User guide

What the reproducible-signal correlation measures, how to calculate it on your own data, and what each part of the site takes in and gives back.

What RSC measures

The reproducible-signal correlation (RSC) compares a prediction with two halves of the measured RNA counts at each spatial scale. Every captured molecule is assigned at random to one of the halves. Given the expression, the two halves are independent Poisson counts with the same expectation, so they share the expected expression and carry independent sampling noise. RSC estimates the correlation between the prediction and that expected expression.

It is computed at each spatial scale, from broad tissue compartments to neighboring spots or cells, and it can be computed within one tissue region or cell class. The first corrects the understatement caused by sampling noise at fine scales; the second avoids the overstatement of whole-section correlation, which mostly rewards differences between regions.

Definition

Let A and B be the two halves after the count transform, Ŷ the prediction, and ⟨·,·⟩_b the inner product of the scale-b components of two matrices, summed over all genes and all bins, spots or cells of a section. At scale b:

C = (⟨Ŷ, A⟩_b + ⟨Ŷ, B⟩_b)/2, the mean covariance of the prediction with the halves;
V_model = ⟨Ŷ, Ŷ⟩_b, the variance of the prediction;
V_RNA = ⟨A, B⟩_b, the covariance between the halves, which estimates the variance of the reproducible signal.

RSC_b = C / √(V_model · V_RNA)

RSC is estimable when V_model and V_RNA are both positive, and negative values are kept. The computation has six steps: split the counts of the test section; transform and center the halves, and center and scale the prediction by gene; project the prediction and both halves onto the scales; sum C, V_model and V_RNA over all genes and locations at each scale; form RSC from these sums; repeat over independent count splits and average.

The scales come from operators that follow the layout of the data: a two-dimensional Fourier basis on a regular grid of bins, the eigenvectors of a neighbor-graph Laplacian on spots, and diffusion operators on a cell graph for single cells.

Split-half reliability and Pearson r with measured RNA expression

With V_A = ⟨A, A⟩_b and V_B = ⟨B, B⟩_b, the split-half reliability ρ_b = V_RNA/√(V_AV_B) is the correlation between the two halves at scale b. A prediction equal to the expected expression correlates with one half at about √ρ_b. For halves of equal variance, RSC is the mean correlation of the prediction with the two halves divided by √ρ_b, and the correlation of the prediction with the mean of the two halves is

r_b(Ŷ, (A + B)/2) = RSC_b · √(2ρ_b/(1 + ρ_b))

Pearson r with the measured RNA expression is therefore lower than RSC wherever the counts are sparse, and it approaches RSC as sampling noise vanishes and ρ_b approaches 1. In the colorectal sections of the paper, a prediction equal to the underlying expression would reach a Pearson r with the measured RNA expression of 1.00 at the broadest scale but only 0.44 to 0.57 at the finest. The same relation links the Fourier shell correlation between two cryo-electron microscopy half-maps to the correlation of the full map with the structure without noise.

When RSC applies

Each count is one captured molecule. Counts deduplicated by unique molecular identifiers, as in Visium and Visium HD, and decoded Xenium transcripts qualify. Normalized, log-transformed or imputed values cannot be split.
The counts are split before any processing. Give the raw counts; the site and the toolkit split them first and normalize, transform and decompose the halves afterwards.
The prediction does not use the counts of the test section. This rules out models trained or tuned on the evaluated section and inputs estimated from its RNA, such as cell-type proportions or sequencing depth.

Overdispersion of the counts can raise the split-half reliability and lower RSC. Technical variation shared by the two halves, such as lateral diffusion, is counted as reproducible signal.

Reading RSC

An RSC of 1 means that the prediction accounts for all reproducible variation at that scale, and 0 means chance agreement. RSC is not limited to the interval from 0 to 1: the reproducible variance is estimated from the halves, so small signals give noisy ratios. Compare means over genes, splits and sections, and compare models on the same sections and genes.

