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ICSpyLab: A Python package for invariant coordinate selection

T0 review · 2 major / 0 minor · reviewed 2026-06-25 · grok-4.3

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Pith's one-line read ICSpyLab supplies the first dedicated Python implementation of invariant coordinate selection.

desk verdict ICSpyLab is a new Python package for invariant coordinate selection that makes an existing method more accessible in standard ML stacks, provided the implementation and 'first' claim hold up. read the letter →

arxiv 2606.24521 v1 pith:OZ5445YF submitted 2026-06-23 stat.ME

Colombe Becquart This is my paper · ORCID
classification stat.ME
keywords invariantcoordinateselectiondimensionalityreductionscattermatricesjointdiagonalizationpythonpackageclusteringanomalydetection
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 introduces ICSpyLab to make invariant coordinate selection available as a standard tool in Python. ICS performs dimensionality reduction by jointly diagonalizing two scatter matrices to locate directions of extreme generalized kurtosis rather than variance alone. The package supplies multiple scatter matrices, several joint-diagonalization algorithms, and component-selection rules, all wrapped in the common estimator interface used by machine-learning libraries. It includes documentation and reproducible examples so users can insert ICS into existing pipelines for clustering or outlier detection. The release under an open license removes the previous barrier that kept the method outside routine Python workflows.

What carries the argument

Joint diagonalization of two scatter matrices to extract invariant coordinates ordered by generalized kurtosis.

What would settle it

An existing Python library that already supplies the same scatter matrices, joint-diagonalization routines, and selection criteria, or a side-by-side numerical check showing that ICSpyLab outputs differ from published ICS results on standard test data.

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Extended reading notes

Core claim

ICSpyLab is presented as the first Python package that implements invariant coordinate selection through a collection of scatter matrices, algorithms for computing invariant components via joint diagonalization, and criteria for choosing which components to retain, all exposed through a standard estimator interface compatible with machine-learning pipelines.

Load-bearing premise

No prior dedicated Python package already performs the full ICS procedure, and the released code reproduces the joint-diagonalization and selection steps described in the existing ICS literature.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 0 minor

Summary. The manuscript introduces ICSpyLab, a Python package for invariant coordinate selection (ICS) based on joint diagonalization of two scatter matrices. It positions the package as the first dedicated Python implementation, offering a collection of scatter matrices, multiple algorithms for invariant components, component-selection criteria, a scikit-learn-compatible estimator interface, detailed documentation, and reproducible examples. The package is released under the MIT license and hosted on GitHub.

Significance. If the implementation is correct and the novelty claim holds, ICSpyLab would enable broader integration of ICS into machine-learning pipelines for clustering and anomaly detection, providing a kurtosis-based alternative to variance-driven methods such as PCA. The use of a standard estimator interface and inclusion of reproducible examples are explicit strengths that support usability and verifiability of the software.

major comments (2)
  1. [Abstract] Abstract: The claim that 'no dedicated Python implementation of ICS is currently available' is asserted without any description of the search protocol, repositories examined (PyPI, GitHub, scikit-learn ecosystem), or cutoff date. This factual premise is load-bearing for the paper's central positioning of ICSpyLab as a novel contribution.
  2. [Implementation / Methods] The manuscript provides no verification (e.g., benchmark comparisons or reproduction of known ICS results on standard datasets) that the implemented joint diagonalization and component-selection steps correctly reproduce the algorithms described in the ICS literature. This is required to substantiate the claim of faithful implementation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments. We address each major comment below and outline revisions to improve the manuscript's transparency and verifiability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that 'no dedicated Python implementation of ICS is currently available' is asserted without any description of the search protocol, repositories examined (PyPI, GitHub, scikit-learn ecosystem), or cutoff date. This factual premise is load-bearing for the paper's central positioning of ICSpyLab as a novel contribution.

    Authors: We acknowledge that the manuscript does not describe the search protocol supporting the novelty claim. We will revise the abstract to include a concise description of the search methodology (repositories examined, search terms, and cutoff date) and add a short methods paragraph detailing this process to substantiate the positioning of ICSpyLab. revision: yes

  2. Referee: [Implementation / Methods] The manuscript provides no verification (e.g., benchmark comparisons or reproduction of known ICS results on standard datasets) that the implemented joint diagonalization and component-selection steps correctly reproduce the algorithms described in the ICS literature. This is required to substantiate the claim of faithful implementation.

    Authors: We agree that explicit verification is necessary to confirm faithful implementation. We will add a new verification subsection (or appendix) presenting benchmark comparisons and reproductions of known ICS results on standard datasets from the literature. This will demonstrate that the joint diagonalization and selection steps match the described algorithms, and we will reference corresponding tests in the package repository. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

Software release paper contains no derivation chain or fitted predictions

full rationale

The manuscript is a package announcement describing ICSpyLab's features and interface. No equations, predictions, component derivations, or parameter-fitting steps appear in the abstract or described content. The claim of being the 'first' dedicated Python implementation is a factual assertion about prior software availability rather than a self-referential reduction of any result to its own inputs. No self-citations, ansatzes, or uniqueness theorems are invoked. The paper is self-contained as a software description with no load-bearing mathematical argument that could exhibit circularity.

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

No free parameters, axioms, or invented entities are introduced; the work is an implementation of a pre-existing statistical procedure.

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Cite this review

Pith. "Pith review of ICSpyLab: A Python package for invariant coordinate selection." pith.science (2026). https://pith.science/paper/OZ5445YF

@misc{pith2026260624521,
  author       = {Pith},
  title        = {Pith review of: ICSpyLab: A Python package for invariant coordinate selection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OZ5445YF}},
  note         = {Machine review of arXiv:2606.24521}
}
read the original abstract

Invariant coordinate selection (ICS) is a dimensionality reduction technique based on the joint diagonalization of two scatter matrices. While principal component analysis relies solely on variance, ICS seeks directions of maximal or minimal generalized kurtosis, making it a powerful alternative for clustering and anomaly detection. Despite its theoretical and practical relevance, no dedicated Python implementation of ICS is currently available, limiting its integration into modern machine-learning workflows. We introduce ICSpyLab, the first Python package implementing ICS. It provides a broad collection of scatter matrices, multiple algorithms for computing invariant components, and several component-selection criteria. Designed for both practitioners and researchers, ICSpyLab follows a standard estimator interface, facilitating its use within machine-learning pipelines while remaining flexible for methodological extensions. The documentation includes detailed explanations and reproducible examples. ICSpyLab is released under the MIT license and is openly available at: https://github.com/cbecquart/ICSpyLab.

Figures

Figures reproduced from arXiv: 2606.24521 by the authors.

Figure 1
Figure 1. Projections of the RANDU dataset: (a) invariant components computed via ICSpyLab revealing the hyperplane alignments, and (b) principal components. 4 Conclusion and Future Work ICSpyLab brings ICS to the Python environment through a unified and extensible implemen￾tation, making the method more accessible for practical applications and methodological research. Future development will focus on strengthening the colla… view at source ↗

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Reviewed June 25, 2026 · model on record in the stance chip above.