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REVIEW 3 major objections 4 minor 22 references

Reconstruction of Partial Dissimilarity Matrices for Cognitive Neuroscience

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A Euclidean median rule can complete sparse dissimilarity matrices without training, preserving high accuracy even when 80% of entries are missing.

desk verdict A useful, well-tested imputation heuristic whose geometric justification does not hold up, and whose Pearson-correlation metric hides a bias that appears even on exact Euclidean data. read the letter →

arxiv 2506.00484 v2 pith:YEMN5NUT submitted 2025-05-31 q-bio.NC

Denise Moerel , Tijl Grootswagers This is my paper
classification q-bio.NC
keywords representationaldissimilaritymatrixdistancecompletiongeometricinferenceEuclideangeometrysimilarityanalysisjudgmentssparseimputationcognitiveneuroscience
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Representational Dissimilarity Matrices (RDMs), tables of pairwise dissimilarity among stimuli, are often incomplete because collecting every pair of similarity judgments becomes impractical as the number of stimuli grows. The paper proposes a simple algorithm that fills each missing entry by looking at items whose distances to both members of the pair are known, combining those distances with Euclidean geometry, and taking a median over all such anchors. It reports that this training-free method reconstructs missing distances with high correlation to the true values across four real behavioural similarity datasets and synthetic data, including correlation around 0.8 when only 20% of entries remain. If this holds, researchers can obtain complete dissimilarity matrices from sparse behavioural data without expensive or opaque deep-learning imputation, and can use existing RSA analysis tools that require complete matrices.

What carries the argument

The load-bearing object is the median-of-two-Euclidean-estimates rule. For a missing distance between items $i$ and $j$, the algorithm collects every item $k$ with known distances to both, forms two candidate values, $\sqrt{d(i,k)^2+d(j,k)^2}$ (the hypotenuse of a right triangle whose legs are the two known distances) and $\sqrt{|d(i,k)^2-d(j,k)^2|}$ (the remaining leg when the larger known distance is the hypotenuse), and assigns the median of all candidates across anchors. Repeating this pass over the matrix, so that newly filled entries serve as anchors for later ones, is what allows the method to propagate information across the whole matrix; the worst-case running time is $O(n^3)$.

What would settle it

Take a dissimilarity matrix computed from great-circle distances on a sphere, mask 50% to 80% of its entries, run the geometric reconstruction, and check whether the correlation between reconstructed and true distances falls toward chance.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a missing pairwise dissimilarity $d(i,j)$ can be accurately estimated from any item $k$ whose distances to $i$ and $j$ are known, using the Euclidean estimates $\sqrt{d(i,k)^2+d(j,k)^2}$ and $\sqrt{|d(i,k)^2-d(j,k)^2|}$, with the median across all valid $k$ as the prediction. The algorithm fills entries iteratively, skipping entries that cannot yet be estimated and retrying after other entries have been filled, and it is guaranteed to complete the whole matrix whenever the known distances connect all items. Evaluated by masking 1% to 80% of entries in four empirical RDMs and in simulated Euclidean distance matrices, the method consistently outperformed a graph shortest-path approach and a multidimensional-scaling approach, with accuracy declining gracefully as sparsity increased.

Load-bearing premise

The load-bearing premise is that the dissimilarity matrix is approximately Euclidean, so that every missing distance can be approximated by the square root of the sum or difference of squares of two known distances to a common third item; if the true space is curved or non-metric, the method can break down.

