Course Project for ESE 559 Data-Integrated Frameworks for Systems Analysis and Control Design
Current topics of interest:
- Delaunay Triangulation is the standard, balanced triangulation algorithm
- Delaunay Triangulation can be calculated efficiently by projection on a convex hull
- Ex. qhull.org
- Interested in efficiently altering triangulations when adding points over time
| Delaunay Triangulation Over Time | Voronoi Graph Over Time |
|---|---|
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- Higher order Delaunay triangulations may also provide better modelling, similar to increasing k in KNN
| Van der Pol Uniformly Sampled | Van der Pol Sampled Over Time |
|---|---|
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- We can find simplex transformations (our method of linearizing the dynamics of a region between points)
- We can measure the similarity of these simplex transformations as a sort of non-linearity measure
- I also believe we can use simplex clustering to "cull" simplices in regions where the system is either very linear or has been oversampled
- Simplex clustering and culling saves memory and makes region lookup faster
- Preserving the full grid of simplices makes Delaunay Triangulation quick and efficient
- How to balance or incorporate these two techniques to make real-time/offline modeling and learning efficient