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REVIEW 6 major objections 6 minor 27 references

Computing Gram Matrix for SMILES Strings using RDKFingerprint and Sinkhorn-Knopp Algorithm

T0 review · 6 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that rebalancing a Gaussian similarity matrix of RDKFingerprints with the Sinkhorn-Knopp algorithm, then reducing with kernel PCA, gives SMILES-string embeddings that beat standard fingerprint and k-mer baselines on…

desk verdict The classification win is likely an artifact of test-set leakage via pre-split kernel PCA, and Equation (3) is not implementable as written—this needs a full rewrite before it can be taken seriously. read the letter →

arxiv 2412.14717 v1 pith:EIZJDNN6 submitted 2024-12-19 cs.LG

Sarwan Ali , Haris Mansoor , Prakash Chourasia , Imdad Ullah Khan , Murray Patterson This is my paper · ORCID
classification cs.LG
keywords SMILESstringskernelmatrixSinkhorn-KnoppalgorithmRDKFingerprintPCAmolecularembeddingsdrugsubcategorypredictionsolubility
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

The paper tries to establish that a kernel-based embedding for SMILES strings can beat standard molecular fingerprints on classification. The method converts each SMILES string to an RDKFingerprint, builds a Gaussian similarity matrix, rebalances it with the Sinkhorn-Knopp algorithm into a balanced similarity matrix, and then applies kernel PCA to get low-dimensional vectors for any classifier or regressor. On the DrugBank drug-subcategory task, the authors report the best average accuracy, precision, recall, weighted F1, and ROC-AUC across seven classifiers compared with Morgan, MACCS, k-mer, and weighted k-mer embeddings. On the ChEMBL activity-type task the advantage is narrower: the proposed kernel leads only in ROC-AUC, while Morgan fingerprint leads on accuracy, precision, recall, and weighted F1. On solubility regression the method is competitive but not best, so the claimed contribution is specifically a classification-oriented embedding that could be used in drug discovery pipelines.

What carries the argument

The central object is the Gram matrix produced by Sinkhorn-Knopp rebalancing. The method normalizes an RBF distance matrix $D$ to a joint probability matrix $P$, then iteratively applies Sinkhorn-Knopp scaling until row and column marginals converge to prescribed sums, with tolerance $\xi = 10^{-6}$, producing scaling vectors $a$ and $b$; the final kernel is $K = \operatorname{diag}(a)\, P\, \operatorname{diag}(b)$. Kernel PCA on $K$ yields the top principal components used as embeddings. The Sinkhorn-Knopp iteration is the load-bearing mechanism: it converts a generic similarity matrix into a matrix with balanced row and column sums, and the paper's evidence for its value is the improved class separation visible in t-SNE plots and class-similarity heatmaps.

What would settle it

Run the pipeline with the 70/30 split placed before the Sinkhorn-Knopp kernel and kernel PCA are estimated: fit the scaling vectors and principal components on the training 70%, project the test 30% through them, and compare accuracy, precision, recall, weighted F1, and ROC-AUC against the same baselines under identical split-before-embedding conditions; if the proposed kernel no longer improves any metric, the central claim fails.

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Extended reading notes

Core claim

The central claim, stated in the abstract and Section 5, is that the proposed kernel-based approach outperforms other embedding methods and classifiers on DrugBank drug-subcategory classification in terms of average accuracy, precision, recall, weighted F1 score, and ROC-AUC. The best reported accuracy is 0.915 with logistic regression, and the kernel also gives the highest weighted F1 (0.8801 with random forest) among the compared embeddings. The authors attribute this to the Sinkhorn-Knopp step, which turns a raw Gaussian kernel into a matrix whose row and column marginals are balanced, making similar classes more similar and different classes less similar in the kernel-PCA embedding. For ChEMBL, the same method only beats all baselines on ROC-AUC, and for regression it trails MACCS with random forest, so the paper's central claim is essentially about classification.

Load-bearing premise

The evaluation rests on the premise that fitting the kernel matrix and kernel PCA on the full dataset before the 70/30 split does not inflate the reported classification gains.