Scale labels are relative on spots (Broadest to Finest, defined by each sample's neighbor graph) and physical on a grid (wavelength windows in µm), so relative scales are not comparable across datasets. A model that recovers broad patterns but not fine ones shows high RSC at broad scales and low RSC at fine scales. Within a tissue region or cell class, RSC scores the variation a prediction captures beyond the region or class labels, and a class-mean baseline scores no RSC there. The paper computes RSC within malignant cells and within TLS; Calculate RSC does both, with a cell class or a region column.

When predictions can be trusted

RSC tells you which analyses a prediction can support. Score candidate methods on independent test sections with matched RNA, and look at RSC at the spatial scales, tissue regions, cell classes and genes your analysis depends on, not only over the whole section.

A high score for locating a structure, or a high whole-section correlation, does not show that a method predicts the expression inside it. In the paper, a class-mean baseline with no variation within regions scores above the median published method on whole sections and locates TLS with an AUROC of 0.99 to 1.00 (Figs. 1b and 5e).

Where an analysis yields low RSC, its predictions warrant experimental validation, or statistical frameworks that model predictive uncertainty, such as TISSUE (Sun et al., Nature Methods 2024), and that correct estimation bias using an assayed subset, such as prediction-powered inference (Angelopoulos et al., Science 2023).

Evaluate each analysis on its own. A change to training can help one analysis and harm another: the pairwise difference loss raised fine-scale RSC, broad-scale RSC and whole-section correlation across 11 models, but lowered the RSC of Ridge–Phikon-v2 between regions and within TLS (Figs. 5f and 6).

RSC also has the limits of the measurement it rests on. It counts technical variation shared by the two halves, such as lateral diffusion, as reproducible signal; overdispersed counts can slightly lower the RSC of the expected expression at fine scales; and at single-cell resolution the evaluation depends on nuclear segmentation and cell classification.

Reporting RSC

So that others can compare and repeat an evaluation, report the settings that determine RSC, as the Methods of the paper do for each dataset:

Layout and scales. A Fourier basis with wavelength windows in µm on a regular grid, the eigenvectors of a neighbor-graph Laplacian with five relative scales on spots, or diffusion operators on a cell graph, with how the graph was built. Relative scales are defined by each sample's graph and are not comparable across datasets.
Count transform. For example √(N_half/(0.5a)) for bins of effective area a, or log(1 + 2N_half) for spots and cells.
Gene weighting. Weights from the agreement of the two halves in the other samples of the same cancer type, as for the HEST spots, or the two halves of each gene divided by a common factor, as for the colorectal bins and the cells.
Count splits. How many independent splits were averaged; the paper used 5 to 32.
Split-half reliability at each scale, next to RSC, so that readers see how much reproducible signal each scale holds.
Fine-scale and broad-scale RSC. Whether they are means of the RSC at two scales or formed from the summed terms of those scales; the paper uses both.
Regions and cell classes. Which ones, and how they were assigned; in the paper, malignant cells are the neoplastic class of CellViT, transferred to Xenium cells by nearest-centroid matching within 5 µm.
Genes and independence. The genes scored, and how the predictions were kept independent of the counts of the test sections.
Toolkit version.

Calculate RSC

Under Calculate RSC, the browser runs strsc.rsc, the toolkit's own function, on your counts and one or more predictions. The same call on your own machine runs the same steps with the same seeds; the page shows it with every result. It gives the same numbers, except where a location has many molecules of a gene: numpy draws the count split of such a location with floating-point steps that can come out differently on another computer or numpy version, and the results then differ within the scatter between count splits. For spots, the browser also projects onto the scales with SciPy's BLAS, in single precision as the toolkit does, so the sums run in another order and the last digits can differ. Made-up data run with one click, one small set per layout, and the test files can be copied as templates.

