4: Multidimensional Visualization With Applications to Multivariate Problems



Sunday, Half Day
1:30 – 5:15 pm
Room 205

Multidimensional perception is limited by our experience within our three-dimensional environment. This course begins with a short literature review of the mathematical foundations of parallel coordinates for visualization of multidimensional geometry. When these coordinates are interlaced with a variety of applications, visualization and recognition of multidimensional relations from their patterns are enabled, and this methodology can be applied to multivariate problems.

Prerequisites
This is a self-contained course for beginners. Mathematical sophistication, familiarity with computer graphics and interest in multidimensional (multivariate) problems are helpful but not necessary.

Topics
Visualization of multidimensional objects without loss of information. Selected applications to visual and automatic data mining (financial, process control, biomedical, military, and other examples with hundreds of variables). Collision-avoidance Algorithms. Computer vision. Non-linear models. Decision-support Systems with occasional numerological anecdotes and palindromic digressions.

Organizer/Lecturer
Alfred Inselberg
Tel Aviv University


Schedule


1:30 Introduction to Multidimensional Visualization
Inselberg
2:00 Parallel Coordinates in 2D + Data Mining Applications on Real Multivariate Datasets
Inselberg
2:35 Multidimensional Lines & Applications -- Automatic Collision Avoidance Algorithms + One-shot Problem -- Demos & Animations
Inselberg
3:15 Break
3:30 Exact and Approximated Planes and Hyperplanes -- Applications to Computer Vision and Geometric Modeling -- Automated Data Mining
Inselberg
4:30 Surfaces and Hypersurfaces -- Interior Point Algorithm -- Application to Decision Support, Feasible Points, Sensitivity and Trade-Off Analysis and Non-Linear Visual Modeling
Inselberg




Additional information from SIGGRAPH 2002 Courses is available in the Course Notes
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