Interpreting single trial data using groupwise regularisation

Univariate statistical approaches are often used for the analysis of neuroimaging data but are unable to detect subtle interactions between different components of brain activity. In contrast, multivariate approaches that use classification as a basis are well-suited to detect such interactions, allowing the analysis of neuroimaging data on the single trial level. However, multivariate approaches typically assign a non-zero contribution to every component, making interpretation of the results troublesome. This paper introduces groupwise regularisation as a novel method for finding sparse, and therefore easy to interpret, models that are able to predict the experimental condition to which single trials belong. Furthermore, the obtained models can be constrained in various ways by placing features extracted from the data that are thought to belong together into groups. In order to learn models from data, we introduce a new algorithm that makes use of stability conditions that have been derived in this paper. The algorithm is used to classify multisensor EEG signals recorded for a motor imagery task using (groupwise) regularised logistic regression as the underlying classifier. We show that regularisation dramatically reduces the number of features without reducing the classification rate. This improves model interpretability as it finds features in the data such as mu and beta desynchronisation in the motor cortex contralateral to the imagined movement. By choosing particular groupings we can constrain the regularised solutions such that a lower number of sensors is used or a model is obtained that generalises well over subjects. The identification of a small number of groups of features that best explain the data make groupwise regularisation a useful new tool for single trial analysis.