Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 7 (1), 16281

Recursive Exponentially Weighted N-way Partial Least Squares Regression With Recursive-Validation of Hyper-Parameters in Brain-Computer Interface Applications

Affiliations

Recursive Exponentially Weighted N-way Partial Least Squares Regression With Recursive-Validation of Hyper-Parameters in Brain-Computer Interface Applications

Andrey Eliseyev et al. Sci Rep.

Abstract

A tensor-input/tensor-output Recursive Exponentially Weighted N-Way Partial Least Squares (REW-NPLS) regression algorithm is proposed for high dimension multi-way (tensor) data treatment and adaptive modeling of complex processes in real-time. The method unites fast and efficient calculation schemes of the Recursive Exponentially Weighted PLS with the robustness of tensor-based approaches. Moreover, contrary to other multi-way recursive algorithms, no loss of information occurs in the REW-NPLS. In addition, the Recursive-Validation method for recursive estimation of the hyper-parameters is proposed instead of conventional cross-validation procedure. The approach was then compared to state-of-the-art methods. The efficiency of the methods was tested in electrocorticography (ECoG) and magnetoencephalography (MEG) datasets. The algorithms are implemented in software suitable for real-time operation. Although the Brain-Computer Interface applications are used to demonstrate the methods, the proposed approaches could be efficiently used in a wide range of tasks beyond neuroscience uniting complex multi-modal data structures, adaptive modeling, and real-time computational requirements.

Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1
The REW-NPLS scheme. When the new tensors of observation {X_t,Y_t} are available, their details are then combined with the previously captured covariance tensors {C_XXt1,C_XYt1}, and the set of projection vectors {wf,t11,,wf,t1n}f=1F with forgetting factor λ. Then the prediction model, represented by the regression coefficients B_t, is generated.
Figure 2
Figure 2
The Recursive-Validation scheme for the number of factors hyper-parameter (F) identification. When the new tensors of observation {X_t,Y_t} are available, the previously defined models {B_t11,,B_t1Fmax} are tested on the new data and resulted in {Y_^t1,,Y_^tFmax}. The prediction errors {etf}f=1Fmax are estimated considering the previous errors with the forgetting factor γ. The number of factors Ft=argminf{etf}f=1Fmax correspond to the minimal error at the current moment t; this is considered to be optimal for the current moment.
Figure 3
Figure 3
ECoG-based primate experiments. (A) 64 electrodes were implanted in the epidural space of the left hemisphere of two Japanese macaques denoted as monkey “B” and “C”. Ps: principal sulcus; As: arcuate sulcus; Cs: central sulcus; IPs: intraparietal sulcus. (B) The scheme of the experiment. The monkey is following the food with its right hand. Monkey’s ECoG activity is recorded simultaneously with 3D coordinates of the right wrist, elbow, and shoulder. (C) For each time t, to form the explanatory variable x_(t)15×10×64, the ECoG signal from 64 channels is mapped by the Continuous Wavelet Transform with 15 frequencies (10, 20, …, 150 Hz). Then, the absolute values of the wavelet coefficients are decimated 100 times along the temporal modality, i.e., 1000 points, representing 1 second; these are decimated to 10 points. The response variable y_(t)3×3 is formed from the corresponding 3D coordinates (x,y,z) of monkey’s wrist, elbow, and shoulder. The next epoch was taken with a time step of 100 ms. (D) Data tensors are split into non-overlapping training (70%) and test (30%) sub-tensors.
Figure 4
Figure 4
MEG-based experiments in human. (A) Elekta Neuromag electrodes scheme. (B) The scheme of the experiment. The subject voluntarily performs up/down movements of the index finger. For each time moment t, to form the explanatory variable x_(t)20×10×306, the MEG signal from 306 channels is mapped by the Continuous Wavelet Transform with 20 frequencies (5, 10, …, 100 Hz). Then, the absolute values of the wavelet coefficients are decimated 100 times along the temporal modality. The response variable y(t){0,1} is formed from the corresponded down/up position of the index finger at the moment t. The next epoch was taken with a time step of 100 ms.
Figure 5
Figure 5
Prediction accuracy and robustness to the factors number parameter (F). The maximal prediction accuracy is represented by the crosses in the figure and is almost equivalent for all the approaches. However, in comparison with vector-oriented methods (PLS, REW-PLS), the tensor-based approaches (NPLS, REW-NPLS) demonstrate better robustness to variability of F. Dotted lines represent the standard deviation of the corresponding correlations.
Figure 6
Figure 6
Comparison of the prediction correlation for REW-NPLS; the preliminary estimate of optimal number of factors (F=200) vs. the Recursive-Validation of the factors number. The size of each data-batch is equal to 10 seconds (100 epochs), and 70 batches are available. The data are averaged through 20 recordings and 9 coordinates. The maximum number of factors Fmax=300 is taken in the Recursive-Validation approach. (A) The method with Recursive-Validation of F* significantly outperforms the one with optimal F=200 until 25 batches are analyzed. The difference then became insignificant (ANOVA test, significance level α=0.05). (B) When 70 batches are treated, the dynamically estimated number of factors is FRV=57F=200, whereas the difference in prediction accuracy is insignificant. Dotted lines represent standard deviations.
Figure 7
Figure 7
The influences on the predictive models of the elements in frequency, temporal, and spatial modalities identified by the REW-NPLS (F=200) on the complete training set, and the REW-NPLS with Recursive-Validation of F*. The batch numbers 10, 25, 40, 55, and 70 (complete dataset) demonstrate the model’s variability over time. The modalities influences are averaged over 20 recordings and 9 coordinates. Dotted lines represent the standard deviation of the corresponding results.
Figure 8
Figure 8
The influences on the predictive models of the elements in frequency, temporal, and spatial modalities identified by the REW-NPLS with Recursive-Validation of F* on the complete training set. The modalities influence was averaged over 8 recordings for the left- and right fingers. Dotted lines represent the standard deviation of the corresponding results.
Figure 9
Figure 9
Implementation scheme of the real-time operating system. The control command for an external device is generated every 100 ms by the Model Application Block. The model is adjusted every 10 seconds by the Model Adaptation Block based on the REW-NPLS algorithm with Recursive-Validation of the factor number.

Similar articles

See all similar articles

Cited by 1 PubMed Central articles

References

    1. Wolpaw JR, Birbaumer N, McFarland DJ, Pfurtscheller G, Vaughan TM. Brain-computer interfaces for communication and control. Clinical neurophysiology: official journal of the International Federation of Clinical Neurophysiology. 2002;113:767–791. doi: 10.1016/S1388-2457(02)00057-3. - DOI - PubMed
    1. Donoghue JP. Bridging the brain to the world: a perspective on neural interface systems. Neuron. 2008;60:511–521. doi: 10.1016/j.neuron.2008.10.037. - DOI - PubMed
    1. Benabid AL, et al. Deep brain stimulation: BCI at large, where are we going to? Progress in brain research. 2011;194:71–82. doi: 10.1016/B978-0-444-53815-4.00016-9. - DOI - PubMed
    1. Pfurtscheller, G. et al. The hybrid BCI. Frontiers in neuroscience4 (2010).
    1. Bouton CE, et al. Restoring cortical control of functional movement in a human with quadriplegia. Nature. 2016;533:247–250. doi: 10.1038/nature17435. - DOI - PubMed

Publication types

Feedback