyperboxes selected as the potential candidates of the expansion step of existing hyperboxes to cover a new input pattern in the online learning algorithms or candidates of the hyperbox aggregation process in the agglomerative learning algorithms. Our proposed approach is based on the mathematical formulas to form a branch-and-bound solution aiming to remove the hyperboxes which are certain not to satisfy expansion or aggregation conditions, and in turn, decreasing the training time of learning algorithms. The efficiency of the proposed method is assessed over a number of widely used data sets. The experimental results indicated the significant decrease in training time of the proposed approach for both online and agglomerative learning algorithms. Notably, the training time of the online learning algorithms is reduced from 1.2 to 12 times when using the proposed method, while the agglomerative learning algorithms are accelerated from 7 to 37 times on average.
Most dynamic ensemble selection (DES) methods utilize the K-Nearest Neighbors (KNN) algorithm to estimate the competence of classifiers in a small region surrounding the query sample. However, KNN is very sensitive to the local distribution of the data. Moreover, it also has a high computational cost as it requires storing the whole data in memory and performing multiple distance calculations during inference. Hence, the dependency on the KNN algorithm ends up limiting the use of DES techniques for large-scale problems. This paper presents a new DES framework based on fuzzy hyperboxes called F…
University of Technology Sydney（悉尼科技大学）；Khalifa University（哈利法大学）
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 environment…
Advanced Analytics Institute（高级分析研究所）；Faculty of Engineering and IT（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）
General fuzzy min-max (GFMM) neural network is a generalization of fuzzy neural networks formed by hyperbox fuzzy sets for classification and clustering problems. Two principle algorithms are deployed to train this type of neural network, i.e., incremental learning and agglomerative learning. This paper presents a comprehensive empirical study of performance influencing factors, advantages, and drawbacks of the general fuzzy min-max neural network on pattern classification problems. The subjects of this study include (1) the impact of maximum hyperbox size, (2) the influence of the similarity …
Advanced Analytics Institute（高级分析研究所）；Faculty of Engineering and Information Technology（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）
This paper proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a generalization error bound of the proposed classifier based on the strength of the individual hyperbox-based classifiers as well as the correlation among them. The effectiveness of the proposed classifier is analyzed using a carefully selected illustrative example and compared empirically with other popular single and ensemble classifiers via 20 datasets usin…
Hyperbox-based machine learning algorithms are an important and popular branch of machine learning in the construction of classifiers using fuzzy sets and logic theory and neural network architectures. This type of learning is characterised by many strong points of modern predictors such as a high scalability, explainability, online adaptation, effective learning from a small amount of data, native ability to deal with missing data and accommodating new classes. Nevertheless, there is no comprehensive existing package for hyperbox-based machine learning which can serve as a benchmark for resea…
Advanced Analytics Institute（高级分析研究所）；University of Technology Sydney（悉尼科技大学）；Data Science Centre（数据科学中心）
This paper proposes an improved version of the current online learning algorithm for a general fuzzy min-max neural network (GFMM) to tackle existing issues concerning expansion and contraction steps as well as the way of dealing with unseen data located on decision boundaries. These drawbacks lower its classification performance, so an improved algorithm is proposed in this study to address the above limitations. The proposed approach does not use the contraction process for overlapping hyperboxes, which is more likely to increase the error rate as shown in the literature. The empirical resul…
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 …
A general fuzzy min-max (GFMM) neural network is one of the efficient neuro-fuzzy systems for classification problems. However, a disadvantage of most of the current learning algorithms for GFMM is that they can handle effectively numerical valued features only. Therefore, this paper provides some potential approaches to adapting GFMM learning algorithms for classification problems with mixed-type or only categorical features as they are very common in practical applications and often carry very useful information. We will compare and assess three main methods of handling datasets with mixed f…
Imperial College London（伦敦帝国学院）；Sciemus Ltd（Sciemus有限公司）；University of Oxford（牛津大学）
In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by calculating the model evidence or marginal likelihood. We explain why this is an attractive alternative over simply minimizing a mean squared error metric of prediction and show the validity of the propos…
Huazhong University of Science and Technology（华中科技大学）
