COMET: Commute-Order Mapping of Expected Topology for Faithful Data Visualization

Visualization methods such as t-SNE, UMAP and their successors are the standard tools for making high-dimensional data visually interpretable. However, they expose hyperparameters that substantially change the embedding, with no ground truth to guide the choice. The settings are often chosen by visual inspection instead, which may bias the result toward the user's prior expectations. The embeddings also tend to break continuous structure into pieces and to distort both scale and global geometry. We introduce COMET (Commute-Order Mapping of Expected Topology), which embeds the geometry of a neighborhood graph. Commute times on that graph supply distances that follow the manifold, and ranking places them on a common scale with the graph's local similarities. Every neighbor and sampled non-neighbor then receives a target probability in the cross-entropy objective that calibrates the repulsive terms alongside the attractive ones, rather than every non-neighbor sharing the same target probability as in UMAP. COMET scales to large datasets and requires no hyperparameter tuning. Against seven established methods on four synthetic datasets with known topology and four real datasets, it ranks first on $21$ of $24$ comparisons under three validation measures built to quantify geodesic distance preservation, fragmentation and scale distortion.