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

New Structural Evolving Algorithms For Fuzzy Systems

Recently, the issue of accuracy and interpretability trade-off has been getting more attention when designing new fuzzy systems. In this thesis, three evolving fuzzy models, namely enhancement of fuzzy term identification (EFTI), structure identification method (SIM) and structural evolving approach (SEA) are proposed to spot the best trade-off between accuracy and interpretability. EFTI, SIM and SEA are designed based on error reducing methods. EFTI is developed to fit with single input single output (SISO) problems (i.e. one dimension), while SIM and SEA are developed to fit with multi input single output (MISO) (medium and high dimension). EFTI begins with a simple fuzzy structure that is composed of two fuzzy terms in the input space. Then EFTI continues evolving by identifying splitting points of the input space that are compatible with the consequent parameters. On the other hand, SIM and SEA start with one fuzzy rule that has no fuzzy term in the input space regardless of the degree level of input dimension. Then they evolve on the basis of either closure or split processes for the selected input attribute of the selected subregion. If the selected attribute has no fuzzy terms, closure is performed, otherwise split is done. The evolving continues until a satisfactory accuracy is fulfilled or maximum number of subregion is reached. A partitioning technique based on the similarity feature and a static partition-selection technique are developed for SIM. While, a partitioning technique based on splitting the selected subregion into two subregions with maximum and minimum average error and a dynamic partition-selection technique are developed for SEA. Furthermore, a pruning technique based on the importance level of the fuzzy rules is proposed to shrink the rule-base of SEA. Compared with SISO models and using three datasets, EFTI produces the lowest RMSE with lowest number of rules. For MISO models and using nine benchmark datasets, SIM achieves the lowest RMSE with the smallest size of rule-base systems. Similarly, for MISO state-of-the-art models and using six benchmark datasets, SEA also produces the lowest RMSE with the smallest size of rule-base systems. In conclusion, the results proved that EFTI, SIM and SEA are able to produce a significant trade-off between accuracy and interpretabilit

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

An Incremental Construction of Deep Neuro Fuzzy System for Continual Learning of Non-stationary Data Streams

Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically extracted from data streams or removed if they play limited role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely gClass, drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of dimensionality of input space due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using seven datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four popular continual learning algorithms and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy. Moreover, it is also shown that the concept drift detection method is an effective tool to control the depth of network structure while the hidden layer merging scenario is capable of simplifying the network complexity of a deep network with negligible compromise of generalization performance.Comment: This paper has been published in IEEE Transactions on Fuzzy System

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

Discovering three-dimensional patterns in real-time from data streams: An online triclustering approach

Triclustering algorithms group sets of coordinates of 3-dimensional datasets. In this paper, a new triclustering approach for data streams is introduced. It follows a streaming scheme of learning in two steps: offline and online phases. First, the offline phase provides a sum mary model with the components of the triclusters. Then, the second stage is the online phase to deal with data in streaming. This online phase consists in using the summary model obtained in the offline stage to update the triclusters as fast as possible with genetic operators. Results using three types of synthetic datasets and a real-world environmental sensor dataset are reported. The performance of the proposed triclustering streaming algo rithm is compared to a batch triclustering algorithm, showing an accurate performance both in terms of quality and running timesMinisterio de Ciencia, Innovación y Universidades TIN2017-88209-C