Privacy-preserving visual analytics using complex single-valued neutrosophic sets and encrypted dimensionality reduction

This article introduces a new concept of complex single-valued neutrosophic sets (CSVNS) and explores their basic set-theoretic characteristics. Based on this framework, an approach to visual analytics that preserves privacy for high-dimensional data, but remains fully encrypted, is proposed. The proposed scheme shows how information about the similarity of the cotangents of functions can be encrypted while retaining its fundamental analytical properties. Three-dimensional (3D) encrypted parallel coordinates visualizations, 3D t-distributed stochastic neighbor embedding (t-SNE) visualizations, and encrypted Pearson correlation heatmaps accurately capture the similarity patterns of the original data while introducing only controlled and minor perturbations to the best matching pairs, variance distribution, class relationships, and correlation structures. The small differences in variance and normalized similarity values show that the encryption mechanism had little effect on the data, which means that the geometric and relational features of the dataset are suitable for analysis in the encrypted domain. The proposed approach is a powerful solution for secure similarity analysis, dimensionality reduction, clustering, and privacy-preserving decision support applications, while retaining analytical accuracy.