# ECE 598ZZ Homework

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.