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Semi-supervised Stacked Label Consistent Autoencoder for Reconstruction and Analysis of Biomedical Signals
Anupriya Gogna, Angshul Majumdar, Rabab Ward
TL;DR
Biomedical signal reconstruction and classification have generally been treated separately, while time-critical monitoring makes slow iterative reconstruction a concern. This paper combines autoencoder reconstruction with a linear class-label map and semi-supervised training. The authors report improved reconstruction and classification results on ECG and EEG tasks, with faster reconstruction than compressed-sensing methods.
Problem
Prior biomedical signal reconstruction approaches assume retrospective analysis, although applications such as seizure monitoring require real-time analysis.
Source: §I · p. 1Method
A semi-supervised stacked autoencoder learns to reconstruct signals and, for labeled samples, maps an inner-layer representation linearly to class labels.
Source: §I · p. 2, B. Combined Classification and… · p. 5Results
The authors report that the method improves reconstruction over compressed-sensing methods and is faster, while augmented ECG classification results are best in accuracy and EEG reconstruction improves with unlabeled data.
Source: A. ECG arrhythmia classification and… · p. 7, B. EEG classification and reconstruction · p. 8Takeaways & Limitations
The authors conclude that a learned reconstruction approach can outperform designed methods when enough training samples are available, and can use labeled and unlabeled data for reconstruction and classification.
Source: §V · p. 8The learned approach requires enough training samples, and labeled data may not always be available.
Source: §V · p. 8
Abstract
from arXiv · showhide
In this work we propose an autoencoder based framework for simultaneous reconstruction and classification of biomedical signals. Previously these two tasks, reconstruction and classification were treated as separate problems. This is the first work to propose a combined framework to address the issue in a holistic fashion. Reconstruction techniques for biomedical signals for tele-monitoring are largely based on compressed sensing (CS) based method, these are designed techniques where the reconstruction formulation is based on some assumption regarding the signal. In this work, we propose a new paradigm for reconstruction we learn to reconstruct. An autoencoder can be trained for the same. But since the final goal is to analyze classify the signal we learn a linear classification map inside the autoencoder. The ensuing optimization problem is solved using the Split Bregman technique. Experiments have been carried out on reconstruction and classification of ECG arrhythmia classification and EEG seizure classification signals. Our proposed tool is capable of operating in a semi-supervised fashion. We show that our proposed method is better and more than an order magnitude faster in reconstruction than CS based methods; it is capable of real-time operation. Our method is also better than recently proposed classification methods. Significance: This is the first work offering an alternative to CS based reconstruction. It also shows that representation learning can yield better results than hand-crafted features for signal analysis.
I. INTRODUCTION
Biomedical tele-monitoring must support both signal reconstruction and analysis, yet prior reconstruction approaches assume retrospective analysis, which can be too slow for time-critical monitoring. The proposed autoencoder combines reconstruction with classification when labels are available, while also learning from unlabeled signals.
I. INTRODUCTION
- Biomedical tele-monitoring over body area networks can support health monitoring for elderly and differently abled people, including in areas with limited medical facilities.Signals such as ECG, EEG, and PPG are acquired and transmitted for manual or automated analysis.Source: §I · p. 1
- Compressed sensing reduces sensor-node computation to a matrix-vector product, but reconstructs signals at the base station using iterative methods.The introduction notes that communication is the largest energy sink in a body area network and that transform coding can be computationally expensive at sensor nodes.Source: §I · p. 1
- Prior CS reconstruction is too slow for time-critical biomedical monitoring because iterative recovery can take longer than the signal duration.Earlier approaches assumed retrospective analysis, limiting their suitability for real-time tasks such as seizure monitoring.Source: §I · p. 1
- Biomedical signal analysis typically targets classification, but the large training datasets required for deep learning are difficult to obtain in this domain.The introduction contrasts automatically learned features with commonly used hand-crafted or statistical features.Source: §I · p. 2
- The framework combines signal reconstruction and classification, using labeled samples for both tasks and unlabeled samples for reconstruction alone.The authors describe the approach as semi-supervised and intended to support automated analysis and manual monitoring of reconstructed signals.Source: §I · p. 2
A. Compressed Sensing based Reconstruction
The section surveys compressed-sensing approaches that recover biomedical signals from compressed measurements, often using sparsity assumptions. It also describes methods that attempt to exploit relationships among channels, while noting limitations in how some formulations model those relationships.
