Combinatorial continuum limits and their applications in data science

Many problems in data science fields including signal processing, machine learning, and data mining involve combinatorial optimization of some kind, e.g., computation of minimal graphs and graph cuts over feature space. Several classes of combinatorial optimization problems have continuum limits as the dimension approaches infinity. These include problems arising in spectral clustering, multi-objective learning, and anomaly detection. In some cases these continuum limits lead to analytical approximations that can break the computational combinatorics bottleneck. In this talk, I will present an overview of the theory and application of continuum limits for combinatorial problems.
Alfred Hero is the R. Jamison and Betty Williams Professor of Engineering at the University of Michigan and co-Director of the Michigan Institute for Data Science (MIDAS) . At the University of Michigan his primary appointment is in the Department of Electrical Engineering and Computer Science (EECS) and he has secondary appointments in the Department of Biomedical Engineering and the Department of Statistics. He is also affiliated with the UM Center for Computational Medicine and Bioinformatics (CCMB), and the UM Graduate Program in Applied and Interdisciplinary Mathematics (AIM).