Sulla fattorizzazione CUR mediante interpolazione empirica discreta

In questa tesi tratteremo una variante della fattorizzazione CUR di una matrice data, ottenuta attraverso l'algoritmo DEIM ("discrete empirical interpolation method") a confronto con un metodo ampiamente usato in letteratura, il metodo dei Leverage Score. A tal fine verrà anche trattato un metodo per ottenere la fattorizzazione QR di una matrice in maniera incrementale. Verrà illustrato il comportamento degli algoritmi sviluppati su due esempi applicativi.

ICE Emissions Estimation through Machine-learning techniques to support real-world R&D experiments

The emissions estimation, both during homologation and standard driving, is one of the new challenges that automotive industries have to face. The new European and American regulation will allow a lower and lower quantity of Carbon Monoxide emission and will require that all the vehicles have to be able to monitor their own pollutants production. Since numerical models are too computationally expensive and approximated, new solutions based on Machine Learning are replacing standard techniques. In this project we considered a real V12 Internal Combustion Engine to propose a novel approach pushing Random Forests to generate meaningful prediction also in extreme cases (extrapolation, very high frequency peaks, noisy instrumentation etc.). The present work proposes also a data preprocessing pipeline for strongly unbalanced datasets and a reinterpretation of the regression problem as a classification problem in a logarithmic quantized domain. Results have been evaluated for two different models representing a pure interpolation scenario (more standard) and an extrapolation scenario, to test the out of bounds robustness of the model. The employed metrics take into account different aspects which can affect the homologation procedure, so the final analysis will focus on combining all the specific performances together to obtain the overall conclusions.

Synthetic generation of amyloid PET images by non-linear dimensionality reduction inversion

Privacy issues and data scarcity in PET field call for efficient methods to expand datasets via synthetic generation of new data that cannot be traced back to real patients and that are also realistic. In this thesis, machine learning techniques were applied to 1001 amyloid-beta PET images, which had undergone a diagnosis of Alzheimer’s disease: the evaluations were 540 positive, 457 negative and 4 unknown. Isomap algorithm was used as a manifold learning method to reduce the dimensions of the PET dataset; a numerical scale-free interpolation method was applied to invert the dimensionality reduction map. The interpolant was tested on the PET images via LOOCV, where the removed images were compared with the reconstructed ones with the mean SSIM index (MSSIM = 0.76 ± 0.06). The effectiveness of this measure is questioned, since it indicated slightly higher performance for a method of comparison using PCA (MSSIM = 0.79 ± 0.06), which gave clearly poor quality reconstructed images with respect to those recovered by the numerical inverse mapping. Ten synthetic PET images were generated and, after having been mixed with ten originals, were sent to a team of clinicians for the visual assessment of their realism; no significant agreements were found either between clinicians and the true image labels or among the clinicians, meaning that original and synthetic images were indistinguishable. The future perspective of this thesis points to the improvement of the amyloid-beta PET research field by increasing available data, overcoming the constraints of data acquisition and privacy issues. Potential improvements can be achieved via refinements of the manifold learning and the inverse mapping stages during the PET image analysis, by exploring different combinations in the choice of algorithm parameters and by applying other non-linear dimensionality reduction algorithms. A final prospect of this work is the search for new methods to assess image reconstruction quality.