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arxiv: 2604.12483 · v1 · submitted 2026-04-14 · 💻 cs.SD · cs.AI

Elastic Net Regularization and Gabor Dictionary for Classification of Heart Sound Signals using Deep Learning

Mahmoud Fakhry , Ascensi\'on Gallardo-Antol\'in This is my paper

Pith reviewed 2026-05-10 14:31 UTC · model grok-4.3

classification 💻 cs.SD cs.AI
keywords heart sound signalsGabor dictionaryelastic net regularizationdeep learningtime-frequency featuresclassificationvalvular conditionsCNN LSTM
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The pith

Feature matrices from elastic net fits to high-time low-frequency Gabor atoms let deep networks classify five heart valvular conditions at 98.95 percent accuracy.

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

The paper establishes that carefully choosing the time and frequency resolution of Gabor atoms along with elastic net regularization produces sparse time-frequency feature matrices from heart sound signals. These matrices, when used as input to specific deep learning architectures, enable high-accuracy classification of five different heart valve conditions. A sympathetic reader would care because this method offers a way to extract meaningful representations that improve automated analysis of heart sounds, which could aid in non-invasive diagnosis. The authors test various combinations of resolution parameters and regularization, along with two network designs and two training algorithms, to identify the setup that delivers the best results on their database.

Core claim

By fitting heart sound signals to an overcomplete Gabor dictionary using elastic net regularization and selecting atoms with high time resolution and low frequency resolution while imposing sparsity, the resulting feature matrices allow a deep learning network with 1D and 2D convolutional layers followed by an LSTM, trained with the ADAM optimizer, to achieve 98.95% accuracy in distinguishing five heart valvular conditions.

What carries the argument

The elastic-net-regularized linear models fitted to the Gabor dictionary, which generate the sparse time-frequency feature matrices used as inputs to the classifiers.

If this is right

  • The combination of high-time low-frequency resolution and sparsity leads to optimal feature matrices for classification.
  • The second deep learning architecture trained with ADAM achieves the highest accuracy of 98.95%.
  • Different resolution and regularization settings affect the classification performance, with the best ones identified through experimentation.
  • The feature matrices support effective discrimination among the five specific valvular conditions.

Where Pith is reading between the lines

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

  • This approach to generating sparse time-frequency features might apply to classifying other types of audio signals in medical or environmental monitoring.
  • If the optimal parameters generalize, the method could support real-time analysis in clinical settings with limited computational resources due to sparsity.
  • The use of elastic net could provide a balance between feature selection and grouping that benefits signal representation in noisy environments.

Load-bearing premise

The resolution and regularization parameters that maximize performance on this particular database will also produce good feature matrices for heart sound recordings from different patients or under varying conditions.

What would settle it

If the same feature extraction and network, when applied to a new collection of heart sound signals recorded with different equipment or from unseen patients, results in accuracy substantially below 98 percent, that would show the claimed optimality does not hold generally.

Figures

Figures reproduced from arXiv: 2604.12483 by Ascensi\'on Gallardo-Antol\'in, Mahmoud Fakhry.

Figure 1
Figure 1. Figure 1: Plots of heart sound signals and their corresponding Fourier transforms and [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the proposed method. non-zero entries in the vector a. This modeling allows us to acquire the most informative set of atoms. However, this depends on the construction of a good analysis dictionary and the use of an efficient regularization technique. The solution to the problem in Equation (1) was largely tackled using greedy matching. This is done by iteratively computing the coefficient vect… view at source ↗
Figure 3
Figure 3. Figure 3: Time and frequency representations of atoms for [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Approximation error measured as the average energy of all residuals [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Average energy ∥aj,α∥ 2 2 , calculated for all the recordings of the dataset [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average number of atoms corresponding to the number of non-zero entries in [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Three different transformation functions for the calculation of features. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Time-frequency feature matrices for PCG signals of five conditions. Each matrix [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: CNN-LSTM network consisting of 1D and 2D CNN, and LSTM layers. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average classification accuracy. Feature matrices used to train and evaluate [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The confusion matrix of the five heart valvular conditions for [PITH_FULL_IMAGE:figures/full_fig_p029_11.png] view at source ↗
read the original abstract

In this article, we propose the optimization of the resolution of time-frequency atoms and the regularization of fitting models to obtain better representations of heart sound signals. This is done by evaluating the classification performance of deep learning (DL) networks in discriminating five heart valvular conditions based on a new class of time-frequency feature matrices derived from the fitting models. We inspect several combinations of resolution and regularization, and the optimal one is that provides the highest performance. To this end, a fitting model is obtained based on a heart sound signal and an overcomplete dictionary of Gabor atoms using elastic net regularization of linear models. We consider two different DL architectures, the first mainly consisting of a 1D convolutional neural network (CNN) layer and a long short-term memory (LSTM) layer, while the second is composed of 1D and 2D CNN layers followed by an LSTM layer. The networks are trained with two algorithms, namely stochastic gradient descent with momentum (SGDM) and adaptive moment (ADAM). Extensive experimentation has been conducted using a database containing heart sound signals of five heart valvular conditions. The best classification accuracy of $98.95\%$ is achieved with the second architecture when trained with ADAM and feature matrices derived from optimal models obtained with a Gabor dictionary consisting of atoms with high-time low-frequency resolution and imposing sparsity on the models.

