Tensor eigenvectors are a generalization of matrix eigenvectors to square, multiway data. They have traditionally been derived and associated with algebraic generalizations of matrix eigenvector equations and polynomial interpretations of matrix and tensor functions. In recent work, we showed how tensor eigenvectors can be interpreted and associated with limiting distributions of generalized vertex reinforced random walks through a stochastic process called a spacey random walk. These stochastic process-based interpretations and ideas establish new opportunities, methods, and applications of tensors. In particular, they suggest a new class of algorithms based on dynamical systems to compute Z-eigenvectors of tensors that is surprisingly effective. In this seminar, we will survey some of the recent results and highlight current and open problems.
David Gleich is the Jyoti and Aditya Mathur Associate Professor in the Computer Science Department at Purdue University whose research is on novel models and fast large-scale algorithms for data-driven scientific computing including scientific data analysis, bioinformatics, and network analysis. He is committed to making software available based on this research and has written software packages such as MatlabBGL with thousands of users worldwide. Gleich has received a number of awards for his research including a SIAM Outstanding Publication prize (2018), a Sloan Research Fellowship (2016), an NSF CAREER Award (2011), the John von Neumann post-doctoral fellowship at Sandia National Laboratories in Livermore CA (2009). His research is funded by the NSF, DOE, DARPA, and NASA. For more information, see his website: https://www.cs.purdue.edu/homes/dgleich/
Faculty Host: Edgar Solomonik