Georgios Drakopoulos

Thesis' title:

Knowledge mining with tensor algebra

Committee:

Phivos Mylonas (supervisor)

Katia-Lida Kermanidou

Spyridon Sioutas

Summary:

Often in knowledge mining appear multidimensional data and higher order dependencies, namely dependencies between three or more input variables. The linear algebraic tool which can be applied to both signal proessing and data mining is the tensor. The latter can naturally represent the simultaneous linear link between a number of not necessarily distinct linear spaces. Tensor applications are multilayer graphs, namely graphs whose edges have distinct labels, and tensor stack networks, a generalization of classic neural networks where each network operates autonomously learning both from its errors and from the errors of other networks. The objective of the proposed PhD thesis is the development of an efficient tensor clustering algorithm as well as a heuristic variant thereof. The latter can be applied in scenaria the size large tensors prohibits the use of existing clustering algorithms.