Is a Vietoris--Rips expansion used, for example?

The paper, the reviews, the author response and the ensuing discussion were all taken into consideration. Two of three reviewers considered the work marginally above the acceptance threshold and one considered it marginally below the threshold. Concerns, after taking the author response into account, included missing (stronger) baselines, stability in practice, and claims about working with multiparameter persistence and it offering more information. On the other hand, the topic and smart aspects of the technical solution were considered interesting, and able to inspire future research. Overall the paper may be of sufficient quality to be presented at NeurIPS.

In the last decade, there has been increasing interest in topological data analysis, a new methodology for using geometric structures in data for inference and learning. A central theme in the area is the idea of persistence, which in its most basic form studies how measures of shape change as a scale parameter varies. There are now a number of frameworks that support statistics and machine learning in this context. However, in many applications there are several different parameters one might wish to vary: for example, scale and density. In contrast to the one-parameter setting, techniques for applying statistics and machine learning in the setting of multiparameter persistence are not well understood due to the lack of a concise representation of the results.

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.