MATLAB implementation of Latent Structure Influence Models (LSIMs) with applications to EEG & ECoG processing.
This repository contains the code and implementation of the algorithms described in the paper "Tractable Maximum Likelihood Estimation for Latent Structure Influence Models With Applications to EEG & ECoG Processing." LSIMs provide a powerful framework for modeling multi-channel brain signals while addressing the limitations of conventional Hidden Markov Models (HMMs) and Coupled Hidden Markov Models (CHMMs).
Brain signals are nonlinear and nonstationary time series, which provide information about spatiotemporal patterns of electrical activity in the brain. CHMMs are suitable tools for modeling multi-channel time-series dependent on both time and space, but state-space parameters grow exponentially with the number of channels. To cope with this limitation, we consider the influence model as the interaction of hidden Markov chains called Latent Structure Influence Models (LSIMs).
LSIMs are capable of detecting nonlinearity and nonstationarity, making them well suited for multi-channel brain signals. We apply LSIMs to capture the spatial and temporal dynamics in multi-channel EEG/ECoG signals. This work extends the scope of the re-estimation algorithm from HMMs to LSIMs and proves that the re-estimation algorithm of LSIMs will converge to stationary points corresponding to Kullback-Leibler divergence.
Our approach develops a new auxiliary function using the influence model and a mixture of strictly log-concave or elliptically symmetric densities, supported by theories from Baum, Liporace, Dempster, and Juang. We provide closed-form expressions for re-estimation formulas using tractable marginal forward-backward parameters.
This repository is organized into the following main components:
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01 convergence_testing_bias_analysis/: Code for testing the convergence of the re-estimation formulas on simulated datasets.
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02 ECoG_Lorenz_modelling/: Implementation of LSIMs for modeling embedded Lorenz systems and ECoG recordings, with comparisons to HMMs and CHMMs using AIC and BIC metrics.
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03 classification_results/: Tools and results for comparing the classification performance of LSIMs against HMMs, SVMs, and CHMMs on 2-class simulated CHMMs.
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04 BED verification/: Implementation of LSIM-based method for EEG biometric verification on the BED dataset, showing improved AUC values compared to existing HMM-based methods.
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LSIMs perform better than HMMs and CHMMs in modeling embedded Lorenz systems and ECoG recordings based on AIC and BIC metrics.
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LSIMs are more reliable classifiers than HMMs, SVMs, and CHMMs in 2-class simulated CHMMs.
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For EEG biometric verification, the LSIM-based method improves AUC values by approximately 6.8% and decreases the standard deviation of AUC values from 5.4% to 3.3% compared to the existing HMM-based method across all conditions on the BED dataset.
If you use this code in your research, please cite our paper:
Karimi, S., & Shamsollahi, M. B. (2023). Tractable maximum likelihood estimation for latent structure influence models with applications to eeg & ecog processing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(8), 10466-10477.
This project is licensed under the terms of the included LICENSE file.