Publications

Data are the blood life of today's society. Revealing interpretable and conceptually stable associations (relationships) within data forms one of the central items on the agenda of data analytics. With this regard, associative memories capturing linkages between data positioned in two (or more) data spaces are examples of commonly considered architectures. In contrast to the existing constructs of memories, we propose a new category of architectures that exhibits several essential features: (i) associative mapping is spanned over a collection of prototypes (viz. representatives) of data and in this way becomes focused on their structural essentials, (ii) prototypes are built through a process of collaborative clustering, (iii) the design process retains privacy aspects by not disclosing locally available data, (iv) optimization of bidirectional and multidirectional recall is presented. In the sequel, we demonstrate how granular mappings engaging granular parameter spaces are developed and assessed. Associative relationships constructed in terms of granular bidirectional and multidirectional associative memories are investigated. We also develop granular autoencoders and stacked granular auto encoders offering further support of the development process.

The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.

In this study, a novel semantic concept-based inference neural network (SCINN) is proposed to develop the design methodology of the explainable deep neuro-fuzzy models and improve their generalization performance in high-dimensional problems. Traditional neuro-fuzzy models exhibit outstanding interpretability in the problems with lower dimensionality. However, when faced with high-dimensional scenarios, the long rule and rule explosion problems damage their interpretability and result in poor generalization performance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , accuracy), even making them unusable. Although deep neuro-fuzzy models show enhanced performance in handling high-dimensional problems compared to traditional neuro-fuzzy models, they often come at the expense of interpretability. In order to establish the neuro-fuzzy model that is capable of addressing the high-dimensional problems while preserving the interpretability, the SCINN is proposed with the aid of the concept-based measure generation paradigm (CMGP) and the multi-view information augmentation strategy (MIAS). The CMGP is designed to adaptively define the membership functions (MFs) that correspond to the human-understandable semantic concepts based on the given data; the defined MFs contribute to the construction of the explainable fuzzy rule that can directly process high-dimensional data. The MIAS is structured to develop a unified paradigm for implementing consequence functions in the fuzzy rules, which enhances the approximation ability of the SCINN. The performance of SCINN is evaluated on various image datasets using different comparison methods, including neuro-fuzzy-based approaches and deep structure-based neural networks. Furthermore, a real-world application is adopted to evaluate its effectiveness. The experimental results show that SCINN outperforms the compared neuro-fuzzy models and is comparable to the deep structure-based neural network.