Dimensionality Transcending: A Method for Merging BCI Datasets With Different Dimensionalities

Objective: We present a transfer learning method for datasets with different dimensionalities, coming from different experimental setups but representing the same physical phenomena. We focus on the case where the data points are symmetric positive definite (SPD) matrices describing the statistical behavior of EEG-based brain computer interfaces (BCI). Method: Our proposal uses a two-step procedure that transforms the data points so that they become matched in terms of dimensionality and statistical distribution. In the dimensionality matching step, we use isometric transformations to map each dataset into a common space without changing their geometric structures. The statistical matching is done using a domain adaptation technique adapted for the intrinsic geometry of the space where the datasets are defined. Results: We illustrate our proposal on time series obtained from BCI systems with different experimental setups (e.g., different number of electrodes, different placement of electrodes). The results show that the proposed method can be used to transfer discriminative information between BCI recordings that, in principle, would be incompatible. Conclusion and significance: Such findings pave the way to a new generation of BCI systems capable of reusing information and learning from several sources of data despite differences in their electrodes positioning.