Visualizing stability: a sensitivity analysis framework for t-SNE embeddings.

Area of Science:

• Bioinformatics
• Computational Biology
• Data Visualization

Background:

• t-distributed Stochastic Neighbour Embedding (t-SNE) is widely used for visualizing high-dimensional biological data.
• Standard t-SNE plots lack information on visualization stability, feature influence, and data uncertainty.

Purpose of the Study:

• To develop a computational framework for extending t-SNE plots with visual clues on embedding stability.
• To identify influential features and quantify positional uncertainty in t-SNE visualizations.

Main Methods:

• Sensitivity analysis using the Implicit Function Theorem and automatic differentiation to compute the Jacobian of first-order derivatives.
• Propagating input data uncertainty through the Jacobian to quantify positional uncertainty of embedded points.
• Visualizing feature influence with heatmaps and positional uncertainty with hypothetical outcomes.

Main Results:

• The framework reveals influential input features and regions of structural instability in t-SNE embeddings.
• Probabilistic quantification and visualization of positional uncertainty for each embedded point when input data uncertainty is available.
• Successful application to bulk RNA-seq, proteomics, and single-cell transcriptomics datasets.

Conclusions:

• The developed framework provides a principled method to assess the robustness and interpretability of t-SNE visualizations.
• Enables more rigorous and informed scientific conclusions by linking visual patterns to biological drivers and revealing ambiguities.
• Enhances the utility of t-SNE in bioinformatics for analyzing complex biological datasets.