Functional Brain Networks Discovery Using Dictionary Learning with Correlated Sparsity

Mohsen Joneidi

arxiv: 1907.03929 · v2 · pith:GZ2Z4MI3new · submitted 2019-07-09 · 📡 eess.SP · eess.IV· q-bio.NC· stat.AP

Functional Brain Networks Discovery Using Dictionary Learning with Correlated Sparsity

Mohsen Joneidi This is my paper

Pith reviewed 2026-05-25 00:34 UTC · model grok-4.3

classification 📡 eess.SP eess.IVq-bio.NCstat.AP

keywords functional brain networksdictionary learningcorrelated sparsityfMRIsparse representationnetwork dependencies

0 comments

The pith

Dictionary learning with correlated sparsity models dependencies among functional brain networks from fMRI data.

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

The paper introduces an alternative to PCA, ICA, and standard dictionary learning for constructing functional brain networks from fMRI data. Prior approaches treat the networks as independent and therefore miss the dependencies that exist between them. The new formulation imposes correlated sparsity patterns on the dictionary coefficients to capture those dependencies explicitly. Two solution approaches are developed to solve the resulting optimization problem. A sympathetic reader would care because this change directly addresses a stated limitation in how brain activity patterns have been extracted so far.

Core claim

The authors formulate the task of discovering functional brain networks as a dictionary learning problem in which dependencies between networks are encoded by correlated sparsity patterns on the coefficients, and they supply two effective algorithms to solve the resulting problem.

What carries the argument

Dictionary learning problem with correlated sparsity patterns imposed on the coefficients

If this is right

The method supplies an explicit mechanism for dependencies that conventional sparse coding omits.
Two concrete algorithms make the correlated formulation computationally tractable.
The resulting networks are positioned as a direct replacement for those produced by PCA or ICA.

Where Pith is reading between the lines

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

The approach could be tested on synthetic fMRI-like data where ground-truth network correlations are known in advance.
It might extend naturally to other multivariate signals where component dependencies matter, such as EEG or financial time series.
If the correlation term improves downstream tasks like classification of brain states, that would supply an indirect test of the modeling choice.

Load-bearing premise

Real functional brain networks exhibit dependencies that are well captured by imposing correlated sparsity patterns on the dictionary coefficients.

What would settle it

Compare networks recovered on the same fMRI datasets with and without the correlation term and check whether the correlated version aligns more closely with known functional or anatomical connections on held-out validation sets.

Figures

Figures reproduced from arXiv: 1907.03929 by Mohsen Joneidi.

**Figure 2.** Figure 2: Soft threshold versus hard threshold. A. Synthesized fMRI Data This experiment examines the performance of proposed methods in separating the sources of some artificially generated fMRI data. Some 3D images are considered as functional brain networks and they are modulated by some principle time series and an additive Gaussian noise is added to generate the final synthetic data [PITH_FULL_IMAGE:figures/… view at source ↗

**Figure 3.** Figure 3: Illustration of synthetic fMRI data generation [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Performance of the different DL algorithms over iterations [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Performance of the proposed algorithm while it observes a portion of the whole data. B. Real fMRI A single subject analysis is performed to compare the traditional dictionary learning with the modified one. Resting-state fMRI data are downloaded from a free access online dataset1 . SPM 12 Matlab toolbox is used to perform the needed pre-processing such as normalization and registration. The spatial resolut… view at source ↗

**Figure 6.** Figure 6: The segmentation results in two slices of brain using pure sparsity constraint (the upper image) versus proposed sparsity. The proposed sparsity is solved using two proposed algorithms. The middle one is the Modified-KSVD and the bottom image is resulted by the EN-KSVD [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Applying brain segmentation on coefficients extracted by the K-SVD and the proposed dictionary learning. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

read the original abstract

Analysis of data from functional magnetic resonance imaging (fMRI) results in constructing functional brain networks. Principal component analysis (PCA) and independent component analysis (ICA) are widely used to generate functional brain networks. Moreover, dictionary learning and sparse representation provide some latent patterns that rules brain activities and they can be interpreted as brain networks. However, these methods lack modeling dependencies of the discovered networks. In this study an alternative to these conventional methods is presented in which dependencies of the networks are considered via correlated sparsity patterns. We formulate this challenge as a new dictionary learning problem and propose two approaches to solve the problem effectively.

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.

