PhD School Lecture, 10/02/2021, 11:00 - 13:00
Department of Computer Engineering, Modeling,Electronics and Systems
University of Calabria - ICAR-CNR
Optimization Models and Classification
We introduce classification as a chapter of Machine Learning. The differences between supervised, unsupervised and semi-supervised classification are highlighted. The focus on classification as a diagnostic problem, that is a decision making one, allows us to emphasize the role that optimization models (often nonlinear and even nonsmooth) play in this context.
From a mathematical point a view classification is presented in its essence of separation of sets of samples in the Euclidean attribute (feature) space.
After discussing some mathematical programming models for unsupervised classification (clustering), we introduce the Support Vector Machine (SVM) paradigm, presenting the basic concepts of separating hyperplane, classification error, separation margin and kernel transformation.
Classification based on nonlinear separating surfaces (polyhedral, elliptic, spherical and conical) is also introduced, as well as the use of the SVM approach in the Multiple Instance Learning (MIL) area, where bags of samples instead of single ones are to be classified.
The reduction of the number of attributes needed to gather good quality classifiers (Feature Selection, FS) is tackled as an optimization problem, with special emphasis on the use of the zero-pseudo-norm.
Some current research trends (e.g. in the Adversarial Machine Learning) are finally indicated.
Manlio Gaudioso has served as full professor of Operations Research at Università della Calabria (1994-2019).
He has also been manager at CRAI (Consorzio per la Ricerca e le Applicazioni di Informatica), member of the Administration Board and President of the Committee for Economic Matters at Università della Calabria.
He published more than seventy papers in international journals in areas such as Optimization, Operations Research and Machine Learning. His research interests include nonsmooth optimization, integer programming, graph optimization, logistic chain optimization and classification.
He has served as Associate Editor of the journal “Optimization” and of “Vestnik of Saint Petersburg University”. He has also acted as Director of some Scientific Schools at “Ettore Majorana” Centre in Erice.
Currently he is Research Associate at ICAR-CNR.