Takagi-Sugeno-Kang (TSK) fuzzy systems are very useful machine learning models for regression problems. However, to our knowledge, there has not existed an efficient and effective training algorithm that ensures their generalization performance, and also enables them to deal with big data. Inspired by the connections between TSK fuzzy systems and neural networks, we extend three powerful neural network optimization techniques, i.e., mini-batch gradient descent, regularization, and AdaBound, to TSK fuzzy systems, and also propose three novel techniques (DropRule, DropMF, and DropMembership) spe…
Huazhong University of Science and Technology（华中科技大学）
This paper presents PyTSK, a Python toolbox for developing Takagi-Sugeno-Kang (TSK) fuzzy systems. Based on scikit-learn and PyTorch, PyTSK allows users to optimize TSK fuzzy systems using fuzzy clustering or mini-batch gradient descent (MBGD) based algorithms. Several state-of-the-art MBGD-based optimization algorithms are implemented in the toolbox, which can improve the generalization performance of TSK fuzzy systems, especially for big data applications. PyTSK can also be easily extended and customized for more complicated algorithms, such as modifying the structure of TSK fuzzy systems, d…
Tel Aviv University（特拉维夫大学）；University of California, San Diego（加利福尼亚大学圣迭戈分校）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
The fuzzy or soft $k$-means objective is a popular generalization of the well-known $k$-means problem, extending the clustering capability of the $k$-means to datasets that are uncertain, vague, and otherwise hard to cluster. In this paper, we propose a semi-supervised active clustering framework, where the learner is allowed to interact with an oracle (domain expert), asking for the similarity between a certain set of chosen items. We study the query and computational complexities of clustering in this framework. We prove that having a few of such similarity queries enables one to get a polyn…
An evidential time-to-event prediction model based on Gaussian random fuzzy numbers
Saw Swee Hock School of Public Health, National University of Singapore（新加坡国立大学苏瑞福公共卫生学院）；Université de technologie de Compiègne（贡比涅技术大学）；CNRS（法国国家科学研究中心）；Heudiasyc（于迪阿斯实验室）；Institut Universitaire de France（法国大学研究院）；Institute of Data Science, National University of Singapore（新加坡国立大学数据科学研究院）
The existence of large volumes of time series data in many applications has motivated data miners to investigate specialized methods for mining time series data. Clustering is a popular data mining method due to its powerful exploratory nature and its usefulness as a preprocessing step for other data mining techniques. This article develops two novel clustering algorithms for time series data that are extensions of a crisp c-shapes algorithm. The two new algorithms are heuristic derivatives of fuzzy c-means (FCM). Fuzzy c-Shapes plus (FCS+) replaces the inner product norm in the FCM model with…
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Centro de Informática（信息中心）
The clustering methods have been used in a variety of fields such as image processing, data mining, pattern recognition, and statistical analysis. Generally, the clustering algorithms consider all variables equally relevant or not correlated for the clustering task. Nevertheless, in real situations, some variables can be correlated or may be more or less relevant or even irrelevant for this task. This paper proposes partitioning fuzzy clustering algorithms based on Euclidean, City-block and Mahalanobis distances and entropy regularization. These methods are an iterative three steps algorithms …
China University of Petroleum (East China)（中国石油大学（华东））；Indian Statistical Institute（印度统计研究所）
A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are hardly any work dealing with datasets with dimensions more than hundred or so. Here, we propose a neuro-fuzzy framework that can handle datasets with dimensions even more than 7000! In this context, we propose an adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of ``numeric underflow" and ``fake minimum" that arise for existing fuzzy syste…
Fuzzy relational identification builds a relational model describing systems behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on simplified max-min relational equation. The algorithm presents an adaptation method applied to gravity-center of each fuzzy set based on error integral value between measured and predicted system output, and uses the concept of time-variant universe of discourses. The identification algorithm also includes a method to attenuate noise influence in extracted system relational model using a fuzzy fi…
School of Computer Science（计算机科学学院）；Electronic Engineering University of Essex Colchester, United Kingdom（埃塞克斯大学电子工程学院伦敦郡，英国）；Department of Mathematics Slovak Academy of Sciences Bratislava, Slovakia（数学系斯洛伐克科学院布拉迪斯拉发，斯洛伐克）
Data mining techniques can be used to discover useful patterns by exploring and analyzing data and it's feasible to synergitically combine machine learning tools to discover fuzzy classification rules.In this paper, an adaptive Neuro fuzzy network with TSK fuzzy type and an improved quantum subtractive clustering has been developed. Quantum clustering (QC) is an intuition from quantum mechanics which uses Schrodinger potential and time-consuming gradient descent method. The principle advantage and shortcoming of QC is analyzed and based on its shortcomings, an improved algorithm through a subt…
