Can high-dimensional data be analysed visually without exposing the original sensitive values?
This study introduces a new concept of complex single-valued neutrosophic sets and applies it to privacy-preserving visual analytics for fully encrypted high-dimensional data.
The proposed framework is designed to allow important structural and relational information to remain analysable even when the original numerical data are hidden through encryption.
The researchers developed an encrypted analytical approach based on cotangent similarity, dimensionality reduction, and visualisation.
The framework uses three-dimensional encrypted parallel coordinates, 3D t-distributed stochastic neighbour embedding, and encrypted Pearson correlation heatmaps to examine relationships within encrypted data.
The results showed that the encrypted visualisations were able to preserve the main similarity patterns of the original data.
Only small, controlled changes were introduced into the best-matching pairs, variance distribution, class relationships, and correlation structures.
The small differences observed in variance and normalised similarity values suggest that the encryption process had little effect on the underlying analytical structure of the data.
This means that important geometric and relational characteristics can still be studied without revealing the original feature values.
The study demonstrates that encrypted data can remain useful for similarity analysis, dimensionality reduction, clustering, and visual exploration while maintaining privacy.
The proposed approach therefore offers a way to balance analytical usefulness with data confidentiality in situations where sensitive information cannot be exposed directly.
The authors conclude that complex single-valued neutrosophic sets combined with encrypted visual analytics can support secure similarity analysis and privacy-preserving decision-support applications while retaining analytical accuracy.
📖 Read the full article here:
https://doi.org/10.46481/jnsps.2026.3254
Published in: Journal of the Nigerian Society of Physical Sciences