Editorial extensions

If this is right

  • On DrugBank, the proposed embedding reaches a best accuracy of 0.915 and best weighted F1 of 0.8801 with logistic regression and random forest respectively, exceeding the best baseline on those metrics.
  • Because the embedding is just a vector per molecule, it can be plugged into any classifier or regressor without changing the downstream model.
  • The method's advantage is classification-specific: on ChEMBL only ROC-AUC improves, and on solubility regression MACCS fingerprints with random forest still lead.
  • The kernel construction is fingerprint-based, so it inherits the low cost and substructure interpretability of RDKFingerprint features while adding a nonlinear, globally balanced similarity.

Reading between the lines

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

  • Beyond the paper, the same Sinkhorn-Knopp rebalancing could be applied to other molecular similarity matrices, such as graph-edit distances or learned fingerprints, to isolate whether the balancing step or the fingerprint features drive the classification gain.
  • Beyond the paper, the reported comparisons leave open how much of the gain comes from fitting kernel PCA on the full dataset before the split; a deployment-oriented evaluation would fit the embedding on training molecules only and project test molecules.
  • Beyond the paper, the row and column scaling is formally related to optimal-transport attention, so a trainable version of this kernel might yield a learnable molecular similarity measure.
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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

6 major / 6 minor

Summary. The paper proposes a kernel-based embedding for SMILES strings: convert SMILES to molecular graphs, compute RDKit fingerprints, form a Gaussian similarity matrix, apply Sinkhorn-Knopp scaling to obtain a kernel matrix, and use kernel PCA for dimensionality reduction. The embeddings are evaluated on DrugBank drug-subcategory classification and solubility regression against several fingerprint baselines. The authors claim the proposed kernel outperforms baselines on classification. The manuscript includes tables of results, t-SNE plots, and heatmaps.

Significance. The problem of representing SMILES strings for machine learning is relevant, and the idea of using Sinkhorn-Knopp balancing to turn a similarity matrix into a kernel is not without interest. However, the paper as written does not provide a coherent description of the kernel (the update equation is undefined), the evaluation protocol leaks test-set information through full-data kernel PCA, and the reported results contradict parts of the abstract. No code or data is provided, and no validation procedure for the free hyperparameters is described. If the technical issues were resolved, the approach might merit further study, but the current claims are unsupported.

