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Öğe A development of coordinate-based fuzzy encoding algorithm in compression of grayscale images(Springer, 2023) Wang, Dan; Zhu, Xiubin; Pedrycz, Witold; Yu, Zhenhua; Li, ZhiwuImage compression techniques realized in various ways have become an indispensable part in the practical storage and transmission of digital images. In this study, we present a novel method of lossy compression based on sampling and fuzzy encoding for grayscale images and discuss the problem of their reconstruction. First, an image is divided into a number of non-overlapping blocks of pixels. Next, we perform multiple rounds of random sampling. In each round, a number of pixels are selected as prototypes for the representing the corresponding block. Each pixel in the block is reconstructed based on the gray levels of the prototypes and membership degrees computed with respect to the distances of each pixel to the prototypes. The reconstruction abilities delivered by the prototypes are quantified by a certain objective fidelity criteria and the prototypes leading to lowest reconstruction error are determined as representatives of current block. Finally, once the representatives in each block have been determined, we reconstruct the whole image based on these prototypes. Experimental studies as well as visual evaluations show that the proposed algorithm is able to achieve high compression ratios while preserving the overall fidelity in the decompressed images.Öğe Privacy-Preserving Realization of Fuzzy Clustering and Fuzzy Modeling Through Vertical Federated Learning(Ieee-Inst Electrical Electronics Engineers Inc, 2024) Zhu, Xiubin; Wang, Dan; Pedrycz, Witold; Li, ZhiwuIn this study, we elaborate on a realization of fuzzy clustering and the construction of fuzzy rule-based models on the basis of vertically partitioned datasets in a privacy-preserving federated learning approach. The main focus of the overall design process is to construct a family of information granules (clusters) and the corresponding fuzzy rules in the presence of a collection of vertically partitioned datasets without compromising data privacy. These datasets are composed of the same data but are described by different features, and due to security considerations, data cannot be shared. The vertical federated fuzzy clustering can be realized as an iterative optimization process composed of successive cycles: 1) computation (update) of the prototypes and partition matrices performed on the basis of local datasets and 2) an integration of the local sources of knowledge carried out on a central coordinator-server. The update of the partition matrices can be completed using a distance-based or gradient-based approach. The communication of findings between local clients and the coordinator-server is realized through exchanging partition matrices, which are more general than numeric data and can avoid leakage of data privacy. Fuzzy models are optimized in a similar manner through exchanging the gradients of the performance index computed with respect to the parameters between the clients and the global coordinator. The proposed mechanism exhibits significant originality since the realization of fuzzy modeling in a vertical federated learning environment has not been studied. Experimental studies show that the proposed federated clustering and fuzzy model design could effectively reveal the structure of the entire dataset and achieve high performance compared with the results obtained in a centralized manner.