The cerebrospinal fluid (CSF) of 19 subjects who received a clinical diagnosis of Alzheimer's disease (AD) as well as of 5 pathological controls have been collected and analysed by Raman spectroscopy (RS). We investigated whether the raw and preprocessed Raman spectra could be used to distinguish AD from controls. First, we applied standard Machine Learning (ML) methods obtaining unsatisfactory results. Then, we applied ML to a set of topological descriptors extracted from raw spectra, achieving a very good classification accuracy (> 87%). Although our results are preliminary, they indicate that RS and topological analysis together may provide an effective combination to confirm or disprove a clinical diagnosis of AD. The next steps will include enlarging the dataset of CSF samples to validate the proposed method better and, possibly, to understand if topological data analysis could support the characterization of AD subtypes.

I am incredibly grateful about how my academic year started so far: four preprints were at least conditionally accepted for publication in a forthcoming book on topological methods in data visualization, while another publication of my new lab was accepted as a poster for ICLR 2019. The underlying theme of all these publications is to shift the focus of machine learning towards topological methods, i.e. methods that focus on connectivity properties of input data. I am convinced that thinking about these types of properties is worthwhile, as the resulting shift in perspective often leads to novel insights. This spring of papers follows two themes: in the first, topology is used directly to drive algorithms, for example to classify data, or to elucidate its properties. In the second theme, topology is used indirectly to learn something about the behaviour of other algorithms. In Persistent Intersection Homology for the Analysis of Discrete Data, Markus Banagl, Filip Sadlo, Heike Leitte, and I describe how to use persistent intersection homology, an extension of persistent homology in order to describe spaces that do not consist of a single manifold, but of multiple ones.