Files

Counts: whole-number molecule counts, before any normalization. A CSV or TSV table with sample_id, unit_id, x, y and one column per gene; an AnnData .h5ad file, with raw counts in layers['counts'] or X and coordinates in obsm['spatial'] (HEST-1k samples open as they are); a Space Ranger filtered_feature_bc_matrix.h5, or the filtered_feature_bc_matrix folder of matrix.mtx.gz, features.tsv.gz and barcodes.tsv.gz, with tissue_positions and scalefactors_json.json; or a Xenium cell_feature_matrix.h5 with cells.csv.gz or cells.parquet. A whole outs folder, a Visium HD bin folder or a Xenium output folder can be chosen at once; only the counts and positions are read from it. Xenium control probes are left out.
Predictions: one file per model, a table with unit_id (and sample_id when there are several sections) and one column per gene, or an .h5ad file whose observation names are the unit IDs. Any units for the spatial scales: each gene is centered and scaled before scoring. Between and within regions, values of log(1 + 10,000 N/total), as in the paper. Genes and locations missing from a prediction are left out, and the page says how many.
Regions or cell classes, optional: a region or cell_class column in the counts, or a separate table with unit_id and that column.

Layouts

Each layout follows the Methods of the paper (“Scales and count transforms”).

Spots, such as Visium or HEST: five relative scales from the eigenvectors of the neighbor-graph Laplacian, log(1 + 2N_half) and twenty count splits, the steps of strsc hest. With two or more sections, each gene is weighted by the agreement of its two halves in the other sections, as for the HEST samples. One section has no other sections, so each gene's two halves are divided by a common factor, as for the colorectal bins and the cells of the paper; the two weightings give different values, and the page says which one was used. Up to 5,000 connected spots per section. Fine-scale and broad-scale RSC are the means at the two finest and the two broadest scales.
Regular grid, such as Visium HD bins: seven physical scales of a two-dimensional Fourier basis, from below 128 µm to 4,096 µm and above, √(N_half/(0.5a)) and five count splits, the steps of strsc.fourier.score. The spacing is read from Visium HD files or given by hand; an optional area column marks bins at the edge of the tissue. Windows below twice the spacing are resolved only in part and are drawn open.
Cells, such as Xenium: five relative scales from lazy diffusion on the graph of the eight nearest neighbors within 40 µm, log(1 + 2N_half) and five count splits, as for the breast cancer cells of the paper. Name a cell class to score its cells on their own graph, as for the malignant cells of Figure 4a,b; all cells can be scored as well. Fine-scale RSC is formed from the summed terms of the two finest scales. Up to 120,000 cells per graph.

Between and within regions, for spots or bins with a region column: each prediction and each RNA half is split into the mean of its region and the residual from it, as for the TLS sections of Figure 5f. RSC is given for the whole section, between regions and within regions; if you name one region, such as TLS, also within it, between its structures (connected groups of its spots) and within one structure. Measured expression is log(1 + 10,000 N/total), each half with its own total, and twenty count splits. In each part, every gene of the RNA halves and of the prediction is divided by the standard deviation of the gene's unsplit expression over the spots of that part, so predictions should be values of log(1 + 10,000 N/total) too. Intervals are 95% percentile intervals from 2,000 resamples of the named region's structures for the parts within it and of blocks of 10 × 10 spots for the others, and a part is scored in a section only when the lower limit of the interval of its reproducible variance is above zero; over several sections, the sections where a part is scored are averaged, in every resample too. This is the computation of the paper: on the TLS section KC1 it gives the paper's V_model to 13 significant digits for every part in which the prediction varies, the same decision on which parts can be scored, and RSC and intervals within the scatter of count splits and resamples. A class-mean baseline scores no RSC within regions: it does not vary there.

Only these genes restricts the scoring to a list, for example the eight TLS genes of Figure 5.

