Choose measures

Choose a measure for the structure you want to preserve. Two projections can have similar neighborhood scores and very different distance or class scores.

Start with the question

Question	Measures	How to read them
Which original neighbors are lost, and which new neighbors appear?	tnc, mrre	Paired scores separate false and missing neighbors; higher is better in ZADU
How much do the two neighbor sets overlap?	lcmc	Overlap corrected for expected random overlap; the upper bound depends on k and n
Do numerical distances match?	stress	Lower is better; sensitive to overall scale
Do distances match after a global rescaling?	sn_stress	Lower is better; fits one scale factor before measuring residuals
Are distances linearly or monotonically related?	pr, srho, nm_stress	Correlations are higher-is-better; non-metric stress is lower-is-better
Are samples with the same label close together?	nh, dsc, ivm, c_evm	Evaluate the projection against labels; do not by themselves establish preservation of original geometry
How does class structure change between spaces?	ca_tnc, l_tnc, cadi	Compare class-related neighborhoods, separation, or angles
Are groups split or merged without class labels?	snc	Steadiness and Cohesiveness use sampled walks; set a seed for comparisons
Does the distribution of local density change?	dtm, kl_div	Compare density estimates; bandwidth sigma affects the result
Does local geometry change?	topo, proc, nd	Compare neighbor ordering, local alignment, or dissimilarity
Do empty scatterplot regions change relative area?	gi	Compares triangles from the 2D projection; lower is better

The measure reference lists parameters, return keys, ranges, and papers. ZADU's MRRE outputs are normalized preservation scores: 1 is best, despite “error” in the metric's name.

Compare neighborhoods and distances

For a first comparison, pair T&C with a distance measure. Using original and projection from the quickstart:

from zadu import ZADU

specs = [
    {"id": "tnc", "params": {"k": 10}},
    {"id": "sn_stress"},
]
scores = ZADU(specs, original).measure(projection)

Use stress instead of sn_stress if absolute distance scale matters. Add gi when empty regions in a two-dimensional scatterplot are part of your question. Add class-based measures when class structure is relevant.

Interpret a comparison

Keep sample selection, preprocessing, and measure parameters fixed when comparing projections. Changing k changes the neighborhood scale being evaluated. Try several values if conclusions depend on the size of a neighborhood, and report each value with its result.

A label score can be high even when the projection separates classes that overlap in the original space. Use a measure that compares both spaces when making a claim about preservation. Scores from different measures have different meanings and units; report them separately.

For reproducibility, record the ZADU version, measure parameters, preprocessing, sample selection, and backend/device/dtype. Set random_state for S&C and random_seed for CADI. A single execution worker does not make an unseeded randomized measure deterministic.