Correntropy-Based Evolving Fuzzy Neural System

In this paper, a correntropy-based evolving fuzzy neural system (correntropy-EFNS) is proposed for approximation of nonlinear systems. Different from the commonly used meansquare error criterion, correntropy has a strong outliers rejection ability through capturing the higher moments of the error distribution. Considering the merits of correntropy, this paper brings contributions to build EFNS based on the correntropy concept to achieve a more stable evolution of the rule base and update of the rule parameters instead of the commonly used meansquare error criterion. The correntropy-EFNS (CEFNS) begins with an empty rule base and all rules are evolved online based on the correntropy criterion. The consequent part parameters are tuned based on the maximum correntropy criterion where the correntropy is used as the cost function so as to improve the non-Gaussian noise rejection ability. The steady-state convergence performance of the CEFNS is studied through the calculation of the steady-state excess mean square error (EMSE) in two cases: i) Gaussian noise; and ii) non-Gaussian noise. Finally, the CEFNS is validated through a benchmark system identification problem, a Mackey-Glass time series prediction problem as well as five other real-world benchmark regression problems under both noise-free and noisy conditions. Compared with other evolving fuzzy neural systems, the simulation results show that the proposed CEFNS produces better approximation accuracy using the least number of rules and training time and also owns superior non-Gaussian noise handling capability

Statistically Evolving Fuzzy Inference System for Non-Gaussian Noises

Non-Gaussian noises always exist in the nonlinear system, which usually lead to inconsistency and divergence of the regression and identification applications. The conventional evolving fuzzy systems (EFSs) in common sense have succeeded to conquer the uncertainties and external disturbance employing the specific variable structure characteristic. However, non-Gaussian noises would trigger the frequent changes of structure under the transient criteria, which severely degrades performance. Statistical criterion provides an informed choice of the strategies of the structure evolution, utilizing the approximation uncertainty as the observation of model sufficiency. The approximation uncertainty can be always decomposed into model uncertainty term and noise term, and is suitable for the non-Gaussian noise condition, especially relaxing the traditional Gaussian assumption. In this paper, a novel incremental statistical evolving fuzzy inference system (SEFIS) is proposed, which has the capacity of updating the system parameters, and evolving the structure components to integrate new knowledge in the new process characteristic, system behavior, and operating conditions with non-Gaussian noises. The system generates a new rule based on the statistical model sufficiency which gives so insight into whether models are reliable and their approximations can be trusted. The nearest rule presents the inactive rule under the current data stream and further would be deleted without losing any information and accuracy of the subsequent trained models when the model sufficiency is satisfied. In our work, an adaptive maximum correntropy extend Kalman filter (AMCEKF) is derived to update the parameters of the evolving rules to cope with the non-Gaussian noises problems to further improve the robustness of parameter updating process. The parameter updating process shares an estimate of the uncertainty with the criteria of the structure evolving process to make the computation less of a burden dramatically. The simulation studies show that the proposed SEFIS has faster learning speed and is more accurate than the existing evolving fuzzy systems (EFSs) in the case of noise-free and noisy conditions

Multi-Objective Evolutionary Optimisation for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs

Multiobjective Evolutionary Optimization for Prototype-Based Fuzzy Classifiers

Evolving intelligent systems (EISs), particularly, the zero-order ones have demonstrated strong performance on many real-world problems concerning data stream classification, while offering high model transparency and interpretability thanks to their prototype-based nature. Zero-order EISs typically learn prototypes by clustering streaming data online in a “one pass” manner for greater computation efficiency. However, such identified prototypes often lack optimality, resulting in less precise classification boundaries, thereby hindering the potential classification performance of the systems. To address this issue, a commonly adopted strategy is to minimise the training error of the models on historical training data or alternatively, to iteratively minimise the intra-cluster variance of the clusters obtained via online data partitioning. This recognises the fact that the ultimate classification performance of zero-order EISs is driven by the positions of prototypes in the data space. Yet, simply minimising the training error may potentially lead to overfitting, whilst minimising the intra-cluster variance does not necessarily ensure the optimised prototype-based models to attain improved classification outcomes. To achieve better classification performance whilst avoiding overfitting for zero-order EISs, this paper presents a novel multi-objective optimisation approach, enabling EISs to obtain optimal prototypes via involving these two disparate but complementary strategies simultaneously. Five decision-making schemes are introduced for selecting a suitable solution to deploy from the final non-dominated set of the resulting optimised models. Systematic experimental studies are carried out to demonstrate the effectiveness of the proposed optimisation approach in improving the classification performance of zero-order EISs

Fuzzy Wavelet Neural Network Using a Correntropy Criterion for Nonlinear System Identification