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 presents a method for classifying heart sound signals into five valvular conditions by deriving time-frequency feature matrices from elastic-net regularized linear fits of the signals to an overcomplete Gabor dictionary. The resolution parameters of the Gabor atoms and the elastic-net regularization strength are optimized by selecting the combination that maximizes the downstream performance of two deep learning architectures (one with 1D CNN+LSTM, the other with 1D/2D CNN+LSTM). The networks are trained using SGDM or ADAM, and the highest reported accuracy is 98.95% for the second architecture with ADAM on features from high-time low-frequency resolution atoms with sparsity.

Significance. If validated properly, the approach offers a principled way to incorporate time-frequency dictionary learning with regularization into DL pipelines for bio-signal classification, potentially yielding more interpretable features than raw spectrograms. The explicit optimization of atom resolution and sparsity level is a strength, as is the comparison of two DL architectures and optimizers. However, without details on data partitioning and validation, the significance of the numerical result remains unclear.

major comments (2)
  1. Abstract: The central performance claim of 98.95% accuracy is presented without any information on the size of the database, number of patients or recordings per class, the train-test split methodology (e.g., patient-wise disjoint splits), cross-validation procedure, or statistical tests for significance. This information is essential to evaluate whether the hyperparameter search over Gabor resolution and elastic-net parameters was conducted in a nested, unbiased manner or risks overfitting to the specific dataset.
  2. Abstract and results description: The selection of 'optimal' Gabor dictionary (high-time low-frequency resolution) and sparsity level is described as the one providing highest performance, but no description is given of how many combinations were tested, whether an independent validation set was used for selection, or if the final accuracy is on a held-out test set after all tuning. This directly impacts the reliability of the reported figure.
minor comments (1)
  1. Abstract: The phrase 'imposing sparsity on the models' could be clarified by explicitly stating the elastic-net mixing parameter or the L1/L2 weights used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments highlighting the need for greater transparency in reporting experimental details. We have revised the manuscript to address these concerns by expanding the abstract and relevant sections with the required information on the dataset, partitioning, validation, and hyperparameter selection process.

read point-by-point responses

  1. Referee: Abstract: The central performance claim of 98.95% accuracy is presented without any information on the size of the database, number of patients or recordings per class, the train-test split methodology (e.g., patient-wise disjoint splits), cross-validation procedure, or statistical tests for significance. This information is essential to evaluate whether the hyperparameter search over Gabor resolution and elastic-net parameters was conducted in a nested, unbiased manner or risks overfitting to the specific dataset.

    Authors: We agree that these details are essential and were insufficiently highlighted in the original abstract. The revised manuscript now includes this information in the abstract and methods: database composition (number of patients and recordings per class), patient-wise disjoint train-test splits to prevent data leakage, the cross-validation procedure, and statistical significance tests. We also explicitly describe that the search over Gabor resolution and elastic-net parameters was performed via nested cross-validation, with the outer loop providing unbiased performance estimates on held-out data. revision: yes

  2. Referee: Abstract and results description: The selection of 'optimal' Gabor dictionary (high-time low-frequency resolution) and sparsity level is described as the one providing highest performance, but no description is given of how many combinations were tested, whether an independent validation set was used for selection, or if the final accuracy is on a held-out test set after all tuning. This directly impacts the reliability of the reported figure.

    Authors: We acknowledge that the original text did not sufficiently detail the selection process. In the revision, we specify the number of resolution and regularization combinations evaluated, confirm the use of a separate independent validation set for choosing the optimal Gabor dictionary and sparsity level, and state that the final 98.95% accuracy is measured on a completely held-out test set after all tuning and selection. This structure ensures the reported performance reflects generalization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical accuracy is independent measurement

full rationale

The paper's derivation consists of constructing time-frequency feature matrices via Gabor dictionary fitting with elastic-net regularization, followed by training two DL architectures and reporting classification accuracy on a five-class heart-sound database. The choice of optimal resolution and sparsity level is made by inspecting performance, but the headline 98.95% figure is a direct empirical evaluation on held-out data rather than a quantity that reduces by construction to the fitted parameters or prior choices. No self-definitional equations, no fitted inputs renamed as predictions, and no load-bearing self-citations appear in the text. The chain remains self-contained against the external benchmark of measured classification performance.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical success of a tuned sparse representation pipeline; free parameters are the regularization weights and atom resolutions chosen by validation performance, while the key domain assumption is that linear combinations of Gabor atoms capture diagnostically relevant structure in heart sounds.

free parameters (2)
  • Elastic net regularization parameters
    Lambda and alpha (or equivalent) control the sparsity-accuracy trade-off and are selected to maximize downstream classification accuracy.
  • Gabor atom resolution parameters
    Time and frequency resolution settings for the dictionary atoms are inspected in combinations and the best-performing pair is retained.
axioms (1)
  • domain assumption Heart sound signals admit useful sparse linear representations in an overcomplete Gabor dictionary
    The fitting model and subsequent feature extraction presuppose that this dictionary is appropriate for the signals.

pith-pipeline@v0.9.0 · 5547 in / 1381 out tokens · 25352 ms · 2026-05-10T14:31:35.954884+00:00 · methodology

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Reference graph

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