Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal Analysis" (AA), an unsupervised method to represent multivariate data points as sparse convex combinations of extremal elements of the dataset. Unlike the original formulation of AA, "Deep AA" can also handle side information and provides the ability for data-driven representation learning which reduces the dependence on expert knowledge. Our method is motivated by studies of evolutionary trade-offs in biology where archetypes are species highly adapted to a single task. Along these lines, we demonstrate that "Deep AA" also lends itself to the supervised exploration of chemical space, marking a distinct starting point for de novo molecular design. In the unsupervised setting we show how "Deep AA" is used on CelebA to identify archetypal faces. These can then be superimposed in order to generate new faces which inherit dominant traits of the archetypes they are based on.

Parkinson's disease is a neurodegenerative disorder requiring motor signs for diagnosis, but showing more widespread pathological alterations from its beginning. Compared to age-matched heathy individuals, patients with Parkinson’s disease bear a six-fold lifetime risk of dementia. For individualized counselling and treatment, prognostic biomarkers for assessing future cognitive deterioration in early stages of Parkinson’s disease are needed. In a case-control study, 42 cognitively normal patients with Parkinson’s disease were compared with 24 healthy control subjects matched for age, sex, and education. Tsallis entropy and band power of the δ, θ, α, β and γ-band were evaluated in baseline EEG at eyes open and closed condition. As the θ-band showed the most pronounced differences between the Parkinson's disease and healthy control groups, further analysis focused on this band. Tsallis entropy was then compared across groups with 16 psychological test scores at baseline and follow-ups at 6 months and 3 years. In group comparison, Parkinson's disease subjects showed lower Tsallis entropy than healthy control subjects. Cognitive deterioration at 3 years correlated with Tsallis entropy in the eyes open condition (p < 0.00079), while correlation at 6 months was not yet significant. Tsallis entropy measured in the eyes closed condition did not correlate with cognitive outcome. In conclusion, the lower the EEG entropy levels at baseline in the eyes open condition, the higher the probability of cognitive decline over 3 years. This makes Tsallis entropy a candidate prognostic biomarker for dementia in Parkinson's disease. The ability of the cortex to execute complex functions underlies cognitive health, while cognitive decline might clinically appear when compensatory capacity is exhausted. EEG-based Tsallis entropy measures signal complexity of brain rhythms. Low complexity of baseline EEG, measured in eyes open condition, correlates with cognitive decline after 3 years in patients with Parkinson’s disease. Tsallis entropy of EEG is, therefore, a candidate prognostic biomarker for cognition in Parkinson’s disease.

Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided.

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Over the last few decades, electroencephalography (EEG) has evolved from being a method that purely relies on visual inspection into a quantitative method. Quantitative EEG, or QEEG, enables the assessment of neurological disorders based on spectral features, dynamic characterizations of EEG resting-state activity, brain connectivity analyzes or quantification of EEG signal complexity. The information contained in EEG is multidimensional: Electrodes, positioned at different scalp locations, provide a spatial dimension to the analysis of EEG while time provides a dynamic dimension: This multidimensional property of EEG makes its quantification a challenging task. In this narrative review we present quantitative models focused on different aspects of EEG: While microstate models focus more on the quantification of the dynamic aspects of EEG, spectral methods, connectivity analysis and entropy based models are more concerned with its spatial aspects. Nevertheless, these diverse approaches have provided neurophysiology based biomarkers, especially for monitoring and predicting the course of various neurodegenerative disorders. However, their translation into clinical practice crucially depends on the ability to automate the analysis of EEG in a user-friendly manner, without compromising on the validity of the provided results. Once this has been accomplished, EEG would provide an inexpensive and widely available method for monitoring disease progression, identifying patients at risk of neurodegeneration—especially before the onset of clinical symptoms, and predicting future cognition. For stratification of patients to clinical trials, EEG would allow shortening the trial duration and lowering the number of necessary participants by identifying patients at risk of fast cognitive decline.