Desk Editor's Note private letter to a colleague

The paper adds correlated sparsity to dictionary learning to capture dependencies among fMRI networks, but the abstract supplies no equations, experiments, or justification for why this inductive bias fits real brain data.

read the letter

The core idea is a dictionary learning formulation that imposes correlated sparsity on the coefficients so that discovered functional networks can share dependencies instead of being treated as independent. This is presented as an improvement over PCA, ICA, and standard sparse coding, which the abstract says ignore those dependencies. Two solution approaches are mentioned but not described. That is the actual new piece: the explicit modeling choice inside the DL objective. It earns credit for naming a limitation that many practitioners have noticed in network extraction work. The writing is straightforward about what prior methods miss. Beyond that, the visible material is thin. No equations appear, no synthetic or real-data results are shown, and there is no argument or test showing that correlated supports in the codes are the right statistical structure for brain-network dependence rather than correlations among atoms, temporal structure, or spatial overlap. The central modeling assumption therefore sits unexamined. If the full paper contains clean derivations and controlled experiments that close this gap, the contribution becomes more substantial; on the abstract alone it remains a proposal. The work is aimed at people already working on sparse methods for neuroimaging who want a concrete variant to try or extend. It is not positioned as a breakthrough that changes how fMRI is analyzed at scale. A serious editor should send it to referees so the math and the empirical checks can be evaluated properly; the idea is specific enough to be worth that step even if the current evidence is limited.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that PCA, ICA, and standard dictionary learning fail to model dependencies among functional brain networks extracted from fMRI data. It proposes a new dictionary learning formulation that incorporates correlated sparsity patterns on the dictionary coefficients to capture these dependencies and introduces two effective solution approaches.

Significance. If the formulation and solutions prove effective, the work could improve the biological plausibility of discovered brain networks by explicitly modeling inter-network dependencies, a gap in conventional methods. However, the abstract supplies neither the mathematical details of the new problem nor any validation results, so the actual significance cannot be determined from the provided text.

major comments (2)

[Abstract] Abstract, paragraph describing the limitation of prior methods: the assumption that real functional brain networks exhibit dependencies that are well captured by imposing correlated sparsity patterns on the dictionary coefficients is presented without biological justification, synthetic validation, or comparison to alternative dependency structures (e.g., correlations among atoms or temporal dynamics). This modeling choice is load-bearing for the central claim.
[Abstract] Abstract: no equations, no description of the two solution approaches, and no validation results are supplied, making it impossible to check whether the math supports the stated claim that the new formulation remedies the limitation of prior methods.

minor comments (1)

[Abstract] The phrase 'provide some latent patterns that rules brain activities' contains a grammatical error ('rules' should be 'rule' or rephrased).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments. We respond point-by-point to the major comments below.

read point-by-point responses

Referee: [Abstract] Abstract, paragraph describing the limitation of prior methods: the assumption that real functional brain networks exhibit dependencies that are well captured by imposing correlated sparsity patterns on the dictionary coefficients is presented without biological justification, synthetic validation, or comparison to alternative dependency structures (e.g., correlations among atoms or temporal dynamics). This modeling choice is load-bearing for the central claim.

Authors: The manuscript introduction and methods sections provide biological motivation drawn from neuroscience literature on interdependent brain networks observed in fMRI studies. Synthetic experiments compare the correlated sparsity model against alternatives and ground-truth dependent networks. We will revise the abstract to include a brief clause referencing this motivation. revision: partial
Referee: [Abstract] Abstract: no equations, no description of the two solution approaches, and no validation results are supplied, making it impossible to check whether the math supports the stated claim that the new formulation remedies the limitation of prior methods.

Authors: Abstracts follow standard length and accessibility constraints that preclude equations or detailed results. The full manuscript defines the new dictionary learning objective, describes the two solution approaches in detail, and presents validation on synthetic data with induced dependencies plus real fMRI experiments. We do not plan to add equations to the abstract. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract formulates a new dictionary learning problem with correlated sparsity to address dependencies among brain networks, but supplies no equations, no fitted parameters renamed as predictions, and no self-citations that bear the central claim. The modeling choice stands as an independent inductive bias rather than a reduction to prior inputs by construction; the derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5629 in / 1021 out tokens · 18848 ms · 2026-05-25T00:34:04.871352+00:00 · methodology

discussion (0)

Reference graph

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Contribution of exploratory meth- ods to the investigation of extended large-scale brain networks in functional mri: methodologies, results, and challenges,

V . Perlbarg and G. Marrelec, “Contribution of exploratory meth- ods to the investigation of extended large-scale brain networks in functional mri: methodologies, results, and challenges,” Jour- nal of Biomedical Imaging , vol. 2008, p. 4, 2008

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Supervised dictionary learning for inferring concurrent brain networks,

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Sparse representation of whole- brain fmri signals for identiﬁcation of functional networks,