Editorial extensions

If this is right

  • Behavioural similarity studies that collect only a fraction of all pairs can obtain complete dissimilarity matrices without training a model or supplying external stimulus features.
  • Reconstruction accuracy remains high with up to 80% of entries missing, and reaches about 0.8 correlation with the true distances when only 20% of entries remain.
  • On the four empirical datasets tested, the geometric method outperformed a graph-based Floyd-Warshall shortest-path completion and a multidimensional-scaling-based completion.
  • Because the algorithm fills entries iteratively, it is guaranteed to complete the entire matrix whenever every item is connected to every other item through a chain of known distances.
  • The method runs in polynomial time, with worst-case $O(n^3)$, making it practical for the matrix sizes used in cognitive neuroscience.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, this completion method could act as a preprocessing step for representational similarity analyses and embedding algorithms that currently require complete dissimilarity matrices, effectively widening the range of behavioural tasks usable with RSA.
  • Beyond the paper, reconstruction accuracy on a new dataset could serve as a practical diagnostic for how Euclidean that dataset's similarity structure is; a sharp drop in accuracy with sparsity would flag non-metric or curved geometry.
  • Beyond the paper, the same median rule could be adapted to other geometries, for example replacing the Euclidean formulas with spherical or hyperbolic distance laws, though the authors only gesture at this as future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a simple algorithm for completing partial dissimilarity matrices (RDMs) in cognitive neuroscience. For each missing distance d(i,j), the algorithm finds every anchor k with known d(i,k) and d(j,k), computes the two quantities sqrt(d(i,k)^2 + d(j,k)^2) and sqrt(|d(i,k)^2 - d(j,k)^2|), and takes their median as the reconstruction. The method is evaluated on four real behavioural dissimilarity datasets and on simulated Euclidean distance matrices, across matrix sizes from 27 to 256 and missing proportions from 1% to 80%, with accuracy measured by Pearson correlation between reconstructed and true distances. The geometric method is compared with a Floyd-Warshall graph-based method and an MDS-based method and is reported to outperform both. The authors provide open-source Python and MATLAB implementations.

Significance. If the accuracy claims hold, this is a useful, transparent, and computationally light tool for a common practical problem in representational similarity analysis: incomplete RDMs. Strengths include the absence of any fitted parameters, broad empirical evaluation on four public datasets and extensive simulations, comparison against two alternative completion methods, and public availability of code and data. However, the central accuracy claim rests entirely on Pearson correlation, which is insensitive to systematic monotone bias, and the geometric derivation in Section 2.1 is not actually a consequence of Euclidean geometry. These issues make the support for 'accurate reconstruction' weaker than the text suggests.

major comments (3)
  1. [Section 2.1] The estimators sqrt(d(i,k)^2 + d(j,k)^2) and sqrt(|d(i,k)^2 - d(j,k)^2|) are exact only for right triangles, not for general Euclidean triangles. The true distance is sqrt(d(i,k)^2 + d(j,k)^2 - 2 d(i,k) d(j,k) cos(theta)) for an unknown angle theta. The triangle inequality alone gives only bounds, not these point values. The statement 'Assuming Euclidean geometry and triangle inequality' does not justify the estimator. Please clarify that this is a heuristic (e.g., a right-angle approximation) or provide a derivation; as written, the paper's central geometric premise is not supported.
  2. [Section 3.1 and 3.2] Reconstruction accuracy is measured exclusively via Pearson correlation between reconstructed and original distances. Pearson correlation is invariant to monotone transformations, so a method that returns half of every true distance, or a constant times the true distance, will yield a high correlation while being useless for estimating embeddings or downstream distance-based analyses. The claim of 'accurate reconstruction' needs additional value-fidelity metrics, such as mean absolute error, root-mean-square error, or calibration slope/scatter plots, at least on the simulated Euclidean data where ground truth is available. Without such metrics, the reported correlations around 0.8 do not establish that the reconstructed distances are accurate in the relevant sense.
  3. [Section 4] The Discussion states the method 'may break down if the true space is curved or non-metric,' but the failure mode is broader: the estimator can be badly biased even for exact Euclidean matrices. For a unit square, a missing side of length 1 is reconstructed as approximately 1.366, and a missing diagonal of length sqrt(2) is also reconstructed as approximately 1.366, collapsing distinct distances. This is not a peripheral concern; it directly affects the interpretation of the high correlations reported in Figures 1 and 2. The limitation statement should acknowledge that the heuristic's bias is present in Euclidean settings as well, and that Pearson correlation may mask such bias.
minor comments (4)
  1. [Section 2.2] The description of '1000 random iterations' should clarify whether the masking (deletion of pairwise distances) is independently resampled in each iteration, and whether the same mask is used across the compared methods in Section 3.3.
  2. [Section 3.1] The chance baseline is described as 'inserting random values,' which yields a Pearson correlation near zero; a more informative baseline would be a constant imputation (e.g., the mean observed distance), especially when evaluating the practical benefit of the method.
  3. [Section 3.2] The simulation description says 'we calculated full distance matrices on randomly placed points' but later specifies sampling from a multivariate Gaussian; please state the exact generation procedure, including whether the coordinates are independent across dimensions, and whether the covariance is isotropic.
  4. [Figure 3] In several panels, the legend order does not appear to match the line order in the plot; direct labeling of the lines or consistent colour/line-style mapping would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the geometric imputation is parameter-free and is evaluated by masking known entries and comparing against those held-out distances.

