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Visualization in parametrizable geometries of sparse data with very high dimension

The project goal is the study and developemnt of specific techniques for the visualization in 3D of multidimensional sparse data (among which, parameterizable geometries are used)
Orientation: research
Department(s) of the thesis director(s): LSI (Software Department), www.lsi.upc.edu
Thesis Directors: Enrique Romero and Jordi Turmo
e-mail: eromero@lsi.upc.edu, turmo@lsi.upc.edu

Extended description:

In Artificial Intelligence, it is usual to work with data sets in very high dimensions (tens, hundreds of thousands of variables), almost impossible to grasp by the human brain. However, no one dobuts that that visual information that the human brain is able to process i extraordinarily valuable.

The human limitation is that we only are able to interpret estatical visualizations of objects in, at most, three dimensions (in dynamic visualizations the human brain is able to visualize also a fourht dimension).

In the literature several algorithms have appeared for the transformation of data that preserve some of the characteristics of the original data (such as, for example, the distance and similarity between them). Underlying these algorithms one can find a problema of function minimization for functions with many parameters that, although the coudl be solved in a reasonable manner, usually don't yield adequate visualizations for sparse data sets. A dataset is considered "sparse" if the proportion of values different from zero is small).

Parameterizable geometries will be considered as a way to obtain a solution for the problem.

Minimal pre-requisites and prior knowledge required

We recommend applicants to have minimal knowledge of mathematical analysis although it is not a sine quan non condition.