J. Lv, X. Jiang, X. Li, D. Zhu, H. Chen, T. Zhang, S. Zhang, X. Hu, J. Han, H. Huang et al., “Sparse representation of whole- brain fmri signals for identiﬁcation of functional networks,” Medical image analysis , vol. 20, no. 1, pp. 112–134, 2015

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Sparse dictionary learning of resting state fmri networks,

H. Eavani, R. Filipovych, C. Davatzikos, T. D. Satterthwaite, R. E. Gur, and R. C. Gur, “Sparse dictionary learning of resting state fmri networks,” in Pattern Recognition in NeuroImaging (PRNI), 2012 International Workshop on . IEEE, 2012, pp. 73–76

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D. Papo, M. Zanin, and J. Martin Buld ´u, “Reconstructing func- tional brain networks: have we got the basics right?” Frontiers in human neuroscience , vol. 8, p. 107, 2014

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[10] [10]

K-SVD: An algorithm for designing overcomplete dictionaries for sparse representa- tion,

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representa- tion,” IEEE Trans. on Signal Processing , vol. 54, no. 11, pp. 4311–4322, 2006

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Robust recovery of signals from a structured union of subspaces,

Y . C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” Information Theory, IEEE Transactions on, vol. 55, no. 11, pp. 5302–5316, 2009

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Detecting functional connectivity in the resting brain: a comparison between ica and cca,

L. Ma, B. Wang, X. Chen, and J. Xiong, “Detecting functional connectivity in the resting brain: a comparison between ica and cca,” Magnetic resonance imaging , vol. 25, no. 1, pp. 47–56, 2007

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Resting-state fmri: a review of methods and clinical applications,

M. H. Lee, C. D. Smyser, and J. S. Shimony, “Resting-state fmri: a review of methods and clinical applications,” American Journal of Neuroradiology , vol. 34, no. 10, pp. 1866–1872, 2013

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Sparse estimation automatically selects voxels relevant for the decoding of fmri activity patterns,

O. Yamashita, M.-a. Sato, T. Yoshioka, F. Tong, and Y . Kami- tani, “Sparse estimation automatically selects voxels relevant for the decoding of fmri activity patterns,” NeuroImage, vol. 42, no. 4, pp. 1414–1429, 2008

work page 2008

[15] [15]

K-lda: An algorithm for learning jointly over- complete and discriminative dictionaries,

J. Golmohammady, M. Joneidi, M. Sadeghi, M. Babaie-Zadeh, and C. Jutten, “K-lda: An algorithm for learning jointly over- complete and discriminative dictionaries,” in 2014 22nd Euro- pean Signal Processing Conference (EUSIPCO) . IEEE, 2014, pp. 775–779

work page 2014

[16] [16]

Matrix coherency graph: A tool for improving sparse coding performance,

M. Joneidi, A. Zaeemzadeh, N. Rahnavard, and M. B. Khalil- sarai, “Matrix coherency graph: A tool for improving sparse coding performance,” in 2015 International Conference on Sampling Theory and Applications (SampTA) . IEEE, 2015, pp. 168–172

work page 2015

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Fast and inco- herent dictionary learning algorithms with application to fmri,

V . Abolghasemi, S. Ferdowsi, and S. Sanei, “Fast and inco- herent dictionary learning algorithms with application to fmri,” Signal, Image and Video Processing , vol. 9, no. 1, pp. 147–158, 2015

work page 2015

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Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions,

J. O. Ogutu, T. Schulz-Streeck, and H.-P. Piepho, “Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions,” in BMC proceedings, vol. 6, no. Suppl 2. BioMed Central Ltd, 2012, p. S10

work page 2012

[19] [19]

Regression shrinkage and selection via the lasso,

R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society. Series B (Methodological), pp. 267–288, 1996

work page 1996

[20] [20]

The group lasso for logistic regression,

L. Meier, S. Van De Geer, and P. B ¨uhlmann, “The group lasso for logistic regression,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) , vol. 70, no. 1, pp. 53–71, 2008

work page 2008

[21] [21]

Least angle regression,

B. Efron, T. Hastie, I. Johnstone, R. Tibshirani et al. , “Least angle regression,” The Annals of statistics , vol. 32, no. 2, pp. 407–499, 2004

work page 2004

[22] [22]

Regularization and variable selection via the elastic net,

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) , vol. 67, no. 2, pp. 301–320, 2005

work page 2005

[23] [23]

Proximal algorithms,

N. Parikh and S. Boyd, “Proximal algorithms,” F oundations and Trends in Optimization , vol. 1, no. 3, pp. 123–231, 2014. Fig. 6: The segmentation results in two slices of brain using pure sparsity constraint (the upper image) versus proposed sparsity. The proposed sparsity is solved using two proposed algorithms. The middle one is the Modiﬁed-KSVD and th...

work page 2014