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Project: The Tesseract Linear-non-linear Dimensionality Reduction Method and a Suitable Visual Metaphor for its Exploration

Description

Among the existing visual representations for the analysis of multidimensional data, Dimensionality Reduction (DR) layouts are one of the most popular, allowing users to analyze similarity relationships. In general, DR techniques aim at reducing a high-dimensional space to 2 or 3 dimensions and are typically classified as linear (global pairwise distance preservation) or non-linear (local neighborhood preservation) methods. 

While linear techniques are good at capturing global trends like distances between groups of instances, non-linear techniques are better at revealing such groups and have recently become the preferred class of techniques in the visualization field. However, non-linear methods suffer from low interpretability since the resulting dimensions are non-linear combinations of the original dimensions, and it is not easy to understand a layout considering the actual high-dimensional space -- something straightforward for linear techniques. 

In this project, the goal is to create a novel DR method that combines linear and non-linear characteristics of DR techniques by reducing the multidimensional space to more than the usual 2 (or 3) dimensions in which some dimensions preserve global linear relationships and others local non-linear relationships. In this process, the challenge is not only to define the technique but also to create a proper visualization metaphor that accommodates more than 3 dimensions. Ideas will be borrowed from the concept of projection pursuit. However, instead of mapping the reduced data to a single plane for visualization, we will focus on mapping to multiple coordinated planes.

Details

Student

YH

Yaron Heerkens

Supervisor

Fernando Paulovich

Secondary supervisor

Leonardo Christino