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A New Computationally Efficient Algorithm to solve Feature Selection for Functional Data Classification in High-dimensional Spaces
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Proposes FSFC, a joint feature selection and classification method for multivariate longitudinal (functional) features with binary responses, combining functional principal component approximation with an adaptive Dual Augmented Lagrangian solver for a logistic-loss elastic-net-type objective.
Problem
Jointly selecting features and classifying binary responses from multivariate functional/longitudinal features in high-dimensional settings where the number of features can exceed the number of units, with limited data and computational cost concerns.
Approach
Approximates functional features by their first k functional principal components, then solves an adaptive group elastic-net logistic problem with a new adaptive DAL algorithm whose Newton step exploits sparsity (active-feature set) so cost depends on the number of active features rather than total features; includes a novel dual conjugate of the functional logistic loss.
Key results
- In simulations, FSFC achieves average test accuracy above 85% for p0=2,5,10 and solves p=2000 problems in under 10 seconds CPU time versus about 142-356 s for SVM and LSTM.
- Using FSFC as a preprocessing step improves test accuracy of r-SVM and r-LSTM relative to standard SVM and LSTM, especially when p is larger.
- On SHARE Experiment 1 (n=20 subjects), FSFC achieves the best median accuracy and boosts SVM and LSTM; selected features (e.g., doctor visits, gender, bmi) align with medical literature.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FSFC for feature screening and dimension reduction before classification | SVM and LSTM · Synthetic simulations, test set | classification accuracy | Helped |
| Use FSFC for feature screening and dimension reduction before classification | LSTM · SHARE Experiment 1 | test accuracy | Helped |
| Use FSFC for feature screening and dimension reduction before classification | LSTM · SHARE Experiment 2 | test accuracy | Helped |
| Use FSFC for feature screening and dimension reduction before classification | SVM · SHARE Experiment 2 | test accuracy | No clear effect |
| Replace functional curves with extracted summary attributes before classification | LSTM and SVM · Synthetic simulations | test accuracy | No clear effect |
| Replace functional curves with extracted summary attributes before classification | SVM · SHARE Experiment 2 | test accuracy | Helped |
| Use FSFC as the classifier instead of SVM or LSTM | FSFC · Synthetic simulations, test set | classification accuracy | Helped |
| Increase the number of active features | FSFC · Synthetic simulations | recall and precision | Hurt |
| Use five FPCs instead of other explored values of k | FSFC · Examined scenarios | classification outcomes | No clear effect |
Surprising findings
- Feature extraction (feLSTM/feSVM) did not improve LSTM and SVM accuracy in simulations while greatly increasing computation time.
Limitations
- Number of FPC components k must be identical across all features.
- Responses are binary categorical; extension to functional responses and multinomial classes left for future work.
- Categorical responses carry weak signal, so precision and test accuracy are limited in some scenarios.
Experimental setup
Datasets: synthetic Gaussian process functional data (Matern covariance) SHARE (EasySHARE)
Benchmarks: synthetic functional classification simulations SHARE chronic disease classification
Metrics: classification accuracy recall precision CPU time
Baselines: SVM LSTM r-SVM r-LSTM feSVM feLSTM
Builds on: Dual Augmented Lagrangian (DAL) adaptive LASSO Elastic Net functional principal components
Closest papers by meaning
- Feature selection in functional data classification with recursive maxima hunting (NeurIPS 2016 · similarity 0.86)
- A Highly-Efficient Group Elastic Net Algorithm with an Application to Function-On-Scalar Regression (NeurIPS 2021 · similarity 0.84)
- Contrastive Functional Principal Component Analysis (AAAI 2025 · similarity 0.82)
- Feature Selection for Latent Factor Models (CVPR 2025 · similarity 0.80)
- SAND: One-Shot Feature Selection with Additive Noise Distortion (ICML 2025 · similarity 0.80)
- Contextual Feature Selection with Conditional Stochastic Gates (ICML 2024 · similarity 0.79)
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