Nicolas Heintz

Nicolas Heintz, Tom Francart, Alexander Bertrand

Linear Discriminant Analysis (LDA) is one of the oldest and most popular linear methods for supervised classification problems. In this paper, we demonstrate that it is possible to compute the exact projection vector from LDA models based on unlabelled data, if some minimal prior information is available. More precisely, we show that only one of the following three pieces of information is actually sufficient to compute the LDA projection vector if only unlabelled data are available: (1) the class average of one of the two classes, (2) the difference between both class averages (up to a scaling), or (3) the class covariance matrices (up to a scaling). These theoretical results are validated in numerical experiments, demonstrating that this minimally informed Linear Discriminant Analysis (MILDA) model closely matches the performance of a supervised LDA model. Furthermore, we show that the MILDA projection vector can be computed in a closed form with a computational cost comparable to LDA and is able to quickly adapt to non-stationary data, making it well-suited to use as an adaptive classifier.

Nicolas Heintz, Tom Francart, Alexander Bertrand

Auditory attention decoding (AAD) algorithms exploit brain signals, such as electroencephalography (EEG), to identify which speaker a listener is focusing on in a multi-speaker environment. While state-of-the-art AAD algorithms can identify the attended speaker on short time windows, their predictions are often too inaccurate for practical use. In this work, we propose augmenting AAD with a hidden Markov model (HMM) that models the temporal structure of attention. More specifically, the HMM relies on the fact that a subject is much less likely to switch attention than to keep attending the same speaker at any moment in time. We show how a HMM can significantly improve existing AAD algorithms in both causal (real-time) and non-causal (offline) settings. We further demonstrate that HMMs outperform existing postprocessing approaches in both accuracy and responsiveness, and explore how various factors such as window length, switching frequency, and AAD accuracy influence overall performance. The proposed method is computationally efficient, intuitive to use and applicable in both real-time and offline settings.