Results

A table of fine-scale and broad-scale RSC (on a grid, the broadest and finest), the broadest-to-finest decline and the whole-section Pearson r of every model and section, with the mean over sections.
RSC, Pearson r with the mean of the two RNA halves and the split-half reliability at each scale, in one figure, with the range of RSC over the count splits. Where the split-half reliability is low, Pearson r falls well below RSC even for a correct prediction.
The RSC of each gene at each scale, to sort, search and download. The paper pools all genes before forming RSC; single genes are noisier.
Checks: the three conditions under which RSC applies, the median number of molecules per location, the split-half reliability at the finest scale, and, on request, the paper's test with the expected expression as the prediction (Methods, “Expected expression as a prediction”): your counts are taken as Poisson rates, new counts are drawn, and the expected expression should score near 1 at every scale (0.956 to 1.000 in the paper).
The same run as Python code and as a command, for your own machine.

Download results saves a file that opens again under Computed results; Download tables holds the scales, the summary, every gene and the settings. The page loads Python and the toolkit into the tab once, about 40 MB, and 2 to 12 MB more for .h5ad, .h5 or Parquet files.

Pairwise accuracy

Under Pairwise accuracy, the browser runs strsc her2 on your counts: normalized pairwise accuracy for unmatched spot pairs, pairs matched for total transcript count and expression profile, and matched pairs in the same region, as in Figure 2. The test cohort can be copied as a template.

The tables are laid out as for Calculate RSC; the counts file may also hold patient_id and region. The analysis takes one section per patient and at least two patients, because the baseline for each patient is learned from the others. Predictions can be in any units, since a pair is scored on which of its two spots is predicted higher.

Pairwise difference loss

Under Pairwise difference loss, the input is the counts and a table of image features, one vector per spot, for two or more sections. Each section is predicted by Ridge models trained on the others, with ρ = 0 and ρ = 0.5 and the settings of the paper (256 principal components, α = 100/(256 × genes)), and both predictions are scored with RSC at relative scales. Fine-scale and broad-scale RSC are the means over the two finest and the two broadest scales, as in Figure 6. The predictions of both trainings are in the download. Deep models are not trained in the browser.

Computed results

Score tables and bundles written by the Python toolkit open under Computed results.

Score tables

A score table compares the same predictions under two conditions, with one row per model, task and sample or patient. The example under Computed results is the table behind Figure 6c,d.

Column	Content
`model`	Model name
`task`	Cohort or tissue group. Figure columns are grouped by it
`unit_id`	Sample or patient ID. A column named `specimen` or `patient` also works
`unit_type`	`specimen` for samples or `patient`, one kind per file
`fine_baseline, fine_intervention`	Fine-scale RSC under the two conditions
`coarse_baseline, coarse_intervention`	Broad-scale RSC under the two conditions
`pcc_baseline, pcc_intervention`	Whole-section Pearson r under the two conditions
`score_definition`	Optional. `band_mean` for the mean RSC at the two scales, `combined_components` for RSC from the summed terms of the two scales
`baseline_condition, intervention_condition`	Optional names of the two conditions
`experiment_id, source_table`	Optional provenance. Keep separate experiments in separate files

All models must cover the same tasks and IDs. Scores of an ID that appears in several tasks are averaged first, then every model and every ID carries equal weight. Pearson r stays between −1 and 1; RSC is corrected for sampling noise and can exceed 1.

Fine-scale and broad-scale RSC come in two forms: the mean RSC at the two scales, or RSC from the summed terms of the two scales, which is what strsc hest writes. Name the form in the file or when you open it.

Intervals in the browser come from 20,000 fixed-seed resamples of IDs within tasks and need at least five IDs. The paper computed its intervals differently; they are in its Source Data.

Analysis bundles

A finished HEST run packed with its expression data, so that maps can be drawn next to the scores. The toolkit writes it with strsc export, which only packs what the run produced and checks each saved gene correlation against the expression it packs (export notes).

