A framework for quantifiable local and global structure preservation in single-cell dimensionality reduction

Dimensionality reduction techniques are essential in current single-cell 'omics approaches, offering biologists a first glimpse of the structure present in their data. These methods are most often used to visualise high-dimensional and noisy input datasets, but are also frequently applied for downstream structure learning. By design, every dimensionality reduction technique preserves some characteristics of the original, high-dimensional data, while discarding others. We introduce ViScore, a framework for validation of low-dimensional embeddings, consisting of novel quantitative measures and visualisations to assess their quality in both supervised and unsupervised settings. Next, we present ViVAE, a new dimensionality reduction method which uses graph-based transformations and deep learning models to visualise important structural relationships. We demonstrate that ViVAE strikes a better balance in preserving both local and global structures compared to existing methods, achieving general-purpose visualisation but also facilitating analyses of developmental trajectories.