full rationale

The paper's reconstruction pipeline is self-contained in the relevant sense. Section 2.1 defines a deterministic, parameter-free estimator: each missing d(i,j) is filled from known distances d(i,k) and d(j,k) via the median of sqrt(d(i,k)^2 + d(j,k)^2) and sqrt(|d(i,k)^2 - d(j,k)^2|), with iterative filling over connected components. No parameter is fit to the masked test entries, and reconstruction accuracy is measured as the Pearson correlation between the reconstructed distances and the originally observed, held-out distances (Sections 2.2 and 3.1). The four benchmark RDMs are pre-existing public empirical datasets (Bracci et al., 2019; Grootswagers et al., 2024; Mur et al., 2013; Robinson et al., 2025). Although two of these are co-authored by the present authors, they are used as external ground-truth data, not as internal derivation steps, and the reconstruction claim does not depend on an unverified self-cited result. The only self-citation used to explain a benchmark's ceiling effect cites Grootswagers and Robinson (2021), and is interpretive rather than load-bearing. The geometric formulas in Section 2.1 are a modeling assumption (a right-triangle approximation) rather than a logical consequence of Euclidean geometry, and the skeptical concern that the estimator can be biased even for exact Euclidean matrices is a validity or correctness issue, not circularity: the estimator is not equivalent by construction to the quantity it predicts. Because the evaluation uses held-out entries and no fitted parameter is renamed as a prediction, no circular step is exhibited.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The method has no fitted parameters. The central assumptions are Euclidean representational geometry, random missingness, and the validity of the two square-root estimators. No new entities are introduced.

assumptions (3)
  • domain assumption Representational space is approximately Euclidean
    Section 2.1 assumes Euclidean geometry; the Discussion states the method 'may break down if the true space is curved or non-metric.'
  • domain assumption Missing data are missing at random
    The evaluation deletes random entries uniformly; real behavioral protocols may produce systematic missingness, which is not tested.
  • ad hoc to paper The estimators sqrt(a^2+b^2) and sqrt(|a^2-b^2|) proxy the missing distance
    This heuristic is not derived from triangle inequality or Euclidean constraints; it corresponds to right-angle and aligned configurations and is adopted to make the algorithm work.

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Cite this review

Pith. "Pith review of Reconstruction of Partial Dissimilarity Matrices for Cognitive Neuroscience." pith.science (2026). https://pith.science/paper/YEMN5NUT

@misc{pith2026250600484,
  author       = {Pith},
  title        = {Pith review of: Reconstruction of Partial Dissimilarity Matrices for Cognitive Neuroscience},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YEMN5NUT}},
  note         = {Machine review of arXiv:2506.00484}
}
read the original abstract

In cognitive neuroscience research, Representational Dissimilarity Matrices (RDMs) are often incomplete because pairwise similarity judgments cannot always be exhaustively collected as the number of pairs rapidly increases with the number of conditions. Existing methods to fill these missing values, such as deep neural network imputation, are powerful but computationally demanding and relatively opaque. We introduce a simple algorithm based on geometric inference that fills missing dissimilarity matrix entries using known distances. We use tests on publicly available empirical cognitive neuroscience datasets, as well as simulations, to demonstrate the method's effectiveness and robustness across varying sparsity and matrix sizes. We have made this geometric reconstruction algorithm, implemented in Python and MATLAB, publicly available. This method provides a fast and accurate solution for completing partial dissimilarity matrices in the cognitive neurosciences.

Figures

Figures reproduced from arXiv: 2506.00484 by the authors.

Figure 2
Figure 2. Reconstruction accuracies for the simulated data. A) The reconstruction accuracies for the missing values only, across varying proportions of missing distances. The reconstruction accuracy was calculated as the correlation between the original and reconstructed distances. We used 4 different sized dissimilarity matrices, shown in different colours. The shaded area around the plot lines shows the 2.5 to 97.5 percenti… view at source ↗

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Works this paper leans on

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