A bundle gives RSC at the five scales and its change, RNA variance and covariance at each scale, expression maps, gene correlations and prediction errors. The scales are relative to the section, not distances in micrometers. The schema is strsc-analysis-bundle-v1: a score_table and a list of specimens, each with genes, spot IDs, coordinates, measured expression and two sets of predictions; the HEST example shows the full layout.

Evaluation bundles

The scores of one toolkit workflow with their definitions, written by strsc export-results. The schema is strsc-evaluation-bundle-v1 (format). Maps need an analysis bundle, which also carries expression and coordinates.

Conventional metrics

Whole-section correlation and AUROC against annotations are kept under Conventional metrics for comparison with RSC. The paper shows that whole-section correlation overstates prediction quality within tissue regions, where a class-mean baseline scores above the median of 11 published methods, and that Pearson r with the measured RNA expression understates it at fine scales.

Expression tables

Choose one file of measured expression and one file per model, name the scale of the measured expression and press Analyze data. Analyze the example opens HER2ST section B1 the same way, and its files can be copied as a template.

Each file has one row per location. It starts with sample_id, unit_id, followed by one column per gene. Coordinates x, y and a region label are optional and can sit in the measured expression file or in a file of their own. patient_id groups the sections of one patient. Rows can be in any order. Genes or locations missing from a file are dropped, and an empty or NA cell stays missing; it is never read as zero. Data details lists what was left out.

If the predictions are in a model's own output units, untick Predictions are on the same scale. Each map then gets its own color scale and no RMSE is given. Correlations do not depend on units.

Each gene is scored on the locations where the measured expression and every compared model have a value, so models are always compared on the same locations. The figure has three views:

Whole section and regions: the correlation over the section and within each region label, or inside a rectangle drawn on a map.
Scoring unit: measured expression and predictions averaged in square bins of 2, 4 and 8 typical spacings, anchored at the smallest x and y, with every occupied bin counted once. It shows how the correlation in one section changes with bin size; it is not the analysis of Figure 4.
Region ranks: where each region sits in the ranks of the measured expression and of the prediction.

These are ordinary Pearson r and Spearman ρ of the supplied values, with tied values sharing their mean rank. RSC needs RNA counts; see Calculate RSC.

Scores and annotations

For a score, such as the expression of a marker gene, that is compared with expert annotations. One table holds sample_id, unit_id, a column of labels, a score from measured expression and one column per predicted score; x, y are optional. For several genes, name the columns score:gene, such as measured:LTB; AUROC can then be averaged over the genes, as in Figure 5e. Pick the columns after choosing the file, or open the external TLS sections.

AUROC compares locations with the chosen label against locations with the labels ticked beside it. Unlabeled locations, and labels left unticked, are drawn but not counted as negatives. Each predicted score is also correlated with the measured score over the whole section. An H&E image can be added; x, y are then its pixel positions.

Figures

The figures follow the paper: Arial at 7 pt when printed 180 mm wide, lower-case panel letters, left and bottom axes only. Expression runs from slate blue through cream to rust. Changes run from brick (lower) through white to teal (higher).

SVG keeps the text editable. PNG is the same figure at 300 dpi. Source data is a CSV of every value in the figure, including genes or locations left out for space.

Rows of patients or samples have one mark per patient, a box for the 95% t interval of the mean (from three patients up) and a white diamond at the mean. Paired changes are drawn as in Figure 6.

Data explorers

HER2ST cohort reopens Figure 2a–c and 2g–i for 11 methods in eight patients, with the class-mean baseline in gray. Clicking a method or a patient marks it in every panel. The cohort values stay as published.

HER2ST section B1 and the external TLS sections open in Analyze data, in the same tools as your own files. B1 has measured expression of 785 genes, the saved predictions of Hist2ST, EGNv2 and DeepSpaCE, and the annotated regions. The TLS sections are two kidney and two lung sections with expert annotations and eight TLS genes, measured and predicted, as in Figure 5.

