NUMERICAL LINEAR ALGEBRA IN DATA EXPLORATION
CSci 8363 -- Fall 2019
MW 4-5:15pm, Room Keller 3-115
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,
• 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,
• recent ideas on sparse approximation methods using L1 regularization.
The class will be be based on recent papers published in these
Examples will be taken from vision recognition systems, biological gene
analysis, document retrieval among others.
Students should be familiar with basic linear algebra concepts and methods
such as Gaussian elimination for systems of linear equations, plus some
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.
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
- 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
Your project will count toward the Project Requirements for a Plan C MS degree
in Computer Science.
- Intro: Basics of Eigenvalues, PCA definition
- Text Mining
- Tensor Decompositions
- Feature extraction
- Kernal Methods
- Dimensionality Reduction
- Multidimensional Scaling and non-linear dimensionality reduction
- Methods related to Spectral Graph Analysis
- Importance Ranking in Graphs and Link Analysis
- Convolutional and Graph Neural Nets
For Further Information
- Class web site: http://www-users.cselabs.umn.edu/classes/Fall-2019/csci8363/
- Contact: Daniel Boley, 4-225C KHKH, firstname.lastname@example.org,