"Seriation is an exploratory data analysis technique to reorder objects into a sequence along a one-dimensional continuum so that it best reveals regularity and patterning among the whole series" [Yvan Saeys]
The goal of the thesis is to investigate all possible seriations of an n-dimensional scalar function and identify interesting example cases. A histogram of a volume data set is one prominent seriation example where the ordering is according to the scalar value and leaving out the spatial information entirely. Dynamic Volume Lines  is another seriation example, where the ordering is along a space-filling curve. Considering all possible seriations of a grid-based n-dimensional scalar functions (i.e., all permuations of the grid-points), it would be interesting to find out which seriations make more sense or are more helpful.
The goal would be to search through all possible arrangements and perhaps find lesser known arrangements in the permutation space in addition to already known ones, classify the space, .... Arrangements/seriations could be along:
- Space-filling curves
- Variation-diminishing way
- ordered according to scalar value (like histogram)
- Interest and knowledge in visualization.
- Good programming skills.
- Creativity and enthusiasm.
The project should be implemented as a standalone application, desktop or web-based (to be discussed depending on the student's prior experience).