HEST sample TENX118 is one lung cancer sample predicted by Ridge–Phikon-v2, after standard training and with the pairwise difference loss.

Xenium breast cancer cells shows Figure 4, including the proliferation hotspots of Figure 4e, for three single-cell methods in five patients, with the four evaluation conditions of Extended Data Fig. 4.

The original source and license of each dataset are listed on the Data explorers page and in Supplementary Table 7 of the paper. Results shows every figure of the paper with its source data.

Python toolkit

The toolkit runs everything on this site on your own machine, with no limit on section size. Install it with pip install strsc (Python 3.10 or later); pip install "strsc[io]" adds Parquet files. One call scores a prediction:

import strsc
counts = strsc.read_counts("sample.h5ad")        # a table, .h5ad, Space Ranger or Xenium folder
result = strsc.rsc(counts, {"my_model": "predictions.csv"}, layout="spots")
print(result.scales)                             # RSC, Pearson r and split-half reliability per scale
result.save("strsc-output")

The same from the command line: strsc rsc sample.h5ad -p my_model=predictions.csv --layout spots --out strsc-output. strsc.regions scores between and within regions, and strsc.ideal_check runs the test with the expected expression. The workflows of the paper are there as well; each writes a file that opens under Computed results.

RSC on your own data strsc.rsc, strsc rsc
RSC at relative scales on the HEST samples strsc hest
RSC at physical scales on a grid strsc fourier
Single cells and aggregated cells strsc.cell_score
Normalized pairwise accuracy strsc her2
Pairwise difference loss strsc.training
Files for this site strsc export-results
Paper analyses and figure code
Questions and problems GitHub Issues

Limits

Calculate RSC: 256 MB per file and 512 MB in total; 5,000 connected spots per section, 120,000 cells per graph and 400,000 bins per section. Near these sizes a run takes minutes and up to about 4 GB of memory, so use a computer with at least 8 GB. In Chrome on a two-core 2.1 GHz virtual machine, made-up data of these sizes took 6 minutes for one section of 5,000 spots with 300 genes, 5 minutes for 120,000 cells with 300 genes, and 1.5 minutes for 400,000 bins with 80 genes, or 4 minutes between and within regions. More genes take longer and need more memory, and a run that needs more than the browser allows stops. Larger data run with the toolkit on your own machine. Pairwise accuracy and Pairwise difference loss: 64 MB per file and 256 MB in total.
Score tables: 2 MB and 500 rows.
Analysis bundles: 64 MB, 2 million expression values, 20,000 locations and 5,000 genes per sample.
Evaluation bundles: 64 MB and 100,000 score rows. Tables show 300 rows; downloads keep all of them.
Expression tables: 32 MB per file, 64 MB in total, 2 million shared expression values.
Scores and annotations: 64 MB. Images: PNG, JPEG or WebP.
Calculate RSC reads .h5ad and 10x .h5 files; the other tabs take CSV or TSV tables. RDS files are converted first, for example to .h5ad.

RNA molecules can only be split from raw integer counts. Normalized or log values give no split-half reliability and no RSC.

