NUMERICAL LINEAR ALGEBRA IN DATA EXPLORATION

We examine many methods for the exploration and analysis of very large data collections and how linear algebra has played a central role. Most of the class will be devoted to recent developments in the areas of • information retrieval, • data mining, • unsupervised clustering, • bioinformatics, • social networking, • machine learning. Examples of methods we will examine are • Latent Semantic Indexing, • Least Squares Fit, possibly under a sparsity constraint, • Spectral graph analysis, including graph Fourier transform and its use in neural networks, • Pagerank and other graph centrality measures, • Support Vector Machines, and • recent ideas on sparse approximation methods using L1 regularization. The class will be be based on recent papers published in these areas. Examples will be taken from vision recognition systems, biological gene analysis, document retrieval among others.

Prerequisites

Students should be familiar with basic linear algebra concepts and methods such as Gaussian elimination for systems of linear equations, plus some familarity with. concepts such as matrix eigenvalues, singular values, and matrix least squares problems, though some time will be spent reviewing these latter topics. Basic concepts in optimization like first order optimality conditions and duality will also be useful.

Work Plan

Students will be expected to do the following.

• Present one or two research or tutorial papers during the course of the semester, by rotation. Papers will be be a mix of those selected by the student via a literature search and those on a list of suggested papers.
• Submit a short weekly synopsis of each week's material, with your own reactions.
• Develop and carry out a research project based on one or more recent research papers devoted to topics studied in this class. A research project can be an experimental study of some methods proposed in a paper or of an application of one of the methods studied in this class. To give an approximate scale of the effort required, you should expect to devote about 50 hours of time during the course of the semester.
• Write a 10-15 page report on your research project.
• Give a short presentation on your project during the last 2-3 weeks of the semester.

Your project will count toward the Project Requirements for a Plan C MS degree in Computer Science.