Why Science? | SpatialPCA, Spatially Aware Dimension Reduction and Tissue-Structure Evidence

Section 1 of 36

1. Begin with a dimension-reduction question

Spatial transcriptomics can measure thousands of genes at thousands of tissue locations. SpatialPCA asks for a smaller set of latent components that retains useful biological variation while explicitly modelling similarity across space. The components are statistical summaries, not newly measured cell states.

Contents · Next section

Section 2 of 36

2. Build on probabilistic PCA

Ordinary PCA finds directions of variation without using coordinates. SpatialPCA begins from a probabilistic factor model, linking the expression matrix to latent factors and gene loadings. The probabilistic form supplies a place to represent noise and spatial covariance rather than smoothing a PCA picture after fitting.

Contents · Previous section · Next section

Section 3 of 36

3. Add location through a kernel matrix

The method constructs a kernel matrix from tissue coordinates to describe expected correlation between latent factors at different locations. Nearby locations can be encouraged to have similar spatial components. The kernel is a mathematical prior about geometry; it does not prove that neighbouring cells communicate.

Contents · Previous section · Next section

Section 4 of 36

4. Infer spatial principal components

Spatial principal components combine expression variation with the assumed spatial correlation. They can feed familiar visualisation, clustering and trajectory tools. A clean component may reveal tissue organisation, but its sign, scale and orientation are not biological labels until compared with anatomy and markers.

Contents · Previous section · Next section

Section 5 of 36

5. Preserve correlation without inventing resolution

Spatial modelling can stabilise noisy structure and predict latent components at unmeasured locations. Prediction is not extra molecular capture. A refined map between spots is a model surface bounded by the assay spacing, kernel, training data and uncertainty.

Contents · Previous section · Next section

Section 6 of 36

6. Use the representation downstream

The primary study demonstrated visualisation, spatial-domain detection, trajectory inference and high-resolution map construction. These are distinct tasks. A representation that helps one task is not automatically optimal for another, and each downstream algorithm adds its own assumptions.

Contents · Previous section · Next section

Section 7 of 36

7. Keep the paper's scope specific

The 2022 Nature Communications study evaluated SpatialPCA with simulations and datasets from several spatial technologies and tissues. Those results establish a method and examples, not universal superiority. New platforms, sparse panels, three-dimensional geometry and unusual tissue boundaries require fresh checking.

Contents · Previous section · Next section

Section 8 of 36

8. Match expression rows to coordinates

Confirm that every location identifier, expression row and coordinate pair agrees. Preserve axis direction, units, duplicates, tissue masks and image registration. A barcode shift can generate plausible spatial components because the algorithm has no independent way to know which point owns a profile.

Contents · Previous section · Next section

Section 9 of 36

9. Map quality before fitting

Display library size, detected genes, mitochondrial or background signal, damaged regions and slide axes. Technical quality often varies spatially. A model designed to preserve spatial correlation can faithfully preserve artefacts unless they are removed, adjusted or clearly bounded.

Contents · Previous section · Next section

Section 10 of 36

10. Choose the expression layer deliberately

Document counts, filtering, normalisation, scaling and selected genes. SpatialPCA often follows selection of informative or spatially variable genes, so that upstream list shapes the latent space. Repeat headline conclusions with one defensible alternative feature set.

Contents · Previous section · Next section

Section 11 of 36

11. Scale coordinates in physical units

Pixels, micrometres and grid steps imply different kernel distances. Record the original units and every transformation. Rescaling one axis or combining sections without aligned coordinates changes spatial correlation even though the expression matrix is unchanged.

Contents · Previous section · Next section

Section 12 of 36

12. Select kernel form and bandwidth visibly

Kernel family and bandwidth determine which spatial scales are favoured. Too broad a kernel can wash across boundaries; too narrow a kernel can chase local noise. Use tissue geometry and prespecified sensitivity checks rather than selecting the most attractive map.

Contents · Previous section · Next section

Section 13 of 36

13. Choose component number with a task in mind

More components retain more variation and noise; fewer components compress more aggressively. Report the selection rule, variance or likelihood evidence and downstream sensitivity. A component count tuned against known labels should not be presented as wholly unsupervised discovery.

Contents · Previous section · Next section

Section 14 of 36

14. Archive numerical diagnostics

Save convergence information, hyperparameters, loadings, spatial components, fitted values, residuals, kernel settings and software commit. Successful completion is not evidence that assumptions fit. Diagnostics help identify boundary estimates or components driven by a few extreme genes.

Contents · Previous section · Next section

Section 15 of 36

15. Practise with an invented component table

This fictional table teaches interpretation, not performance.

Contents · Previous section · Next section

Section 16 of 36

16. Read loadings and maps together

A component map shows where a latent score changes; its gene loadings show which measurements contribute. Inspect both directions because a smooth map can be dominated by technical genes, and a biologically familiar loading can be spatially weak.

Contents · Previous section · Next section

Section 17 of 36

17. Detect domains without treating borders as measured

Clustering spatial components can partition tissue into domains. Boundaries depend on component number, clustering method and resolution. Report uncertainty and compare with histology rather than drawing a crisp line that implies a directly observed anatomical border.

