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The prospect of future treatment warrants the development of cost-effective screening for Alzheimer's disease (AD). A promising candidate in this regard is electroencephalography (EEG), as it is one of the most economic imaging modalities. Recent efforts in EEG analysis have shifted towards leveraging spatial information, employing novel frameworks such as graph signal processing or graph neural networks. Here, we systematically investigate the importance of spatial information relative to spectral or temporal information by varying the proportion of each dimension for AD classification. To do so, we test various dimension resolution configurations on two routine EEG datasets. We find that spatial information is consistently more relevant than temporal information and equally relevant as spectral information. These results emphasise the necessity to consider spatial information for EEG-based AD classification. On our second dataset, we further find that well-balanced feature resolutions boost classification accuracy by up to 1.6%. Our resolution-based feature extraction has the potential to improve AD classification specifically, and multivariate signal classification generally.

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Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on the graph topology. Here, we combine the graph heat equation with the stochastic heat equation, which ultimately yields a model for multivariate time signals on a graph. We show theoretically how the model can be used to directly compute the diffusion-based connectivity structure from multivariate signals. Unlike other connectivity measures, our heat model-based approach is inherently multivariate and yields an absolute scaling factor, namely the graph thermal diffusivity, which captures the extent of heat-like graph propagation in the data. On two datasets, we show how the graph thermal diffusivity can be used to characterise Alzheimer's disease. We find that the graph thermal diffusivity is lower for Alzheimer's patients than healthy controls and correlates with dementia scores, suggesting structural impairment in patients in line with previous findings.

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Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these multivariate signals, while at the same time taking the spatial structure between the time signals into account. A central idea in GSP is the graph Fourier transform, which projects a multivariate signal onto frequency-ordered graph Fourier modes, and can therefore be regarded as a spatial analog of the temporal Fourier transform. This chapter derives and discusses key concepts in GSP, with a specific focus on how the various concepts relate to one another. The experimental section focuses on the role of graph frequency in data classification, with applications to neuroimaging. To address the limited sample size of neurophysiological datasets, we introduce a minimalist simulation framework that can generate arbitrary amounts of data. Using this artificial data, we find that lower graph frequency signals are less suitable for classifying neurophysiological data as compared to higher graph frequency signals. Finally, we introduce a baseline testing framework for GSP. Employing this framework, our results suggest that GSP applications may attenuate spectral characteristics in the signals, highlighting current limitations of GSP for neuroimaging.

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