Distance Preserving

Distance-preserving methods in machine learning aim to create representations of data that maintain the original relationships between data points, ensuring that similar data points remain close in the transformed space. Current research focuses on integrating distance preservation into various model architectures, including generative models (like variational autoencoders) and deep neural networks, often employing techniques such as Riemannian metrics or continuous k-nearest neighbor graphs to achieve this. These advancements improve the accuracy and reliability of models in diverse applications, ranging from spatial transcriptomics analysis to uncertainty quantification in safety-critical systems, by leveraging the inherent structure within the data. The ability to faithfully represent distances enhances model interpretability and generalizability.