Contents · Previous section · Next section

Section 18 of 36

18. Infer trajectories cautiously

Ordering locations along a latent path can suggest gradual tissue organisation. Spatial proximity does not establish time, lineage or direction. A root choice and trajectory algorithm can reverse or bend the story; developmental claims need temporal, lineage or perturbation evidence.

Contents · Previous section · Next section

Section 19 of 36

19. Reconstruct maps with uncertainty

SpatialPCA can infer component values at new coordinates from the fitted spatial model. Publish the prediction grid, distance from observations and uncertainty. Mask predictions outside sampled tissue and across tears so interpolation does not bridge empty space as if it were measured continuity.

Contents · Previous section · Next section

Section 20 of 36

20. Separate tissue composition from cell state

A component can vary because cell types occupy different regions, because the same type changes state, or both. Use reliable cell-type information and within-type analysis before claiming regulation. Domain structure and cell-intrinsic change are different biological owners.

Contents · Previous section · Next section

Section 21 of 36

21. Replicate at the specimen level

Locations within one section share preparation and biology. Show components or derived findings across independent donors or animals, not only thousands of correlated spots. Aligning components across specimens may require careful sign, rotation or matching procedures.

Contents · Previous section · Next section

Section 22 of 36

22. Audit kernel sensitivity

Refit a representative subset over prespecified bandwidths and kernel forms. Compare component stability, loadings, domains and trajectories. Stable conclusions are stronger; sensitivity identifies the spatial scale actually supporting the claim.

Contents · Previous section · Next section

Section 23 of 36

23. Audit gene-selection sensitivity

Repeat analysis with all defensibly variable genes and with a prespecified spatial-gene set. If a tissue domain appears only after using genes discovered on the same labels, acknowledge circularity. Feature selection is part of the model, not clerical preparation.

Contents · Previous section · Next section

Section 24 of 36

24. Audit cluster and trajectory choices

Apply one reasonable alternative clustering or trajectory method to the same spatial components. Agreement supports shared structure. Disagreement should narrow the claim and guide validation rather than be hidden by choosing the preferred picture.

Contents · Previous section · Next section

Section 25 of 36

25. Validate on the original measurement scale

Return from components to raw expression, histology and independent assays. Confirm representative broad, local, unstable and negative patterns. A latent component is useful because it summarises observations, not because the summary replaces them.

Contents · Previous section · Next section

Section 26 of 36

26. Compare with ordinary PCA

Fit ordinary PCA with the same genes and processed matrix. SpatialPCA should add value through preserved spatial correlation, not through unrelated preprocessing. Differences reveal what the spatial prior contributes and whether it smooths biology or technical variation.

Contents · Previous section · Next section

Section 27 of 36

27. Report negative findings with a detection envelope

Failure to recover a domain may mean weak contrast, the wrong feature set, a spatial scale outside the kernel or inadequate sampling. Simulate plausible islands and gradients on the observed geometry before concluding that tissue lacks organisation.

Contents · Previous section · Next section

Section 28 of 36

28. Turn a map into a testable experiment

A useful SpatialPCA result identifies genes, regions and scales for the next measurement. Select probes, sections or perturbations that can distinguish competing explanations. A beautiful component map becomes science when it produces a falsifiable tissue-level prediction.

Contents · Previous section · Next section

Section 29 of 36

29. Try a transparent classroom model

Give students a noisy grid with three measured variables. Compare ordinary PCA-like summaries with a neighbour-weighted summary, then discuss what became clearer and what may have been smoothed away. Keep the measured values, transformation, model output and interpretation in separate columns. That small audit makes assumptions visible and transfers to practical reports, data-response questions and fair comparisons.

Contents · Previous section · Next section

Section 30 of 36

30. Start the habit in Primary Science

Primary Science develops observation, comparison, classification and fair testing. A child need not run SpatialPCA to practise the foundation: record consistently, look for a pattern, change one condition and avoid claiming more than the evidence shows. Those habits support PSLE Science and later quantitative work.

Contents · Previous section · Next section

Section 31 of 36

31. Strengthen PSLE Science reasoning

The useful PSLE connection is not memorising software names. It is reading tables and graphs, identifying variables, linking evidence to a conclusion and explaining what the investigation cannot prove. SpatialPCA shows the same discipline at a scale where one attractive picture may summarise thousands of measurements.

Contents · Previous section · Next section

Section 32 of 36

32. Connect Secondary and O-Level Science

Secondary Science and O-Level Biology develop cells, organisation, variation, experimental design and evaluation. SpatialPCA provides a modern case where gene expression, tissue position and computation meet. Students can practise controls, alternative explanations and uncertainty while keeping syllabus concepts—not specialist jargon—central.

Contents · Previous section · Next section

Section 33 of 36

33. Use Computing as a partner

Computing contributes data structures, algorithms, optimisation, visualisation and reproducibility. Science contributes the specimen, question, controls and biological interpretation. Code can compress or cluster observations efficiently, but it cannot repair a biased sample or convert an assumption into a measured mechanism.

