Mini-Course: Introduction to Tensor Decompositions

The class is targeted to graduate and advanced undergraduate students. Space permitting, faculty and postdocs are also welcome.

Description: Tensors are multidimensional arrays, and many datasets are most naturally represented in this framework. This mini-course will introduce attendees to tensors decompositions, whose applications range from analysis of fluorescence data in chemistry, to brain imaging in neuroscience, to data compression of combustion simulations, to Internet traffic analysis in cybersecurity, and much more. The goals of this course are as follows:

• Introduction to tensors – relationship to matrices, basic manipulations and operations
• Tucker decomposition – utility for compression, key kernels, computational algorithms, approximation theory, applications
• CP decomposition – utility for data analysis, key kernels, computation algorithms, choosing the rank, applications
• Special topics – Depending on time and the interest of the students, special topics could include working with large scale and/or sparse tensors, alternative loss functions, decompositions of symmetric tensors, randomized methods, applications to moment tensors and Gaussian Mixture Models, etc.

Students will gain experience analyzing real data sets (in MATLAB).

Students should ideally have had a class in linear algebra or numerical analysis.

EVERY TUESDAY and THURSDAY, MAY 3 - MAY 17, 2022

10am - 11am

TECH C211

This is a combined CS and IEMS zero-credit course.