In the design of fuzzy rule-based models, in the presence of high-dimensional data, we are faced with conceptual and algorithmic challenges. Conceptually, as the dimensionality of data increases, the notion of distance starts to be questionable, resulting in the well-known concentration effect. This has a direct detrimental effect given the fact that the distance is used in fuzzy clustering, using which the condition parts of the rules are being formed. Computationally, with the increase of dimensionality, the computing overhead becomes significant and has to be carefully addressed. In this article, we advocate a construction of distributed fuzzy rule-based models, where instead of a single monolithic (multivariable) rule-based model, we construct a collection of low-dimensional (in particular, 1- or 2-D) rule-based models and aggregate their results through some linear transformations. A suite of experimental studies realized using publicly available data are reported along with a comparative analysis engaging accuracy criteria and computing overhead. Interestingly, building distributed models exhibits some tangible benefits over the construction of the monolithic rule-based models. In terms of accuracy and computing costs, the gains of 1-D rule-based models with optimal linkage matrix (on average) are around 43.46% and 98.85%, respectively.

Performance of direction of arrival (DOA) estimation is one of the most important issues in array signal processing. Subspace-based algorithms provide a good compromise between the estimation accuracy and computational complexity. However, these methods are exposed to performance breakdown at low SNR scenarios. A major reason for such performance breakdown is the subspace swap phenomenon (intersubspace leakage). In this article, we elaborate on a novel modified signal subspace model through exploiting a supervised index for the estimation of DOA. With the developed model we refine the signal subspace so as to enhance the performance of the DOA estimation. In the proposed scheme, we define a fuzzy similarity matrix for the eigenvalues of the array output correlation matrix to capture the distribution of the eigenvalues. Then, we build up a transformation matrix between the fuzzy similarity matrix and the eigenspace of the correlation matrix, and construct a nonlinear transformation function to adjust the fuzzy similarity matrix. Subsequently, we define a supervised evaluation index named signal subspace reconstruction error for DOA estimation and construct a cost function of the signal subspace to develop a supervised model for the signal subspace. The signal subspace can be modified through adjusting the parameter in the nonlinear transformation function and optimizing the abovementioned cost function. Finally, the performance of DOA estimation can be enhanced with the modified signal subspace. The main characteristic of the proposed model is circularly applied feedback of the estimated DOA for refining the estimated subspace. It is a closed loop and supervised method not reported before. This article opens a specific way for improving the performance of the DOA estimation in array signal processing by a supervised index. However, the proposed method is still unsatisfying in some scopes of signal-to-noise ratio. We believe that exploiting a validity index for DOA estimation in array signal processing is still a general and interesting problem.

Generally, fuzzy models, especially rule-based models, are designed in a monolithic manner, meaning that all data are used en bloc to design the model. At the same time, there is a visible need to cope with the ever-increasing volumes of data (both in terms of the number of data and their dimensionality) as well as being faced with distributed data located at various locations. The objective of this study is to develop a concept and provide a design framework as well as assess its performance for constructing a collection of rule-based models on a basis of a randomly sampled repository of data and then realize their aggregation. More specifically, for the sampled data, the design of each model is carried out in a standard way as commonly encountered in the case of Takagi-Sugeno (TS) rule-based models and next augmented by gradient boosting. The aggregation is realized by optimizing a weighting scheme applied to the results of the individual models. Our intent is also to carefully demonstrate the performance offered by the mechanisms of machine learning applied in the setting of rule-based models, which is an original task completed before. A number of high-dimensional data are used in the experimental studies to complete a thorough assessment. A comparative performance analysis is reported with respect to the monolithically developed TS models.

In this article, an augmented subspace-based algorithm for detecting the direction of arrival (DOA) of signals is presented. In the developed scheme, a uniform circular antenna array with a full range of lateral capacity is first transformed into a uniform linear antenna array in which the steering matrix has a Vandermonde form. This kind of structure can be exploited to formulate computationally efficient search-free estimation methods. In the process of virtual transformation, a novel DOA unit matrix of an assumed sector where the signals to be detected are located is built and optimized to find response matrices of the real and virtual antenna arrays to signals from the sector. By utilizing singular value decomposition (SVD) of the response matrix of the real antenna array to possible signals from the sector, a stable virtual transformation matrix between the real and virtual antenna arrays is obtained. Meanwhile, the aperture of the original array is also expanded during this process. Then, a virtual cyclic optimization algorithm is introduced to thoroughly mine information from the correlation matrices of the virtual antenna array receiving data and to optimize the signal subspace. Subsequently, the DOA can be efficiently determined through the reconstruction of the steering matrix. In the experimental part of the study, root-mean-square errors and probability of success are used to evaluate the performance of the algorithms. In particular, simulation results demonstrate that the proposed methods provide significant accuracy improvements, especially for low signal-to-noise ratio thresholds.

This article is concerned with a problem of relational factorization which engages fuzzy relational calculus. It forms an interesting alternative to the method of nonnegative matrix factorization that has been commonly discussed and found in numerous applications. The relational factorization takes original n -dimensional data located in the unit hypercube and factorizes it into data of lower dimensionality and some fuzzy relations. Owing to the logic nature of processing delivered by relational calculus, the dimensionality reduction exhibits transparency as the reduction mechanism itself is described in terms of logic expressions. Two types of factorizations mechanisms are investigated by using s–t and t–s composition operators where t and s are triangular norms and conorms, respectively. A two-level process of factorization is designed. A gradient-based learning scheme is developed. The quantification of the performance of the factorization process is realized by bringing a concept of information granularity: The obtained fuzzy relations are formed based on granular constructs and the quality of the produced factorization is assessed in terms of the coverage and specificity of the obtained granular results. A collection of experiments is included to present the performance of factorization and its parametric analysis. In addition, the proposed algorithm comes with sound interpretability in terms of both the structure of the model and an intuitive meaning of the fuzzy relations being the result of factorization.