major comments (6)
  1. [Section 3.4, Eq. (3)] The Sinkhorn-Knopp update formula is mathematically incoherent. The expression 'BipartiteGraph ← −δP + (ζ × log(− →a1)) + (ζ × log(− →b1 )) / ζ' mixes a matrix P with vectors a1 and b1 and scalars ζ and δ in a way that is undefined (dimension mismatch, log of a vector with negative sign). The initialization and iterative updates of a, b, a1, b1 are not described. As a result, the kernel matrix K in Eq. (4) cannot be computed from the paper's description. This is a load-bearing error because the entire method rests on this kernel.
  2. [Sections 3.5 and 4] The evaluation protocol leaks test-set information. The kernel matrix D in Eq. (1) is computed over all i,j ∈ N, and kernel PCA is applied to the full kernel matrix in Section 3.5. Section 4 then describes a 70/30 train/test split but provides no procedure for refitting kernel PCA on the training portion or for projecting held-out molecules (e.g., via Nyström). Thus, test molecules influence the embedding used to train classifiers, and the comparison against baselines is confounded. This invalidates the headline classification results in Table 2.
  3. [Section 5, Table 2] The claim in Section 5 that the proposed approach 'outperforms other embedding methods and classifiers in terms of average accuracy, precision, recall, weighted F1 score, and ROC-AUC' is not supported by the table. For example, on DrugBank, the Morgan fingerprint with LR achieves ROC-AUC 0.6215, while the best SMILES-kernel ROC-AUC is 0.5733 (DT), and several baselines have higher ROC-AUC. The statement should be restricted to specific metrics and classifiers where it actually holds, and the contradiction should be resolved.
  4. [Section 3.2] The fingerprint is mislabeled. The authors state they use 'RDKit fingerprint' generated using the Morgan algorithm and refer to it as 'RDKFingerprint' and 'Morgan Fingerprint' interchangeably. In RDKit, the RDKFingerprint and Morgan fingerprints are distinct algorithms with different substructure definitions and bit generation. Citing reference [16] for the RDKFingerprint is incorrect, and this inconsistency makes the method difficult to reproduce.
  5. [Section 5, Table 3] The abstract claims the proposed method 'outperforms several baseline methods in terms of supervised analysis,' but this is not supported for regression. In Table 3, the MACCS fingerprint with random forest regression achieves R² = 0.7804 on DrugBank, whereas the proposed SMILES kernel with random forest regression achieves R² = 0.7009, and several other baselines also outperform the proposed method. The discussion correctly acknowledges this, but the abstract's broad statement is misleading and should be qualified.
  6. [Section 5, Table 2] Table 2 contains apparent duplicated entries. For the Morgan fingerprint, the logistic regression row reports identical values for DrugBank and ChEMBL (Acc 0.4934, Prec 0.4868, Recall 0.4934, F1(Wt) 0.4870, F1(Mac) 0.2689, ROC-AUC 0.6215, TrainTime 10.2591). Similarly, the k-mers random forest row for ChEMBL is identical to the MACCS fingerprint random forest row for ChEMBL. These duplicates cannot be correct and undermine the reliability of the reported results.
minor comments (6)
  1. [Section 3.3, Eq. (1)] The matrix D is called a 'distance matrix' but Eq. (1) defines a Gaussian similarity (kernel) between feature vectors. This terminology is misleading and should be corrected.
  2. [Section 3.2] The notation is inconsistent: X1 and X2 are introduced as sets of molecular graphs, but Eq. (1) uses X_i and X_j as feature vectors. The fingerprint length 'n = 2048' is also conflated with the number of molecules.
  3. [Section 3.4] The initialization of vectors a, b, a1, b1 is described as 'zero vectors' and 'unit vectors,' but the standard Sinkhorn algorithm requires positive vectors for row and column scaling. This description is unclear and should be specified precisely.
  4. [Section 5, Figure 4] The statement 'smaller kernel value is better' is not justified. If the kernel value measures similarity, a smaller value indicates less similarity, but the paper does not explain why this is beneficial for the proposed method.
  5. [Section 5, Table 3] The k-mers linear regression results on DrugBank are numerically absurd (MAE 8.3616e+10, R² −2.7267e+19), indicating overflow or a broken implementation. These values should be removed or a stable procedure should be used, and the issue should be discussed.
  6. [Section 4] The paper reports averages over 5 runs but provides no standard deviations, confidence intervals, or significance tests, making it difficult to judge whether the observed differences are reliable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the proposed kernel is an empirical pipeline whose construction does not reduce to its own inputs or to self-citations.

full rationale

The paper makes no formal derivation claim that could be circular. The proposed SMILES kernel is constructed from RDKFingerprint features through a Gaussian distance matrix (Eq. 1), probability normalization (Eq. 2), Sinkhorn-Knopp scaling (Eqs. 3-4), and kernel PCA (Section 3.5). None of these steps references the target labels or the downstream classification results; the kernel is defined from input fingerprints alone, so there is no self-definitional reduction. The classification and regression numbers in Tables 2-4 are empirical outcomes, not predictions forced by fitted parameters: the paper does not describe fitting sigma, Sinkhorn tolerance, or the number of kernel PCA components to the test labels, and no fitted parameter is renamed as a prediction. The potential evaluation issue that kernel PCA is computed on the full dataset before the 70/30 split (Sections 3.5 and 4) is a correctness/leakage concern rather than a circularity of the derivation, and it is explicitly outside the circularity scoring rubric. The references cited for the building blocks (Sinkhorn-Knopp, kernel PCA, Morgan fingerprint) are standard external methods, and no load-bearing self-citation or imported uniqueness theorem appears. Therefore the derivation chain is self-contained with respect to circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method relies entirely on standard optimal transport and kernel PCA machinery, so no new entities are invented. However, the paper leaves several free parameters unspecified and makes domain assumptions about fingerprint quality and the validity of the scaled kernel. The unspecified marginals for Sinkhorn-Knopp are a notable gap: the resulting matrix and the final kernel are not well-defined as described.