A. Compressed Sensing based Reconstruction
- Compressed sensing represents an EEG signal as compressed measurements and assumes sparsity in a transform domain to recover its coefficients.The measurements are formed by applying a projection matrix to the signal; recovery uses l1-norm minimization.Source: A. Compressed Sensing based… · p. 2
- A joint reconstruction formulation processes all channels together but is described as equivalent to reconstructing each channel separately, without exploiting cross-channel structure.The section contrasts this with later approaches that model common sparsity or low-rank structure across channels.Source: A. Compressed Sensing based… · p. 2
- A feature-transmission approach is limited to specific tasks such as seizure detection and cannot be generalized to other applications.It sends selected features instead of the full signal, but requires more computation than standard compressed sensing.Source: A. Compressed Sensing based… · p. 2
- Some EEG recovery methods exploit a shared sparsity pattern across channels, represented by a row-sparse coefficient matrix and recovered using l2,1-minimization.The outer l1-norm promotes selection of rows, while the inner l2-norm promotes dense solutions within selected rows.Source: A. Compressed Sensing based… · pp. 2–3
- Other channel-correlation approaches model stacked signals as low-rank matrices or learn a sparsifying basis from data.The section describes matrix completion for low-rank recovery and identifies blind compressive sensing as learning the basis rather than fixing one.Source: A. Compressed Sensing based… · p. 3
B. Autoencoder
An autoencoder maps inputs into a latent representation and decodes that representation back into data. The section also introduces stacked and regularized variants, alongside approaches for learning denoising or robust features.
B. Autoencoder
- An autoencoder encodes an input into a latent space and decodes the representation back into data.The basic formulation learns encoding and decoding weights by minimizing Euclidean reconstruction cost.Source: B. Autoencoder · p. 3
- The decoder maps latent features to the data space, with no sigmoid applied because the data space is assumed to be real-valued.The encoder may use a linear or nonlinear mapping.Source: B. Autoencoder · p. 3
- The basic autoencoder objective is non-convex, and deep or stacked autoencoders add multiple hidden layers.The section says weights are often learned greedily, one layer at a time.Source: B. Autoencoder · p. 3
- Denoising autoencoders train on noisy inputs with clean outputs, while marginalized denoising autoencoders marginalize over noisy samples without augmenting the dataset.The section notes that features learned by stacked denoising autoencoders appear more robust.Source: B. Autoencoder · p. 3
- Autoencoder regularization may encourage sparsity or use Jacobian weight decay, and a group-sparse variant applies l2,1 regularization by class.The group-sparse approach seeks similar sparsity signatures within each class.Source: B. Autoencoder · p. 3
III. PROPOSED APPROACH
The proposed label-consistent autoencoder is developed in two stages: first explain signal recovery with autoencoders, then add a label-consistency term to complete the formulation.
III. PROPOSED APPROACH
- The proposed approach first motivates autoencoder-based signal recovery, then adds a label-consistency term to complete the formulation.The section divides its explanation into those two parts.Source: §III · p. 4
A. Reconstruction
The section frames reconstruction as learning an inverse mapping rather than relying on iterative compressed-sensing recovery. It trains an autoencoder on noisy inverse estimates to produce cleaner signals.
A. Reconstruction
- OMP recovers a sparse solution by detecting one nonzero support position at a time and estimating its value.It updates a residual after estimating values at the selected support positions.Source: A. Reconstruction · p. 4
- Compressed-sensing recovery is nonlinear and iterative, making it unsuitable for the paper’s real-time reconstruction setting.The authors contrast designing an inversion technique with learning to reconstruct.Source: A. Reconstruction · p. 4
- A poor man’s inverse provides noisy versions of the solution that can serve as autoencoder training inputs.The autoencoder’s denoising role is presented as an alternative to progressively removing noise through soft-thresholding.Source: A. Reconstruction · p. 4
- Autoencoders learn a mapping from noisy inverse estimates to clean signals, using paired noisy inputs and clean outputs during training.At inference, a single-layer autoencoder requires two matrix-vector products.Source: A. Reconstruction · p. 4
B. Combined Classification and Reconstruction
The paper proposes an autoencoder that reconstructs signals while also mapping its innermost-layer features to class targets. Its semi-supervised formulation uses labels when available and still trains reconstruction on unlabeled samples.
B. Combined Classification and Reconstruction
- A conventional autoencoder cannot classify, while attaching a softmax classifier after training prevents the resulting model from reconstructing.The paper therefore motivates a model that performs both tasks.Source: B. Combined Classification and… · p. 5
- The proposed two-layer stacked autoencoder learns a linear map from innermost-layer features to targets as its label-consistency criterion.Fig. 3 is identified as the proposed Label Consistent Autoencoder.Source: B. Combined Classification and… · p. 5, Figure 3 · p. 5
- The semi-supervised formulation uses labeled samples for the target map and unlabeled samples for reconstruction, and the authors solve it with Split Bregman.The passage identifies training samples, targets, and the linear map as X, T, and D, respectively.Source: B. Combined Classification and… · p. 5
C. Derivation
The derivation applies variable splitting and Split Bregman relaxation to the semi-supervised objective. It breaks the resulting optimization into subproblems, many of which are recast as least-squares problems.