Contents · Previous section · Next section

Section 34 of 36

34. Choose schools by fit, not a buzzword

Families comparing Singapore schools should verify current subject combinations, laboratories, Applied Learning Programmes, CCAs, mentoring and timetable fit on official school and MOE pages. A mention of SpatialPCA, AI or genomics is not proof of programme quality. Look for sustained inquiry, sound teaching and opportunities to explain results.

Contents · Previous section · Next section

Section 35 of 36

35. See the career pathways

The reasoning behind SpatialPCA appears in biostatistics, spatial biology, genomics, pathology, computational imaging and scientific software. Routes may pass through polytechnic, junior college, university and continuing education, with different blends of biology, mathematics, statistics, computing and communication. Check current institutional entry requirements; one school project cannot guarantee a course or career.

Contents · Previous section · Next section

Section 36 of 36

36. Finish with a bounded claim

A careful conclusion keeps the limit visible: SpatialPCA infers a spatially correlated low-dimensional representation; it does not measure new locations, prove anatomical boundaries or establish developmental direction. Report inputs, settings, effect or separation, uncertainty, sensitivity, replication and validation together. This measured language is how a computational pattern becomes evidence another person can reproduce, challenge and improve.

A publication-ready SpatialPCA analysis starts with an explicit representation contract. Record the assay, specimens, coordinate units, expression layer, gene filters, kernel family, bandwidth candidates, component count and downstream task. Preserve raw coordinates and the fitted analysis coordinates separately. A spatial principal component can only be interpreted relative to the geometry supplied to the model.

Pre-register the primary task. Domain detection, trajectory inference and map reconstruction ask different questions and need different performance checks. Define the main outcome, sensitivity range and validation before looking at the most attractive component. Do not let one colourful embedding become evidence for every possible task.

Publish a quality atlas before a latent atlas. Show depth, detected genes, background, tissue edges, damaged regions, batch and exclusions in the same orientation as the component maps. Spatial correlation can arise from anatomy or processing. A method that preserves correlation cannot decide the cause without experimental context.

Feature selection is a scientific choice. List every tested gene and explain whether variable, marker or spatially variable genes were used. If spatial genes were selected on the same specimen and then used to claim discovered domains, acknowledge the circular route. Repeat headline findings with one independent or broader feature set.

Kernel sensitivity should appear in the main evidence rather than an invisible notebook. Fit a prespecified range of bandwidths and compare components, loadings, domains and predicted surfaces. A conclusion stable across nearby values is stronger. A result that exists only under one scale may still be valuable, but its scale dependence is part of the claim.

Component matching across specimens needs care. Principal components can reverse sign or rotate when variance is similar. Use loading correlation, subspace measures or task-based matching instead of assuming that “component 1” has the same meaning everywhere. Show each donor or animal before presenting a consensus map.

High-resolution reconstruction requires a measurement boundary. Display measured locations, prediction locations, uncertainty and distance from the nearest observation. Do not extrapolate beyond tissue masks or across tears. A smooth surface between capture sites is a probabilistic prediction, not extra sequencing.

Trajectory figures require an explicit root and direction rationale. Compare at least one plausible alternative root and show whether the biological conclusion changes. Spatial order can support an anatomical gradient, but developmental time and lineage need independent temporal or lineage-tracing evidence.

For domains, publish a stability matrix over component and clustering choices. Show marker genes, histology and boundary uncertainty. If a known annotation determined the number of clusters, call the exercise benchmark evaluation. Reserve discovery language for settings where labels did not select the answer.

Compare ordinary PCA using the identical processed matrix. This baseline isolates the contribution of the spatial covariance rather than confounding it with different genes or normalisation. If both methods recover the same broad domain, the spatial prior may improve smoothness or stability rather than create unique biology.

Empirical null checks can permute coordinates or simulate latent factors over the observed geometry. Examine false domains, component smoothness and interpolation behaviour when no biological spatial structure is present. Null maps are especially important because spatial methods are designed to make coherent patterns visible.

Reproducibility materials should include raw and processed matrices, coordinates, masks, selected genes, kernel formulas and bandwidths, component count, loadings, scores, fitted surfaces, uncertainty, clustering or trajectory settings, software commit, environment, figures and checksums. Archive negative and sensitivity results with the preferred map.

Did you know? Ordinary PCA is free to place two neighbouring tissue locations far apart if their expression differs. SpatialPCA changes the model so location helps shape the latent factors. That is why the method may reveal coherent tissue organisation—and why a strong spatial prior can also smooth a real sharp boundary.

For students, a small grid is enough to explore the idea. Give each square three measurements, make one broad gradient and add noise. Ask for a non-spatial summary and then a neighbour-aware summary. The important conversation is not which picture is prettier, but which assumptions explain the difference and which new measurement could decide.

A defensible final sentence might say: ‘Across independent tissue sections, SpatialPCA recovered spatially coherent low-dimensional structure that remained stable across prespecified feature, component and kernel choices, aligned with independent tissue evidence, and was reported with prediction uncertainty.’ It should not call interpolated locations measured, clusters anatomical facts or spatial order developmental time.

Contents · Previous section · Continue to the Science Learning Hub