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arxiv: 2606.12021 · v1 · pith:MSUJ55MQnew · submitted 2026-06-10 · 📊 stat.ME

Adaptive spatial blocking for scalable clustering inference with applications to high-throughput spatial proteomics

Mingyu Go , Julia Wrobel , Hoseung Song This is my paper

Pith reviewed 2026-06-27 08:43 UTC · model grok-4.3

classification 📊 stat.ME
keywords spatial clusteringRipley's K-functionadaptive blockingpoint patternsspatial proteomicsasymptotic approximationscalable inferencecolocalization
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The pith

Adaptive spatial blocking makes Ripley's K-function clustering tests feasible on large point pattern images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an adaptive spatial blocking algorithm that carves large images into disjoint blocks meeting point-count and shape constraints. These blocks allow aggregation of local clustering evidence from Ripley's K-function, followed by an asymptotic normal approximation to obtain p-values without processing every point in the full image. The approach targets the computational limits of existing K-based methods when applied to high-throughput spatial proteomics data containing many thousands or millions of points. Numerical studies show the method balances power and speed, and an application to human intestine tissue data identifies plasma cell aggregation and colocalization with macrophages.

Core claim

The proposed adaptive spatial blocking algorithm constructs blocks satisfying point-count and shape constraints, enabling scalable spatial clustering inference and fast p-value computation through an asymptotic normal approximation. Numerical studies demonstrate that the proposed method provides a favorable balance between statistical power and computational efficiency. In an application to healthy human intestine spatial proteomics data, the method detects strong spatial aggregation of plasma cells and colocalization between plasma cells and macrophages, while scaling favorably to large images.

What carries the argument

The adaptive spatial blocking algorithm, which partitions the image into disjoint blocks meeting point-count and shape constraints so that local K-function signals can be aggregated and approximated by a normal distribution for p-values.

If this is right

  • Clustering inference becomes practical for high-throughput spatial proteomics images that were previously too large for full K-function calculations.
  • P-values can be obtained rapidly via the normal approximation once blocks are formed.
  • The method maintains statistical power while reducing computation time, as shown in the numerical studies.
  • Real-data analysis can identify biologically relevant patterns such as cell aggregation and colocalization at scale.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same blocking idea might extend to other spatial summary statistics that also suffer from quadratic scaling with point count.
  • Parallel implementation of block construction and local K calculations could further reduce wall-clock time on multi-core hardware.
  • If the shape and count constraints prove too restrictive in some domains, relaxing them while preserving the normal approximation would be a direct next test.

Load-bearing premise

Aggregating clustering evidence from the constructed disjoint blocks still permits a reliable asymptotic normal approximation for p-value calculation.

What would settle it

Compare p-values and detected clusters from the blocked method against those from the full-image K-function calculation on the same large simulated or real datasets; substantial mismatch in either quantity would undermine the claim.

Figures

Figures reproduced from arXiv: 2606.12021 by Hoseung Song, Julia Wrobel, Mingyu Go.

Figure 1
Figure 1. Figure 1: Simulated point patterns under the null (left) and alternative (right) hypotheses. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of extracting block candidates. (a) A binary matrix [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Result of applying the adaptive spatial blocking algorithm to a simulated point [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of block complement (Phase III). [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Normal quantile-quantile plots of 𝑍(𝑟). 2.3 Extension to bivariate spatial clustering While Section 2.2 focuses on the spatial clustering of a single point type, spatial interactions between two point types are also of substantial interest in many practical applications. In spatial proteomics, for instance, quantifying the spatial colocalization of distinct immune cell types is a common objective (Schürch … view at source ↗
Figure 6
Figure 6. Figure 6: Empirical type I error rate and power across different values of radii [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Power comparison across different radii and abundance levels at [PITH_FULL_IMAGE:figures/full_fig_p029_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of the cell organization in the selected tissue image. [PITH_FULL_IMAGE:figures/full_fig_p031_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Resulting blocks from the proposed blocking algorithm applied to the image in [PITH_FULL_IMAGE:figures/full_fig_p032_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance comparison of 𝐵-𝐾𝐴𝑀𝑃 and baseline methods for univariate plasma cell clustering and bivariate plasma cell-macrophage colocalization. The left panels show − log(𝑝-value) across 65 images over different radii with the red horizontal line in￾dicating − log(0.05). The right panels show execution times in seconds for representative small, moderate, and large images. These findings provide formal st… view at source ↗
read the original abstract

