FAQ

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FAQ#

What does quadsv stand for?

“Quadratic-form spatial variability.” Every test in the library reduces to the quadratic form

\[Q_n = \mathbf{z}^\top \tilde{\mathbf{K}} \mathbf{z},\]

where \(\tilde{\mathbf{K}} = \mathbf{H}\mathbf{K}\mathbf{H}\) is the double-centred kernel matrix. See Theoretical Results.

Why is Moran’s I problematic for SVG detection?

Moran’s I uses an indefinite adjacency matrix as its kernel, so its eigenvalues span both signs. Patterns aligned with positive eigenspaces cancel patterns aligned with negative ones, which produces false negatives. Use the CAR kernel \(\mathbf{K} = (\mathbf{I} - \rho \tilde{\mathbf{W}})^{-1}\) instead. It is strictly positive definite for any \(0 < \rho < 1\). See Theoretical Results (Theorem 2).

from quadsv import MatrixKernel

kernel = MatrixKernel.from_coordinates(
    coords, method="car", k_neighbors=4, rho=0.9
)
What is the difference between Q-test and R-test?

spatial_q_test() is univariate: \(Q = \mathbf{z}^\top \mathbf{K} \mathbf{z}\). It asks whether one feature is spatially structured under the kernel. Use it to identify spatially variable genes.

spatial_r_test() is bivariate: \(R = \mathbf{x}^\top \mathbf{K} \mathbf{y}\). It asks whether two features share a spatial pattern. Use it to find spatially co-expressed gene pairs.

Which backend should I pick?

You can let the Detector() factory decide from your input type:

from quadsv import Detector

# AnnData → DetectorIrregular
det = Detector(adata, kernel_method="matern", backend="nufft").setup_data(adata)

# SpatialData → DetectorGrid
det = Detector(sdata, kernel_method="car", rho=0.9).setup_data(sdata, ...)

For explicit control:

Backend

When to use

backend="matrix" (MatrixKernel)

Any coordinate cloud or graph. Pick this for car, moran, or graph_laplacian kernels, or when you have a precomputed adjacency in adata.obsp. Storage (dense / sparse / sparse-precision) is selected from n.

backend="nufft" (NUFFTKernel)

Irregular 2-D coordinates with around \(10^4\) spots or more. Runs at O(n log n) per feature. Pairs with Gaussian or Matérn.

DetectorGrid (FFTKernel)

Regular rasterised grids (Visium HD). Reads spatialdata.SpatialData directly and uses an FFT.
Can I use quadsv on non-spatial data?

Yes, as long as you can encode “closeness” as coordinates or as a graph. Common cases:

  • A k-NN graph in PCA space (single-cell trajectories).

  • A pseudo-time ordering or a lineage tree.

  • A custom adjacency in adata.obsp.

Pass coordinates to quadsv.MatrixKernel.from_coordinates(), or a precomputed kernel or precision matrix to quadsv.MatrixKernel.from_matrix(). To use an adata.obsp[key] directly, call setup_data() with obsp_key=key. Add is_distance=True if the matrix stores distances rather than affinities.

Does quadsv support 3-D coordinates?

The MatrixKernel family does. Pass 3-D coords to quadsv.MatrixKernel.from_coordinates() the same way you would for 2-D. The FFT and NUFFT backends are 2-D only for now. If you need 3-D Fourier acceleration, please open a feature request on GitHub.

Further help#

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