CSci 8363 -- Fall 2008 -- Course Syllabus

Class Hours
Lecture: TTh 4-5:15pm, in MechE 102.

Instructor: Prof. Daniel Boley (boley _at_ cs.umn.edu)
Office: EE/CSci bldg, room 6-209, Phone: 612-625-3887
Office Hours: Tues. 5:15-6:15pm plus another hour TBA.
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Work Plan

Students will make an oral presentation of one research paper drawn from the list "papers.html" during the course of the semester, by rotation. Talks should highlight the main points the author is trying to make, and indicate the principal linear algebra tools being used in the paper. experimental results present in the paper being presented. Several papers will be very theoretical and technical -- in these cases you will not be expected to follow all the details, but you should be able to point out the main result and indicate which linear algebra tools and/or mathematical methods the paper depends on. (30%)
Students should submit a short weekly synopsis of each week's material, with your own reactions. This synopsis should not be over one page, and should be submitted each Tuesday in class. It should consist of your take on the main point of the paper and your reaction to the paper (e.g. does the paper make sense? Does it lead you to any ideas for further developments? etc.) (15%)
Attend class and participate in class discussions. (15%)
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 a literature survey, an experimental study of some methods proposed in a paper or of an application of one of the methods studied in this class. It can be based on a paper presented in class or on a more recent research paper on a similar topic. 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. (20%)
Give a short presentation on your project during the last 2-3 weeks of the semester. (20%)

General Information
Linear Algebra has contributed many methods for handling very large quantities of numerical data. Here we examine many of these linear algebra methods and how they have been applied to the exploration and analysis of very large data collections. After a brief review of some basic concepts in linear algebra, most of the class will be devoted to how these linear algebra methods have been used in information retrieval, data mining, unsupervised clustering, bioinformatics, and the like. Examples of methods we will examine are Latent Semantic Indexing, Linear Least Squares Fit, Principal Direction Divisive Partitioning, Hubs and Authorities Analysis, Support Vector Machines, and recent ideas on non-negative matrix decompositions. A collection of basic research papers, some of a tutorial nature, will be used for the class. Examples will be taken from vision recognition systems, biological gene analysis, document retrieval. This course introduces the basic numerical techniques to solve mathematical problems on a digital computer. Algorithms for several common problems encountered in mathematics, science and engineering are introduced. The pitfalls and errors that can arise when solving mathematical problems with methods taking finite time and in finite precision arithmetic are discussed, and measures to predict when such pitfalls are encountered will be introduced.

TOPICS

• General
• Basics of Eigenvalues, PCA definition
• Information retrieval and clustering using vector-based similarities
• SVD/PCA in Biology -- Microarray analysis.
• Linear discrinimant Analsys (LDA)
• Multidimensional Scaling
• ISOMAP, Local Linear Embedding and visualization
• Non-Negative Matrix Factorization
• Link Analysis -- PageRank. HITS
• Eigenfaces
• Spectral Clustering
• Spectral Graph Partitioning
• co-clustering
• Support Vector Machines