Ripley's K-function is a widely used spatial summary statistic for assessing clustering in point patterns. However, existing K-based methods can be computationally prohibitive for large-scale data, particularly in high-throughput spatial proteomics, because they rely on spatial information from all points in the image. To address this challenge, we propose a computationally efficient block-based testing framework that extracts disjoint local blocks from an image and aggregates clustering evidence across them. The proposed adaptive spatial blocking algorithm constructs blocks satisfying point-count and shape constraints, enabling scalable spatial clustering inference and fast p-value computation through an asymptotic normal approximation. Numerical studies demonstrate that the proposed method provides a favorable balance between statistical power and computational efficiency. In an application to healthy human intestine spatial proteomics data, our method detects strong spatial aggregation of plasma cells and colocalization between plasma cells and macrophages, while scaling favorably to large images.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes an adaptive spatial blocking algorithm that extracts disjoint blocks from large point patterns subject to point-count and shape constraints. Clustering evidence is aggregated across blocks using Ripley's K-function, and p-values are obtained via an asymptotic normal approximation. Numerical studies are claimed to demonstrate a favorable power-efficiency tradeoff, and the method is applied to healthy human intestine spatial proteomics data to detect plasma-cell aggregation and colocalization with macrophages.

Significance. If the asymptotic normality of the aggregated statistic remains valid after data-dependent block selection, the framework would address a genuine computational bottleneck in spatial statistics for high-throughput proteomics and similar large-scale point-pattern applications, enabling routine analysis of images that are currently intractable.

major comments (2)
  1. [Abstract] Abstract: the claim that numerical studies demonstrate a favorable power-efficiency balance supplies no quantitative details on type-I error rates, coverage probabilities of the normal approximation, or sensitivity of results to block-construction parameters. Without these, the central claim of reliable scalable inference cannot be evaluated.
  2. [Method (adaptive blocking)] Method (adaptive blocking construction): blocks are selected using the same observed point pattern that enters the aggregated K-statistic. Standard central-limit arguments for fixed blocks do not automatically extend to this data-dependent selection; the manuscript provides neither additional regularity conditions nor simulation evidence confirming that the null distribution of the aggregated quantity remains asymptotically normal after adaptation.
minor comments (1)
  1. [Application] Application section: the reported detections of aggregation and colocalization are stated qualitatively; quantitative p-values, effect sizes, and block counts used should be reported for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of the abstract presentation and the theoretical justification for the asymptotic approximation under adaptive blocking. We respond to each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that numerical studies demonstrate a favorable power-efficiency balance supplies no quantitative details on type-I error rates, coverage probabilities of the normal approximation, or sensitivity of results to block-construction parameters. Without these, the central claim of reliable scalable inference cannot be evaluated.

    Authors: We agree that the abstract would benefit from greater specificity. The numerical studies section already contains the requested quantities (empirical type-I error rates near nominal levels, coverage of the normal approximation, and sensitivity checks to block parameters), but these are not summarized in the abstract. In the revised manuscript we will update the abstract to include concise quantitative statements drawn from those studies. revision: yes

  2. Referee: [Method (adaptive blocking)] Method (adaptive blocking construction): blocks are selected using the same observed point pattern that enters the aggregated K-statistic. Standard central-limit arguments for fixed blocks do not automatically extend to this data-dependent selection; the manuscript provides neither additional regularity conditions nor simulation evidence confirming that the null distribution of the aggregated quantity remains asymptotically normal after adaptation.

    Authors: We acknowledge that data-dependent block selection requires justification beyond the fixed-block case. The selection rules depend only on local point counts and shape constraints, which under the null are independent of the spatial clustering structure that the K-function targets. The numerical studies section already reports Monte Carlo experiments under the null in which the aggregated statistic exhibits close-to-normal behavior and type-I error control across a range of image sizes and block-parameter settings. We will add an explicit paragraph in the methods section discussing why the adaptation does not invalidate the asymptotic normality and will include a supplementary table summarizing the simulation diagnostics for the normal approximation. revision: partial

Circularity Check

0 steps flagged

No circularity; asymptotic approximation treated as standard external tool

full rationale

The provided abstract and description present the adaptive blocking algorithm as a computational device that extracts disjoint blocks satisfying point-count and shape constraints, after which clustering evidence is aggregated and an asymptotic normal approximation (a standard statistical result) is invoked for p-value computation. No equations, fitted parameters, or self-citations are shown that define the normal approximation in terms of the blocks or reduce the reported performance to a quantity fitted from the same data. The derivation chain therefore remains self-contained against external benchmarks; the reader's suggested concern about data-dependent block selection is a question of regularity conditions for the CLT, not a circular reduction by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The central claim rests on the validity of the asymptotic normal approximation for the block-aggregated statistic and on the assumption that the adaptive block construction preserves the essential spatial dependence structure.

axioms (1)
  • domain assumption Aggregated evidence across disjoint blocks follows an asymptotic normal distribution suitable for p-value calculation
    Invoked to replace exact permutation or Monte Carlo p-value computation with a fast normal approximation

pith-pipeline@v0.9.1-grok · 5673 in / 1297 out tokens · 16754 ms · 2026-06-27T08:43:17.466057+00:00 · methodology

discussion (0)

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Reference graph

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