Brain-Computer Interface with Corrupted EEG Data: a Tensor Completion Approach

Abstract

Background / Introduction: One of the current issues in Brain-Computer Interface (BCI) is how to deal with noisy Electroencephalography (EEG) measurements organized as multidimensional datasets (tensors). On the other hand, recently, significant advances have been made in multidimensional signal completion algorithms that exploit tensor decomposition models to capture the intricate relationship among entries in a multidimensional signal. We propose to use tensor completion applied to EEG data for improving the classification performance in a motor imagery BCI system with corrupted measurements. Noisy measurements (electrode misconnections, subject movements, etc.) are considered as unknowns (missing samples) that are inferred from a tensor decomposition model (tensor completion). Methods: We evaluate the performance of four recently proposed tensor completion algorithms, CP-WOPT (Acar et al, 2011), 3DPB-TC (Caiafa et al, 2013), BCPF (Zhao et al, 2015) and HaLRT (Liu et al. ( 2013), plus a simple interpolation strategy, first with random missing entries and then with missing samples constrained to have a specific structure (random missing channels), which is a more realistic assumption in BCI applications. Results:We measured the ability of these algorithms to reconstruct the tensor from observed data.Then, we tested the classification accuracy of imagined movement in a BCI experiment with missing samples. We show that for random missing entries, all tensor completion algorithms can recover missing samples increasing the classification performance compared to a simple interpolation approach. For the random missing channels case, we show that tensor completion algorithms help to reconstruct missing channels, significantly improving the accuracy in the classification of motor imagery (MI), however, not at the same level as clean data. Summarizing, compared to the interpolation case, all tensor completion algorithms succeed to increase the classification performance by 7 -9% (LDA -SVD) for random missing entries and 15 -8% (LDA -SVD) for random missing channels.Conclusions: Tensor completion algorithms are useful in real BCI applications. The proposed strategy could allow using motor imagery BCI systems even when EEG data is highly affected by missing channels and/or samples, avoiding the need of new acquisitions in the calibration stage.

Different Approaches to SCADA Data Completion in Water Networks

“…For instance, the CP-Wopt is able to recover the correct underlying components from noisy data with up to 99% of missing data for third-order tensors; in contrast, two-way methods become unstable with missing data levels of only 25-40% [9]. However, for some applications, the recovery of missing data can be improved by using a specialized solution, such as in the presented case or the one in [43]. In the present work, in which the missing data were lost in bursts, combining an imputation method followed by a low-range tensor approximation with an ad-hoc offset correction to ensure continuity in the extremes of the missing burst produced a better performance over all the other tested completion methods.…”

Classification Analysis of Tensor-Based Recovered Missing EEG Data

“…Content may change prior to final publication. The notation ⟦ (1) , (2) , … , ( ) ⟧ defines a tensor of size ℝ 1 × 2 ×…× whose elements are given by:…”

“…In this paper, we focus on invasive EEG signals. Now-a-days, EEG signals are combined with machine learning algorithms to improve Brain-computer interface (BCI) [1]. BCI has many applications such as controlling prosthesis [2][3][4][5], navigating robots [6][7][8][9], controlling home automation system [10], controlling mobile phone applications [11], controlling movements of wheelchair [12][13][14][15] and speech recognition system [16].…”

Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets

“…This can occur due to the lack of connection between wireless EEG headset and the computer, or because artifacts appear due to muscle movements, eye movements or electromagnetic interference, among others. Since EEG measurements can be organized as multidimensional datasets, in [57] a tensor completion approach was proposed, which consists in fitting a tensor decomposition model to the available clean measurements and then infer the noisy or missing parts based on those models (see Figure 2a). The advantage of using tensor methods, compared to classical interpolation algorithms, lies in the ability of these models to handle multidimensional information, in other words, they can capture the intricate relationship among entries in a multidimensional signal.…”

“…For example, to infer a missing entry in an EEG data tensor, these methods can efficiently exploit the available information in other channels, time samples and trials. Several tensor decomposition models and tensor completion algorithms were compared on a freely available dataset (http://mon.uvic.cat/data-signal-processing/software/) in [57], which are based on the CP model of the whole tensor, such as the CP Weighted Optimization (CP-WOPT) [58], the High accuracy Low Rank Tensor Completion (HaLRTC) [59] and the Bayesian CP factorization (BCPF) for tensor completion [60]; and one method that uses the Sparse Tucker decomposition of every 6 × 6 × 6 tensor patch (subtensors), the 3D Patch-based Tensor Completion (3DPB-TC) [50]. In the latter case, a Kronecker dictionary was first learned from a clean EEG training dataset.…”