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This study elaborates on a novel Hidden Markov Model (HMM)-based fuzzy model for time series prediction. Fuzzy rules (rule-based models) are employed to describe and quantify the relationship between the input and output time series, while the HMM is regarded as a vehicle for efficiently capturing the temporal behavior or changes of the multivariate time series which are not capable to capture through commonly encountered fuzzy rule-based models. Essentially, the proposed strategies control the contribution of different fuzzy rules so that the proposed model can well model the dynamic behavior of time series. Fuzzy C-Means clustering technique is an alternative way to construct fuzzy rules. Particle swarm optimization serves as a tool to optimize the parameters of the model (e.g., transition matrix and emission matrix). We construct and investigate the performance of the HMM-based fuzzy model by using a series of synthetic and publicly available multivariate time series. Experimental results demonstrate that the proposed model shows better performance than the fuzzy rule-based models used without the involvement of HMMs. [ABSTRACT FROM AUTHOR]

In this article, we introduce a design methodology of reinforced fuzzy models based both on univariate analysis and multivariable analysis to cope with high-dimensional problems. This approach is aimed at reducing the design process and curbing computing overhead inherently associated with the increasing volume of data in terms of both their number and the dimensionality of the feature space. The critical features of the proposed fuzzy models are highlighted as follows: First, the essential input variables of the model are selected by running the univariable and multivariable analyses. In univariate analysis, input variables with a strong linear relationship with the output variable are selected through correlation analysis completed for each input space and output space. On the contrary, in multivariable analysis, input variables are chosen by comparing the determination coefficients obtained from the subsets of input variables. Second, according to the analysis of the input variable, we construct two different kinds of fuzzy models. The first fuzzy model comprises the design of the univariable-based fuzzy model (UFM) and its aggregation. The UFMs are made by the individual input variables selected from the univariable analysis using a correlation coefficient. The subspaces formed by correlation analysis are applied for determining the centers of the membership function (MF). The results produced by individual fuzzy models are aggregated through some t-conorms. The second fuzzy model is with the fuzzy clustering for improving the form of fuzzy space in the premise part of a fuzzy rule. To curb the dramatic increase in size of fuzzy rule in high-dimensional problems, the clustering space is employed as the fuzzy space, and the partition matrix produced by fuzzy provided the required degrees of the MF. Experimental studies include a suite of synthetic and publicly available data. The superiority of the proposed design methodology was demonstrated by using 34 publicly available datasets and also compared with the conventional models associated with the fuzzy rule-based models as well as the state-of-the-art models reported in the literature. [ABSTRACT FROM AUTHOR]

Fuzzy clustering techniques, especially fuzzy C-means (FCM) and its weighted variants, are typical partitive clustering models that are widely used for revealing possible hidden structures in data. Although they can quantitatively depict the overlapping areas with a partition matrix, their performances deteriorate when dealing with high-dimensional data because the distance computations may be negatively impacted by the irrelevant features, and then the concentration effect may arise. Moreover, they are sensitive to noisy environments. To tackle these obstacles, a robust jointly sparse fuzzy clustering method (RJSFC) is proposed in this study. The representative prototypes, sparse membership grades, and an orthogonal projection matrix are simultaneously learnt when optimizing RJSFC. The obtained low-dimensional embeddings can preserve the local neighborhood structure, and the clustering is conducted in the transformed lower dimensional space rather than the original space, which improves the capability of fuzzy clustering for dealing with high-dimensional scenarios. Furthermore, ${L_{2,1}}$ -norm is exploited as the basic metric for both loss and regularization parts in RJSFC, the robustness of the model and the interpretability of the extracted features are enhanced. The notions of fuzzy clustering, neighborhood structure preservation, and feature extraction are seamlessly integrated into a unified model. The limitation of the previous two-stage clustering framework when dealing with high-dimensional data entailing dimensionality reduction and clustering procedures separately can be effectively addressed. Extensive experimental results on various well-known datasets demonstrate the usefulness of RJSFC when comparing with some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Financial time series are generally high-dimensional, nonstationary, and exhibit heteroscedasticity. To derive a suitable way to cluster financial time series, these characteristics have to be taken into consideration. With this aim, in this article, the financial time series is firstly modeled using generalized autoregressive conditional heteroscedasticity (GARCH) models, where the parameters of GARCH models can represent the dynamic feature of the volatility in each time series. Therefore, the following clustering is realized based on the GARCH model parameters, which can help reduce the dimensionality of the original time series at the same time. Then, to produce semantically sound clustering results, we granulate the parameters based on the axiomatic fuzzy set (AFS) theory and structure them into a collection of meaningful and semantically sound entities, i.e., AFS information granules. Furthermore, the hierarchical structure of AFS information granules is built to realize time series clustering under the framework of granular computing. In the proposed approach, the characteristics of financial time series is fully considered to proceed dimensionality reduction, and the semantic clustering results obtained for different numbers of clusters are guaranteed to be the most informative. In the experiments, an application for clustering the time series coming from Chinese Yuan exchange rates against international currencies is presented to demonstrate the performance of the proposed clustering method. The results of clustering of the proposed method are the same as those of the fuzzy C-means algorithm and the hierarchical clustering with ward linkage, where the clustering results produced by the AFS hierarchical clustering exhibit well-articulated semantics at each level of the hierarchy. [ABSTRACT FROM AUTHOR]

In this study, we introduce novel fuzzy neural networks designed with the aid of linear function prototype-driven fuzzy clustering (LFPFC) and layer reconstruction-based network design strategy to deal with the regression problem. The LFPFC constitutes a new clustering technique inspired by the fuzzy c-regression model (FCRM) clustering unlike fuzzy c-means (FCM) clustering LFPFC represents the prototypes of clusters as linear functions, and this can lead to more reliable data analysis of complex regression problems. We propose two types of LFPFC such as an estimated output-based LFPFC and a distance-based LFPFC. The estimated output-based LFPFC uses the output estimated on a basis of the simple model instead of the target output to calculate the centroid of LFPFC. A centroid of distance-based LFPFC is computed through the Euclidean distance between input data and the centroid of the cluster. By using two kinds of LFPFC approaches, we propose three different types of fuzzy neural networks: i) the fuzzy neural networks through layer reconstruction-based network design strategy consists of two models. The first model serves as an estimate of the desired output and the estimated output is used in the LFPFC of the second model. ii) In the fuzzy neural networks applied to the basic architecture of distance-based LFPFC, the hidden layer using the membership function changes to basic distance-based LFPFC, and the partition matrix obtained from LFPFC is used as the output of the hidden layer. iii) in the fuzzy neural network with the advanced architecture of distance-based LFPFC, an additional auxiliary layer is considered between the hidden and output layers to estimate the membership function of output space through LFPFC. In the experiments, we evaluate the performance index of the proposed models using publicly available machine learning datasets. The superiority of the proposed fuzzy neural networks designed by using LFPFC is demonstrated through the comparative analysis with the diverse regression models offered in the Weka data mining software. By conducting the Friedman test we show that the proposed model exhibits visible competitiveness from the viewpoint of performance. In addition, a real-world Portland cement dataset is dealt with to demonstrate the superiority of the models designed with the aid of LFPFC and reinforced layer reconstruction-based network design strategy. [ABSTRACT FROM AUTHOR]