Graph regularised tensor factorisation of EEG signals based on network connectivity measures

Tensor factorisation is a decomposition method for high dimensional data that is used to estimate the prominent factors in some signal. Recently it has been employed with success in the biomedical fields. Regularised tensor factorisation attempts to alleviate overfitting and small sample size estimation errors by constraining the obtained solution to satisfy some metric. In this work, we provide a novel extension to the theory of graph regularisation for regularising multiple graphs and we employ graph regularised tensor factorisation on an electroencephalogram (EEG) dataset. We utilise brain connectivity networks as the basis of our graphs. Subsequently, we perform graph regularised tensor factorisation on the EEG data in order to reduce the noise and interference inherent to the EEG. Furthermore, we employ custom graphs that incorporate prior knowledge of our dataset. We demonstrate the efficacy of the algorithm theoretically and on some real EEG examples. Further applications of the algorithm can be neuroscience applications where there is prior knowledge of the relations between the data and in general in network science for datasets that can be expressed as tensors.