What this is. Dimensionality reduction is a workhorse for both exploratory visualization and downstream prediction, yet the stability of its output under small perturbations of the input is rarely examined directly. This notebook takes a narrow, empirical approach: a three-dimensional point cloud (§ 1) is perturbed by a controlled amount at each of a short sequence of timesteps, the selected reducer (§ 2) is applied independently to every snapshot, and the resulting trajectory of two-dimensional embeddings is recorded.
What it measures. Two stability views are logged alongside each run and plotted on the metrics page. Per-timestep travel — ‖ y(t) − y(t−1) ‖ — captures how much the 2-D layout moves between consecutive frames. kNN retention captures how much of the input-space neighborhood graph survives projection. Together they separate reducers that are globally stable but locally noisy from those with the opposite failure mode.
Why this matters. A reducer that looks well-behaved on a single snapshot is not automatically the right tool for a streaming or longitudinal setting. Used as the substrate for a visualization, frame-to-frame motion will read as change the user did not request; used as a feature-extraction step inside a classification pipeline, drift between training and inference will quietly erode accuracy. The aim here is to build intuition for those regimes before committing the reducer to either role.
Six candidate generators for the embedding pipeline. Drag to rotate, scroll to zoom, ← → or 1 … 6 to select.
figs/ after the flow completes.