Overview:
After many years as a Pure Mathematician, I realised that I had spent a good amount of time studying Applied Mathematics, Computer Sciences, Artificial Intelligence and applications of Pure Maths to other fields simply because I was very interested in all of them. As a consequence, I had to start doing research in these fields becoming more involved in real world projects.
Works:
Mathematics of Deep Learning:
Sheaf theory for Graph Neural Networks (in preparation, work in progress).
R. Fioresi, F. Zanchetta, Deep Learning and Geometric Deep Learning: an introduction for mathematicians. International Journal of Geometric Methods in Modern Physics, to appear. (link)
M. Lapenna, F. Faglioni, F. Zanchetta, R.Fioresi, Geometric Deep Learning: a temperature based analysis of graph neural networks. Proceedings of GSI 23 (link) .
Applied AI:
Michela Lapenna, Athanasios Tsamos, Francesco Faglioni, Rita Fioresi, Ferdinando Zanchetta, Giovanni Bruno, Geometric Deep Learning for enhancedb quantitative analysis of Microstructures in X-ray Computed Tomography Data. Submitted
A Geometric deep learning approach to blood pressure regression, F. Zanchetta, A. Simonetti, G. Faglioni, A. Malagoli and R. Fioresi. Extended abstract accepted to GeoMedIA workshop 2022 (Link ). (Paper in Preparation).
A. Simonetti, F. Zanchetta, Graph Neural Networks and Time Series as Directed Graphs for Quality Recognition. Submitted. Preprint (link ).
C. P. Coutinho, F. Zanchetta, A. Galzignato, M. Batista, G. Lari, A. Stefano, E. Borrelli, G. Savini, M. L. Cascavilla, F. Bandello, R. Fioresi, P. Barboni, Machine Learning application in Visual Field Loss for Dominant Optic Atrophy. Submitted.
F. Zanchetta, A. Simonetti, G. Faglioni, A. Malagoli and R. Fioresi, A Geometric deep learning approach to ECG and PPG quality recognition. In progress.
J. Bertozzi, K. Carlin, I. Di Silvestro, R. Fioresi, A. Ghetti, B. Krause, G. Perini, F. Zanchetta, Gene Selection for RNA HTT and Neuropathic Pain vs no Pain Classification, based on a Machine Learning approach. In preparation.
Projects I am working on:
Blood pressure regression and forecasting from Photoplethysmogram and ECG data.
Covid-19 severity prediction from genetic data.
Clustering and forecasting of neuronal activity for diagnosis of diseases and drug design.
Genetic data analysis for diagnosis of diseases and drug design (supervising two students).
Archetypal analysis (deep and classical) for understanding eye diseases.
Deep Learning methods for more efficient image-based defect recognition in industrial pipelines.
(More will come after the above list reduces).
Methods Used and Research Interests:
Graph Neural Networks (and their applications to time series).
Applications of Sheaf Theory and Geometry (of the flavour coming from my Pure Research) to Machine Learning and AI.
Deep Learning.
Standard Machine learning techniques (regression, SVM, clustering algos, random forests, etc.).
Topological Data Analysis (beginning).