C. Derivation
- Split Bregman is applied through successive substitutions that introduce proxy variables for the network mappings.The proxy variables include supervised and unsupervised parts.Source: C. Derivation · p. 5
- The augmented Lagrangian relaxation variable is updated to adjust equality between variables and proxies as they converge.The authors contrast this automatic adjustment with heuristically increasing the penalty parameter.Source: C. Derivation · pp. 5–6
- The formulation is segregated into subproblems, with several recast as linear least-squares problems solvable analytically.The text identifies P1–P3 as analytically solvable and describes least-squares reformulations for other subproblems.Source: C. Derivation · pp. 5–6
- Iterations stop when the objective has no significant successive change or when a fixed iteration count is reached.The implementation also reports using hyperparameters μ1 = μ2 = μ = 0.01.Source: C. Derivation · p. 6
A. ECG arrhythmia classification and reconstruction
The ECG experiments assess reconstruction and arrhythmia classification, including whether unlabeled data improves the proposed method. The reported results show faster, more accurate reconstruction than compressed-sensing methods and strong classification accuracy with augmentation.
ECG experimental setup
- The experiments use MIT-BIH arrhythmia data with five AAMI beat classes, and a second condition adds European ST-T samples without class labels for semi-supervised learning.The European ST-T results are not reported in Table II to keep comparisons in sync.Source: A. ECG arrhythmia classification and… · pp. 6–7
- For preprocessing, MIT-BIH is down-sampled to 250 Hz and normalized; sparse F and Q classes are merged with V under the AAMI2 protocol.Training uses one-second, 250-point samples, with 125 outer-layer and 63 inner-layer nodes; test-sequence class assignment uses row averages and the maximum value.Source: A. ECG arrhythmia classification and… · p. 7
- The health-monitoring benchmark reconstructs compressed ECG with BSBL, then classifies it using methods based on hand-crafted features, including OPF, SVM, PNN, and ELM.The compared feature extraction approach is the one reported to yield the best results.Source: A. ECG arrhythmia classification and… · p. 7
ECG results
- About 0.3 seconds versus about 12 seconds for BSBL reconstructing 1-second signals, the proposed autoencoder is reported as more accurate and faster than required for real-time operation.Table II reports MIT-BIH results only, although the proposed method uses additional data; the authors say added data improves reconstruction.Source: A. ECG arrhythmia classification and… · p. 7, Table II · p. 7
- With augmentation, the proposed method achieves the best classification accuracy, although sensitivity and specificity are marginally low in a few cases.Table III results use reconstructed signals at 50% compression and are not directly comparable with, which uses ground-truth signals.Source: A. ECG arrhythmia classification and… · p. 7, Table III · p. 7
B. EEG classification and reconstruction
The EEG experiments evaluate reconstruction and five-class classification, with and without unlabeled-data augmentation. Augmentation substantially improves reconstruction and classification, while supervised-only training performs poorly.
EEG experimental setup
- The Bonn dataset contains five sets of 100 single-channel EEG segments, each 23.6 seconds long, and augmentation uses BCI competition data resampled to 128 Hz.The proposed model is evaluated with and without this unsupervised-data augmentation; reconstruction comparisons include compression to 25% and 50%, while classification uses 50%.Source: B. EEG classification and reconstruction · p. 8
- The study classifies all five Bonn EEG classes A–E, whereas cited prior work commonly treats seizure detection as binary classification,.Comparisons include EMD with SVM, Rational Discrete Short-Time Fourier transform with a neural network, and LPE with thresholding.Source: B. EEG classification and reconstruction · p. 8
EEG results
- With unsupervised-data augmentation, reconstruction improves dramatically over using only the test dataset and is reported to outperform sparsity-based methods; the proposed method takes 1.8 seconds versus about a minute for BSBL to reconstruct 23.6 seconds of data.The authors attribute poor reconstruction without augmentation to insufficient data for learning the mapping.Source: B. EEG classification and reconstruction · p. 8, Table IV · p. 8
- With augmentation, the proposed method achieves the best overall classification results; supervised-only training performs poorly, which the authors suggest may reflect autoencoder overfitting.The comparison uses reconstructed rather than ground-truth samples, and the authors note that reconstruction artifacts affect classification accuracy.Source: B. EEG classification and reconstruction · p. 8, Table V · p. 8
V. CONCLUSION
The framework combines learned reconstruction with a linear label map, addressing the gap between signal reconstruction and downstream analysis where reconstruction artifacts can impair classification. It accommodates labeled and unlabeled samples and solves its nonlinear architecture using Split Bregman.
V. CONCLUSION
- Reconstruction artifacts can corrupt signal peaks and troughs, reducing automated-analysis accuracy in methods dependent on hand-crafted features.Source: §V · p. 8
- Unlike designed compressed-sensing techniques, the learned reconstruction approach makes no assumptions about signal structure and is said to excel when enough training samples are available.Source: §V · p. 8
- The framework jointly learns to reconstruct signals and map labeled samples to class labels, while unlabeled samples contribute to reconstruction alone.The authors note that learning this structure requires a sizable portion of the data, while labeled data may not always be available.Source: §V · p. 8
- Split Bregman is used to solve the architecture because its nonlinearity prevents use of backpropagation.Source: §V · pp. 8–9
- The proposed semi-supervised stacked autoencoder can also serve as a classifier when reconstruction is unnecessary, with benchmark deep-learning evaluation left for future work.Source: §V · p. 9