Robust Spatial Filtering with Beta Divergence
The efficiency of Brain-Computer Interfaces (BCI) largely depends upon a reliable extraction of informative features from the high-dimensional EEG signal. A crucial step in this protocol is the computation of spatial filters. The Common Spatial Patterns (CSP) algorithm computes filters that maximize the difference in band power between two conditions, thus it is tailored to extract the relevant information in motor imagery experiments. However, CSP is highly sensitive to artifacts in the EEG data, i.e. few outliers may alter the estimate drastically and decrease classification performance. Inspired by concepts from the field of information geometry we propose a novel approach for robustifying CSP. More precisely, we formulate CSP as a divergence maximization problem and utilize the property of a particular type of divergence, namely beta divergence, for robustifying the estimation of spatial filters in the presence of artifacts in the data. We demonstrate the usefulness of our method on toy data and on EEG recordings from 80 subjects.
This paper shows that the CSP algorithm (a very common 
      algorithm for spatial filtering EEG data to increase the discriminability 
      between classes characterized by differences in power/variance as in motor 
      imagery) can be understood as a divergence maximization algorithm. They 
      then use that insight to develop a CSP algorithm that is more robust to 
      outliers by using the beta divergence. Clarity The paper 
      is very clearly written. Figure 1 is a very nice summary of the early 
      parts of the paper. Quality This paper is a very nice 
      example of a theoretical contribution that ends up having practical 
      application to real data. One minor concern I had was that I am not sure 
      how realistic adding independent noise to each electrode is as many EEG 
      artifacts are visible across multiple electrodes (e.g. blinks, muscle 
      movements, EM noise, physical movements), however the authors do show an 
      example of exactly this type of artifact in their real data. It would be 
      nice to see how the algorithm performs on other types of artifacts and 
      non-stationarities. Significance Improving the CSP 
      algorithm could have a big impact on motor-imagery and steady-state evoked 
      potential BCIs. Originality The authors mention that the 
      proof that CSPs maximize divergence has been proved for the special case 
      of 1 CSP filter. The rest of the work appears to be 
      novel.