Multiresolution analysis over simple graphs for brain computer interfaces

Abstract

Abstract. Objective: Multiresolution analysis (MRA) offers a useful framework for signal analysis in the temporal and spectral domains, although commonly employed MRA methods such as Daubechies wavelets may not be the best approach for brain computer interface (BCI) applications. Approach: Hereby we propose the use of a lifting scheme transform over graphs and a tailored simple graph representation for EEG data which results on a MRA system where temporal, spectral and spatial characteristics are used to extract motor imagery features. The transformed data is processed within a simple experimental framework to test the classification performance. Main Results: The proposed method can significantly improve the classification results obtained by various wavelet families using the same methodology. Preliminary results using common spatial patterns as feature extraction method show that we can achieve comparable classification accuracy to more sophisticated methodologies. From the analysis of the results we can obtain insights into the pattern development in the EEG data, which provide useful information for feature basis selection and thus for improving classification performance. Significance: Applying wavelet lifting over graphs is a new approach for handling BCI data. The inherent flexibility of the lifting scheme could lead to new approaches based on the proposed method which could further improve the classification performance here presented.

Optimized Update/Prediction Assignment for Lifting Transforms on Graphs

“…This even/odd assignment has been also employed for lifting-based compact image representation (Figure 2(b)): pixels along odd rows or columns are assigned to P [24]- [26]. Figure 2(c) shows a UPA proposed for liftingbased video coding, where even frames are used to predict the odd frames [27]- [29], and Figure 2(d) shows a UPA for a brain computer interface (BCI) application, where samples at odd time stamps are assigned to P [30], [31]. While straightforward UPAs have been proposed for these specific examples, optimizing the UPA for arbitrary weighted non-planar graphs of practical interest becomes a complex problem, and just a few solutions have been proposed in the literature.…”

A Label-Aided Filter Method for Multi-objective Feature Selection in EEG Classification for BCI

“…It was recorded with a sampling frequency of 256 Hz during four different runs and includes a total of 120 trials for each class and subject. More details about this dataset can be found in [6].…”

“…Each pattern was obtained from an EEG trial by the feature extraction procedure based on the MRA described in [6]. Thus, each signal obtained from each electrode contains several segments to which a set of wavelet detail and approximation coefficients are assigned.…”

“…4. Characterization of an EEG signal (pattern) in [6] In [6] a simple approach to reduce the number of coefficients is applied, in which only one coefficient is assigned to each electrode and each level of approximation and detail. This coefficient is obtained by computing the second moment of the coefficient distribution (variance) and normalizing the value between 0 and 1.…”

“…This paper deals with multi-objective feature selection in supervised classification problems. To evaluate the proposed method, motor imagery (MI) based BCI tasks have been used as benchmark EEG classification problems where multi-resolution analysis (MRA) has been applied for feature extraction [6]. An MRA system applies a sequence of successive approximation spaces that satisfy a series of constraints to reach a description as close as possible to the target signal [7], and thus it is useful whenever the target signal presents different characteristics in the successive approximation spaces.…”