free parameters (5)
  • sigma (Gaussian kernel width) = Not reported
    Appears in Eq (1) as the width of the Gaussian kernel used to construct D. Its value strongly affects the kernel and no tuning or validation procedure is described.
  • k (number of kernel PCA components) = Not reported, except an example with k=100 in Figure 4
    Section 3.5 uses top principal components, but no value is specified for the experiments; embeddings shown in Figure 4 use k=100.
  • xi (Sinkhorn-Knopp convergence tolerance) = 1e-6
    Given in Section 3.4 as the tolerance on max(|a1-a|) and max(|b1-b|).
  • delta (small constant in Eq 3) = 1e-10
    Introduced in Eq (3) without a clear role.
  • Target marginal distributions for Sinkhorn scaling = Unspecified
    The desired row and column sums of the scaled matrix are never defined; the algorithm description says to match 'desired marginal distributions' but does not state what they are.
assumptions (4)
  • standard math Sinkhorn-Knopp iteration converges to a matrix with specified marginals for positive matrices.
    Invoked in Section 3.4 as the basis for computing the kernel matrix.
  • standard math The Gaussian kernel matrix is positive semidefinite and valid for kernel PCA.
    Used in Sections 3.3 and 3.5 without proof.
  • domain assumption RDKit fingerprints (and the algorithm described as Morgan fingerprint) capture molecular structure relevant for property prediction.
    The entire method depends on the discriminative power of these fingerprints; this is asserted rather than evidenced in this paper.
  • domain assumption The Sinkhorn-scaled matrix K can serve as a kernel for kernel PCA.
    The paper assumes K has the necessary properties for kernel PCA without establishing positive semidefiniteness or the validity of the scaling.

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Cite this review

Pith. "Pith review of Computing Gram Matrix for SMILES Strings using RDKFingerprint and Sinkhorn-Knopp Algorithm." pith.science (2026). https://pith.science/paper/EIZJDNN6

@misc{pith2026241214717,
  author       = {Pith},
  title        = {Pith review of: Computing Gram Matrix for SMILES Strings using RDKFingerprint and Sinkhorn-Knopp Algorithm},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EIZJDNN6}},
  note         = {Machine review of arXiv:2412.14717}
}
read the original abstract

In molecular structure data, SMILES (Simplified Molecular Input Line Entry System) strings are used to analyze molecular structure design. Numerical feature representation of SMILES strings is a challenging task. This work proposes a kernel-based approach for encoding and analyzing molecular structures from SMILES strings. The proposed approach involves computing a kernel matrix using the Sinkhorn-Knopp algorithm while using kernel principal component analysis (PCA) for dimensionality reduction. The resulting low-dimensional embeddings are then used for classification and regression analysis. The kernel matrix is computed by converting the SMILES strings into molecular structures using the Morgan Fingerprint, which computes a fingerprint for each molecule. The distance matrix is computed using the pairwise kernels function. The Sinkhorn-Knopp algorithm is used to compute the final kernel matrix that satisfies the constraints of a probability distribution. This is achieved by iteratively adjusting the kernel matrix until the marginal distributions of the rows and columns match the desired marginal distributions. We provided a comprehensive empirical analysis of the proposed kernel method to evaluate its goodness with greater depth. The suggested method is assessed for drug subcategory prediction (classification task) and solubility AlogPS ``Aqueous solubility and Octanol/Water partition coefficient" (regression task) using the benchmark SMILES string dataset. The outcomes show the proposed method outperforms several baseline methods in terms of supervised analysis and has potential uses in molecular design and drug discovery. Overall, the suggested method is a promising avenue for kernel methods-based molecular structure analysis and design.

Figures

Figures reproduced from arXiv: 2412.14717 by the authors.

Figure 1
Figure 1. Workflow of the proposed method. 3.5 Kernel PCA-Based Embeddings In practice, a large dataset leads to a large K, and storing K may become a problem. Kernel-PCA can help in this regard to convert K into a low-dimensional [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The t-SNE plots using feature embedding for the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Heatmap for classes in DrugBank dataset for different drug subtypes. The figure is best seen in color. An example of a pair of sample SMILES strings belonging to different classes (i.e., drug subcategories) is shown in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Comparing two pairs of classes. (a) and (b) belong to different classes. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 11, 2026 · model on record in the stance chip above.