Choose measures

There is no universally best projection-quality score. Start from the scientific structure you need to preserve, then use complementary measures rather than selecting only the most favorable result.

Match the question to a measure family

Question	Useful starting points	What they emphasize
Are local neighbors preserved?	T&C, MRRE, LCMC	Missing and false neighbors or neighborhood overlap
Are labels or classes visually coherent?	Neighborhood Hit, DSC, class-aware T&C, label T&C, CADI	Separation, mixing, and class-relative distortions
Are pairwise distances preserved?	Stress, scale-normalized stress, Pearson	Magnitude or linear association of distances
Is the ordering of distances preserved?	Spearman, non-metric stress	Monotonic rather than metric agreement
Are density patterns preserved?	DTM, KL divergence	Changes in local density estimates
Is local topology preserved?	Topographic Product, Procrustes	Neighborhood ordering or locally aligned geometry
Do apparent empty regions represent real separation?	Gap Index	Empty triangular regions in a 2D projection
Are cluster structures stable without labels?	Steadiness & Cohesiveness	False and missing groups discovered through random walks

The measure reference lists exact IDs, parameters, ranges, optimum directions, return keys, and original literature.

A practical baseline

For an unlabeled two-dimensional projection, a useful first pass combines one local, one global, and one structural measure:

specs = [
    {"id": "tnc", "params": {"k": 20}},
    {"id": "stress", "params": {}},
    {"id": "gi", "params": {"metric": "euclidean"}},
]

This is not a universal prescription. Change k, add scale-aware or class-aware measures, and validate that the selected definition matches the claim you intend to make.

Interpret scores carefully

• Some measures are maximized at 1; others are minimized at 0.
• k defines the neighborhood scale. Report it with the score and, when possible, examine more than one scientifically meaningful scale.
• Label-based visual-quality measures assume that the labels describe meaningful structure in the original space. A visually separated projection is not automatically faithful if those labels overlap before projection.
• Scores from different measures do not share a common unit. Do not average them without a justified model.
• A faster backend or float32 changes execution characteristics, not the published definition, but floating-point tolerances can differ by dtype.

Reproducibility checklist

Record the ZADU version, measure IDs, all non-default parameters, preprocessing, sample selection, backend/device/dtype, and whether local or global scores were used. For randomized measures such as S&C or sampled CADI, also set and report the seed.