Fuzzy-rough set models and fuzzy-rough data reduction

Rough set theory is a powerful tool to analysis the information systems. Fuzzy rough set is introduced as a fuzzy generalization of rough sets. This paper reviewed the most important contributions to the rough set theory, fuzzy rough set theory and their applications. In many real world situations, some of the attribute values for an object may be in the set-valued form. In this paper, to handle this problem, we present a more general approach to the fuzzification of rough sets. Specially, we define a broad family of fuzzy rough sets. This paper presents a new development for the rough set theory by incorporating the classical rough set theory and the interval-valued fuzzy sets. The proposed methods are illustrated by an numerical example on the real case

GBG++: A Fast and Stable Granular Ball Generation Method for Classification

Granular ball computing (GBC), as an efficient, robust, and scalable learning method, has become a popular research topic of granular computing. GBC includes two stages: granular ball generation (GBG) and multi-granularity learning based on the granular ball (GB). However, the stability and efficiency of existing GBG methods need to be further improved due to their strong dependence on $k$-means or $k$-division. In addition, GB-based classifiers only unilaterally consider the GB's geometric characteristics to construct classification rules, but the GB's quality is ignored. Therefore, in this paper, based on the attention mechanism, a fast and stable GBG (GBG++) method is proposed first. Specifically, the proposed GBG++ method only needs to calculate the distances from the data-driven center to the undivided samples when splitting each GB instead of randomly selecting the center and calculating the distances between it and all samples. Moreover, an outlier detection method is introduced to identify local outliers. Consequently, the GBG++ method can significantly improve effectiveness, robustness, and efficiency while being absolutely stable. Second, considering the influence of the sample size within the GB on the GB's quality, based on the GBG++ method, an improved GB-based $k$-nearest neighbors algorithm (GB$k$NN++) is presented, which can reduce misclassification at the class boundary. Finally, the experimental results indicate that the proposed method outperforms several existing GB-based classifiers and classical machine learning classifiers on $24$ public benchmark datasets

Evidential Clustering: A Review

International audienceIn evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibilistic and rough partitions, which are recovered as special cases. Three algorithms to generate a credal partition are reviewed. Each of these algorithms is shown to implement a decision-directed clustering strategy. Their relative merits are discussed

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

LEARNFCA: A FUZZY FCA AND PROBABILITY BASED APPROACH FOR LEARNING AND CLASSIFICATION

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Jitender Deogu

Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method

Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory

An empirical evaluation of imbalanced data strategies from a practitioner's point of view

This research tested the following well known strategies to deal with binary imbalanced data on 82 different real life data sets (sampled to imbalance rates of 5%, 3%, 1%, and 0.1%): class weight, SMOTE, Underbagging, and a baseline (just the base classifier). As base classifiers we used SVM with RBF kernel, random forests, and gradient boosting machines and we measured the quality of the resulting classifier using 6 different metrics (Area under the curve, Accuracy, F-measure, G-mean, Matthew's correlation coefficient and Balanced accuracy). The best strategy strongly depends on the metric used to measure the quality of the classifier. For AUC and accuracy class weight and the baseline perform better; for F-measure and MCC, SMOTE performs better; and for G-mean and balanced accuracy, underbagging

A fuzzy probabilistic inference methodology for constrained 3D human motion classification

Enormous uncertainties in unconstrained human motions lead to a fundamental challenge that many recognising algorithms have to face in practice: efficient and correct motion recognition is a demanding task, especially when human kinematic motions are subject to variations of execution in the spatial and temporal domains, heavily overlap with each other,and are occluded. Due to the lack of a good solution to these problems, many existing methods tend to be either effective but computationally intensive or efficient but vulnerable to misclassification. This thesis presents a novel inference engine for recognising occluded 3D human motion assisted by the recognition context. First, uncertainties are wrapped into a fuzzy membership function via a novel method called Fuzzy Quantile Generation which employs metrics derived from the probabilistic quantile function. Then, time-dependent and context-aware rules are produced via a genetic programming to smooth the qualitative outputs represented by fuzzy membership functions. Finally, occlusion in motion recognition is taken care of by introducing new procedures for feature selection and feature reconstruction. Experimental results demonstrate the effectiveness of the proposed framework on motion capture data from real boxers in terms of fuzzy membership generation, context-aware rule generation, and motion occlusion. Future work might involve the extension of Fuzzy Quantile Generation in order to automate the choice of a probability distribution, the enhancement of temporal pattern recognition with probabilistic paradigms, the optimisation of the occlusion module, and the adaptation of the present framework to different application domains.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Dr Jitender Deogu