Syllabus
1. Matrix representations and matrix decompositions
2. Eigenvalue decomposition, least squares regression, singular value decomposition
3. Numerical linear algebra in data science applications a. principal component analysis, low-rank approximation and compression b. clustering and classification c. Pagerank and semantic indexing d. non-negative matrix decomposition
4. Current research directions and applications
Annotation
The goal of this course is to introduce students to underlying concepts of numerical linear algebra which appear in methods for data science and informatics. After an introduction and review of matrix representations of data and basic matrix decompositions, these concepts are illustrated in various applications, including data compression, clustering, classification, and neural networks.
The course will also illustrate these concepts via software implementations and an introduction to tools for cluster computing.