Common questions

Why is Pearson r with my measured RNA expression so much lower than RSC at fine scales?: Because fine scales are where the counts are sparse. Sampling noise lowers the split-half reliability ρ_b, and Pearson r with the measured RNA expression is RSC_b · √(2ρ_b/(1 + ρ_b)). A prediction equal to the expected expression scores near 1 by RSC at every scale, while its Pearson r with the measured RNA expression falls toward fine scales (Fig. 1c and Extended Data Fig. 1c of the paper).
Can I use normalized, log-transformed or imputed values?: Not for the measured RNA: only whole-number molecule counts can be split into two halves. Predictions can be in any units for the spatial scales, because they are centered and scaled by gene. Between and within regions they should be values of log(1 + 10,000 N/total), as in the paper, because each gene is divided by the standard deviation of the measured expression.
I have only one section.: One section is enough for every layout. On spots, two or more sections are scored as the HEST samples of the paper, with each gene weighted by the agreement of its halves in the other sections; a single section is scored with a common factor per gene, as the colorectal bins and the cells of the paper. The two weightings give different values, so compare models under the same one.
Why can RSC fall below 0 or rise above 1?: Below 0, the prediction runs against the reproducible signal at that scale. Values above 1 occur when the reproducible signal is small, because its variance is itself estimated from the two halves. Means over genes, count splits and sections are steadier than single values.
How many count splits are enough?: As in the paper: twenty on spots and between regions, five on a grid and on cells; the paper used 5 to 32 across its analyses. More splits make the average more precise and leave its expected value unchanged. The range over splits is shown with every result.
My model was trained on the section I am scoring.: Then RSC does not apply: the derivation assumes that the prediction does not use the counts of the test section. The same holds for inputs estimated from its RNA, such as cell-type proportions or sequencing depth.

Definitions

Output resolution: The spot, bin or cell for which a model returns a prediction. A prediction for every cell does not by itself mean that the model is accurate among cells of the same class or within a neighborhood.
Count splitting: For the count N of each gene in each bin, spot or cell, N_A ~ Binomial(N, 0.5) and N_B = N − N_A. Given the expression, the two halves are independent Poisson counts with equal expectations: they share the expected expression and carry independent sampling noise.
Split-half reliability: The correlation between the two RNA halves at a given spatial scale. Its square root is the correlation with one half that a prediction equal to the expected expression would reach.
Reproducible-signal correlation, RSC: A correlation corrected for attenuation: the mean covariance of the prediction with the two halves, divided by the square root of the variance of the prediction times the covariance between the halves, at one spatial scale. For halves of equal variance it is the correlation with one half divided by the square root of the split-half reliability. It is 1 when the prediction accounts for all reproducible variation at that scale and 0 for chance agreement. In the bundles the toolkit writes, the metrics are rsc_B1 to rsc_B5, rsc_broad, rsc_fine, physical_rsc and cell_rsc; the raw result tables of each workflow keep their own column names, in which RSC is the column q.
Relative scales: Broadest, Broad, Mid, Fine and Finest, from section-wide gradients to differences between neighboring spots. They are defined relative to the neighbor graph of each sample, so scale labels are not comparable across datasets.
Physical scales: Wavelength windows in micrometers on a regular grid, from 4,096 µm and above to below 128 µm in the colorectal sections of the paper.
Fine-scale and broad-scale RSC: For spot models, fine-scale RSC is the mean RSC at the Fine and Finest scales, and broad-scale RSC the mean at the Broadest and Broad scales. For cells, the terms of the two finest scales are summed before the ratio is formed.
Whole-section Pearson r: For each gene, the Pearson correlation between predicted and measured expression across the spots of a section, averaged over genes and then over the sections of a patient. A gene predicted as constant scores 0.
Class-mean baseline: A control that assigns every spot of an annotated region the mean expression of that region class in the training data. It has no variation within regions, so whatever it scores comes from differences between regions.
Normalized pairwise accuracy, G: Pairwise accuracy is the fraction of spot pairs for which a prediction identifies which spot expresses a gene more highly. It is scaled so that 0% is the majority-order baseline and 100% the split-half agreement, the accuracy with which one RNA half predicts the order in the other. G can be negative or exceed 100%.
Majority-order baseline: Gives every spot pair of a gene the direction observed most often across the training patients.
Unmatched pairs, matched pairs, within-region pairs: The three sets of spot pairs in HER2ST. Unmatched pairs are drawn at random across the section. Matched pairs are matched for total transcript count and expression profile. Within-region pairs are matched pairs in the same annotated region.
Pairwise difference loss: A training loss that also penalizes errors in the predicted expression differences between neighboring training spots.