Clinic 18

Manifold Choice

A two-dimensional plot suggests clusters. Check what the projection preserves before turning islands into labels.

Back To Clinics Open DR Topic Open Advanced Clustering

Situation

A two-dimensional view of high-dimensional embeddings shows several islands. The first two PCA components explain only 12.3% of variance. A teammate wants to turn the apparent islands into customer labels.

Artifact Packet

These diagnostics are illustrative. Silhouette is measured in each projected space for a fixed candidate partition; it is not an original-space clustering score. Neighbor overlap is the mean fraction of each point's ten original-space neighbors retained among its ten projected-space neighbors, excluding the point itself.

method	2D silhouette	10-neighbor overlap with original space
pca_2d	0.31	0.29
tsne	0.62	0.18
umap_neighbors_15	0.58	0.24
umap_neighbors_50	0.43	0.28

method	useful interpretation	limitation
truncated PCA	linear projection maximizing retained variance	generally discards distances and structure outside retained components
t-SNE	approximate neighborhood visualization	cluster areas, densities, and large-scale spacing can mislead
UMAP	graph-based neighborhood embedding	results depend on representation, parameters, and optimization

Full-dimensional orthogonal PCA coordinates preserve Euclidean distances; the two-component truncation used here does not. t-SNE adjusts to local density and can expand dense regions and contract sparse regions. Do not read plotted point density as original-space density. How to Use t-SNE Effectively

Decision Prompt

1. Can the largest 2D silhouette establish clusters in the original space?
2. What do truncated PCA and t-SNE actually preserve?
3. What does sensitivity to seed or neighborhood size tell you?
4. Which original-space or task-based check would you do next?

Run The Clinic In Browser

The runner prints this fixed illustrative packet and recalculates any derived columns. It does not run a new training experiment. Edit its PACKET values to explore the decision.

Reference Reveal

Open after writing your note

**Do not assign production labels from this plot alone.** The largest plotted silhouette occurs with the lowest neighbor overlap here. Inspect original-space neighbors, an appropriate clustering diagnostic in the original representation, and domain or downstream-task evidence before using the apparent groups. Repeat seeds and a justified parameter range. Stability supports reproducibility, not proof that a grouping is real. Sensitivity indicates that a particular visual conclusion is fragile; it does not prove that every underlying structure is artificial. A low two-component PCA variance fraction also does not establish that PCA or the representation is useless for every task.

What To Do Next

1. open Dimensionality Reduction for the method-to-claim mapping in detail
2. open Advanced Clustering and Dimensionality Reduction for the stability discipline
3. open Cluster Stability for the companion clinic on seed-driven cluster drift
4. rerun all three methods on your data with parameter sweeps; if the cluster count changes with knob settings, the cluster count is a knob output, not a finding