DENFIS: Dynamic Evolving Neural-Fuzzy Inference System and its Application for Time Series Prediction

This paper introduces a new type of fuzzy inference systems, denoted as DENFIS (dynamic evolving neural-fuzzy inference system), for adaptive on-line and off-line learning, and their application for dynamic time series prediction. DENFIS evolve through incremental, hybrid (supervised/unsupervised), learning and accommodate new input data, including new features, new classes, etc. through local element tuning. New fuzzy rules are created and updated during the operation of the system. At each time moment the output of DENFIS is calculated through a fuzzy inference system based on m-most activated fuzzy rules which are dynamically chosen from a fuzzy rule set. Two approaches are proposed: (1) dynamic creation of a first-order TakagiSugeno type fuzzy rule set for a DENFIS on-line model; (2) creation of a first-order TakagiSugeno type fuzzy rule set, or an expanded high-order one, for a DENFIS off-line model. A set of fuzzy rules can be inserted into DENFIS before, or during its learning process. Fuzzy rules can also be extracted during the learning process or after it. An evolving clustering method (ECM), which is employed in both on-line and off-line DENFIS models, is also introduced. It is demonstrated that DENFIS can effectively learn complex temporal sequences in an adaptive way and outperform some well known, existing models

Heuristic design of fuzzy inference systems: a review of three decades of research

This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi–Sugeno–Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper offers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems

Learning Opposites with Evolving Rules

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.Comment: Accepted for publication in The 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), August 2-5, 2015, Istanbul, Turke

Evolving Ensemble Fuzzy Classifier

The concept of ensemble learning offers a promising avenue in learning from data streams under complex environments because it addresses the bias and variance dilemma better than its single model counterpart and features a reconfigurable structure, which is well suited to the given context. While various extensions of ensemble learning for mining non-stationary data streams can be found in the literature, most of them are crafted under a static base classifier and revisits preceding samples in the sliding window for a retraining step. This feature causes computationally prohibitive complexity and is not flexible enough to cope with rapidly changing environments. Their complexities are often demanding because it involves a large collection of offline classifiers due to the absence of structural complexities reduction mechanisms and lack of an online feature selection mechanism. A novel evolving ensemble classifier, namely Parsimonious Ensemble pENsemble, is proposed in this paper. pENsemble differs from existing architectures in the fact that it is built upon an evolving classifier from data streams, termed Parsimonious Classifier pClass. pENsemble is equipped by an ensemble pruning mechanism, which estimates a localized generalization error of a base classifier. A dynamic online feature selection scenario is integrated into the pENsemble. This method allows for dynamic selection and deselection of input features on the fly. pENsemble adopts a dynamic ensemble structure to output a final classification decision where it features a novel drift detection scenario to grow the ensemble structure. The efficacy of the pENsemble has been numerically demonstrated through rigorous numerical studies with dynamic and evolving data streams where it delivers the most encouraging performance in attaining a tradeoff between accuracy and complexity.Comment: this paper has been published by IEEE Transactions on Fuzzy System

Optimization of Evolutionary Neural Networks Using Hybrid Learning Algorithms

Evolutionary artificial neural networks (EANNs) refer to a special class of artificial neural networks (ANNs) in which evolution is another fundamental form of adaptation in addition to learning. Evolutionary algorithms are used to adapt the connection weights, network architecture and learning algorithms according to the problem environment. Even though evolutionary algorithms are well known as efficient global search algorithms, very often they miss the best local solutions in the complex solution space. In this paper, we propose a hybrid meta-heuristic learning approach combining evolutionary learning and local search methods (using 1st and 2nd order error information) to improve the learning and faster convergence obtained using a direct evolutionary approach. The proposed technique is tested on three different chaotic time series and the test results are compared with some popular neuro-fuzzy systems and a recently developed cutting angle method of global optimization. Empirical results reveal that the proposed technique is efficient in spite of the computational complexity

PAC: A Novel Self-Adaptive Neuro-Fuzzy Controller for Micro Aerial Vehicles

There exists an increasing demand for a flexible and computationally efficient controller for micro aerial vehicles (MAVs) due to a high degree of environmental perturbations. In this work, an evolving neuro-fuzzy controller, namely Parsimonious Controller (PAC) is proposed. It features fewer network parameters than conventional approaches due to the absence of rule premise parameters. PAC is built upon a recently developed evolving neuro-fuzzy system known as parsimonious learning machine (PALM) and adopts new rule growing and pruning modules derived from the approximation of bias and variance. These rule adaptation methods have no reliance on user-defined thresholds, thereby increasing the PAC's autonomy for real-time deployment. PAC adapts the consequent parameters with the sliding mode control (SMC) theory in the single-pass fashion. The boundedness and convergence of the closed-loop control system's tracking error and the controller's consequent parameters are confirmed by utilizing the LaSalle-Yoshizawa theorem. Lastly, the controller's efficacy is evaluated by observing various trajectory tracking performance from a bio-inspired flapping-wing micro aerial vehicle (BI-FWMAV) and a rotary wing micro aerial vehicle called hexacopter. Furthermore, it is compared to three distinctive controllers. Our PAC outperforms the linear PID controller and feed-forward neural network (FFNN) based nonlinear adaptive controller. Compared to its predecessor, G-controller, the tracking accuracy is comparable, but the PAC incurs significantly fewer parameters to attain similar or better performance than the G-controller.Comment: This paper has been accepted for publication in Information Science Journal 201

Evolving Large-Scale Data Stream Analytics based on Scalable PANFIS

Many distributed machine learning frameworks have recently been built to speed up the large-scale data learning process. However, most distributed machine learning used in these frameworks still uses an offline algorithm model which cannot cope with the data stream problems. In fact, large-scale data are mostly generated by the non-stationary data stream where its pattern evolves over time. To address this problem, we propose a novel Evolving Large-scale Data Stream Analytics framework based on a Scalable Parsimonious Network based on Fuzzy Inference System (Scalable PANFIS), where the PANFIS evolving algorithm is distributed over the worker nodes in the cloud to learn large-scale data stream. Scalable PANFIS framework incorporates the active learning (AL) strategy and two model fusion methods. The AL accelerates the distributed learning process to generate an initial evolving large-scale data stream model (initial model), whereas the two model fusion methods aggregate an initial model to generate the final model. The final model represents the update of current large-scale data knowledge which can be used to infer future data. Extensive experiments on this framework are validated by measuring the accuracy and running time of four combinations of Scalable PANFIS and other Spark-based built in algorithms. The results indicate that Scalable PANFIS with AL improves the training time to be almost two times faster than Scalable PANFIS without AL. The results also show both rule merging and the voting mechanisms yield similar accuracy in general among Scalable PANFIS algorithms and they are generally better than Spark-based algorithms. In terms of running time, the Scalable PANFIS training time outperforms all Spark-based algorithms when classifying numerous benchmark datasets.Comment: 20 pages, 5 figure