Recent researches have demonstrated that the Fuzzy Wavelet Neural Networks (FWNNs) are an efficient tool to identify nonlinear systems. In these structures, features related to fuzzy logic, wavelet functions, and neural networks are combined in an architecture similar to the Adaptive Neurofuzzy Inference Systems (ANFIS). In practical applications, the experimental data set used in the identification task often contains unknown noise and outliers, which decrease the FWNN model reliability. In order to reduce the negative effects of these erroneous measurements, this work proposes the direct use of a similarity measure based on information theory in the FWNN learning procedure. The Mean Squared Error (MSE) cost function is replaced by the Maximum Correntropy Criterion (MCC) in the traditional error backpropagation (BP) algorithm. The input-output maps of a real nonlinear system studied in this work are identified from an experimental data set corrupted by different outliers rates and additive white Gaussian noise. The results demonstrate the advantages of the proposed cost function using the MCC as compared to the MSE. This work also investigates the influence of the kernel size on the performance of the MCC in the BP algorithm, since it is the only free parameter of correntropy

Self-Organizing Fuzzy Belief Inference System for Classification

Evolving fuzzy systems (EFSs) are widely known as a powerful tool for streaming data prediction. In this paper, a novel zero-order EFS with a unique belief structure is proposed for data stream classification. Thanks to this new belief structure, the proposed model can handle the inter-class overlaps in a natural way and better capture the underlying multi-model structure of data streams in the form of prototypes. Utilizing data-driven soft thresholds, the proposed model self-organizes a set of prototype-based IF-THEN fuzzy belief rules from data streams for classification, and its learning outcomes are practically meaningful. With no requirement of prior knowledge in the problem domain, the proposed model is capable of self-determining the appropriate level of granularity for rule base construction, while enabling users to specify their preferences on the degree of fineness of its knowledge base. Numerical examples demonstrate the superior performance of the proposed model on a wide range of stationary and nonstationary classification benchmark problems

Particle Swarm Optimized Autonomous Learning Fuzzy System

The antecedent and consequent parts of a first-order evolving intelligent system (EIS) determine the validity of the learning results and overall system performance. Nonetheless, the state-of-the-art techniques mostly stress on the novelty from the system identification point of view but pay less attention to the optimality of the learned parameters. Using the recently introduced autonomous learning multiple model (ALMMo) system as the implementation basis, this paper introduces a particles warm-based approach for EIS optimization. The proposed approach is able to simultaneously optimize the antecedent and consequent parameters of ALMMo and effectively enhance the system performance by iteratively searching for optimal solutions in the problem spaces. In addition, the proposed optimization approach does not adversely influence the “one pass” learning ability of ALMMo. Once the optimization process is complete, ALMMo can continue to learn from new data to incorporate unseen data patterns recursively without a full retraining. Experimental studies with a number of real-world benchmark problems validate the proposed concept and general principles. It is also verified that the proposed optimization approach can be applied to other types of EISs with similar operating mechanisms

Self-Organizing Fuzzy Inference Ensemble System for Big Streaming Data Classification

An evolving intelligent system (EIS) is able to self-update its system structure and meta-parameters from streaming data. However, since the majority of EISs are implemented on a single-model architecture, their performances on large-scale, complex data streams are often limited. To address this deficiency, a novel self-organizing fuzzy inference ensemble framework is proposed in this paper. As the base learner of the proposed ensemble system, the self-organizing fuzzy inference system is capable of self-learning a highly transparent predictive model from streaming data on a chunk-by-chunk basis through a human-interpretable process. Very importantly, the base learner can continuously self-adjust its decision boundaries based on the inter-class and intra-class distances between prototypes identified from successive data chunks for higher classification precision. Thanks to its parallel distributed computing architecture, the proposed ensemble framework can achieve great classification precision while maintain high computational efficiency on large-scale problems. Numerical examples based on popular benchmark big data problems demonstrate the superior performance of the proposed approach over the state-of-the-art alternatives in terms of both classification accuracy and computational efficiency

Multi-label Classification via Adaptive Resonance Theory-based Clustering

This paper proposes a multi-label classification algorithm capable of continual learning by applying an Adaptive Resonance Theory (ART)-based clustering algorithm and the Bayesian approach for label probability computation. The ART-based clustering algorithm adaptively and continually generates prototype nodes corresponding to given data, and the generated nodes are used as classifiers. The label probability computation independently counts the number of label appearances for each class and calculates the Bayesian probabilities. Thus, the label probability computation can cope with an increase in the number of labels. Experimental results with synthetic and real-world multi-label datasets show that the proposed algorithm has competitive classification performance to other well-known algorithms while realizing continual learning