Machine Learning: Theory and Applications

Machine Learning (ML) comprises an ensemble of techniques which are suitable to be applied in a variety of fields, wherever learning, inference or prediction are needed. Our current research mainly focuses on classical machine learning paradigms such as kernel methods and Riemannian geometric methods on the one side, and the more recent deep learning on the other side. We both carry out fundamental and applied research, mostly related to computer vision and biomedical engineering.

Kernel Methods and Riemannian Geometry

Our work in kernel methods spans three levels: theory, algorithms, and applications. We study mathematical properties of kernels and the corresponding Reproducing Kernel Hilbert Spaces (RKHS), formulate new kernel-based methods, and investigate statistical properties of learning algorithms in general. Our present focus is on RKHS of vector-valued functions, with promising applications in color image processing, multi-label image classification and text categorization.

Besides, we investigate the application of Riemannian geometry, both theoretically and algorithmically, to problems in computer vision and biomedical imaging. Some Riemannian manifolds of particular interest are the manifold of symmetric positive definite matrices, the Grassmannian manifolds, and their generalizations. Our work in this direction is closely linked with RKHS methodology.

Kernel Methods and Riemannian Geometry


Deep Learning

Deep learning is a branch of ML, where hierarchical representations are learned from data and further exploited for classification, regression or other purposes. Such paradigm aims at substituting hand-crafted feature representation with learned ones. At PAVIS we investigate deep learning methods and apply it in two main research fields:  

  • Activity recognition and intention prediction. We exploit the capabilities of Recurrent Neural Networks to model temporal sequences of inputs. More in detail, we investigate LSTM cells augmented with attention mechanisms, in order to perform fine-grained analyses of motion patterns.
  • Retinal signal and animal behaviour analysis. The main goal is to analyses the effectiveness of unsupervised learning techniques (RBMs) in modelling biological phenomenons.
  • Generative Adversarial Networks for forensics. Splicing detection is accomplished by generating image masks to locate the tampered area.

We also investigate deep learning from a more theoretical perspective, in order to shed ligth to its principles.

Deep Learning