# ECE 598ZZ Project

## Final Project Recommendations

- Your project report will be due
**12/15/2019 at 11:59pm** **Report Contents: read the project istructions at the link above.****Report Format:**typeset text and equations (LaTeX or MSWORD), capions on figures, legible legends and axis markings (if used) on all figures. One column or two column format. Font size at least 10 point. Margin 1" (2.5cm) on all sides. Up to 4 pages with unlimited appendix- To submit your report, email to the instructor and TAs a PDF version of your report + a link to a Box directory that contains copies (in PDF) of the papers that you used as references
- A PDF or PowerPoint version of your presentation will be due (by emailing a Box link) on
**12/09/2019 at 10pm** __All students must attend all presentation sessions.__- Location: TBA
- Time: 12/10

No other question has ever moved so profoundly the spirit; no other idea has so fruitfully stimulated the intellect; yet no other concept stands in greater need of clarification than that of the infinite. David Hilbert

ECE 598ZZ (High-Dimensional Geometric Data Analysis): This course aims to establish the mathematical foundation of many recent algorithms for tasks such as organization and visualization of data clouds, dimensionality reduction, clustering, and regression. Data analysis is an interdisciplinary field. It combines mathematics (both pure and applied), computer science (machine learning, theoretical CS, AI, computer vision), electrical engineering (signal and image processing), statistics, structural biology, neuroscience, computational biology (microarray data for gene expression), biophysics and chemical engineering (molecular dynamics simulations), and more. We will focus on a few particular methods and explain what they are good for, what are their limitations, what is the underlying math, in order to develop a good sense of when to apply them and develop a sound basis for designing new data analysis algorithms. The course will have three main sections: 1) high dimensional probability, 2) geometric data analysis, and 3) other recent advances with applications. The high-dimensional probability section of the course aims at getting insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. In the second part of the course, we introduce spectral methods that are useful in the analysis of big data sets. Particular applications involve cryo-electron microscopy single particle reconstruction and density functional theory with strongly correlated electrons. Prerequisite: ECE 534.