Fig. 7: Comparing perturbation scores with three diagnostic scores for the t-SNE embedding on the simulated Swiss roll dataset.

a The t-SNE embedding of n = 1000 simulated points from the Swiss roll manifold under perplexity 150. The colors correspond to the ground-truth spiral angles of the points. t-SNE algorithm erroneously breaks the smooth manifold into two disconnected parts, which indicates OI discontinuity. b Perturbation scores clearly mark the unreliable embedding points where disconnection (discontinuity) occurs. c EMBEDR uses the p-values from one-sided permutation tests to identify unreliable embedding points. It suggests that most embedding points are unreliable (lower p-values are more reliable). But it does not identify the discontinuity location. d ScDEED evaluates most embedding points as dubious, but similar to EMBEDR, it does not identify the discontinuity location. e DynamicViz marks both the discontinuity location and the areas at both ends of the Swiss roll as unstable, making it difficult to distinguish the actual discontinuity locations. Furthermore, while it can roughly identify the discontinuity location, it still fails to pinpoint the exact points where the split occurs. Source data are provided as a Source Data file.