Leonidas J. Guibas : 2014 Plenary Session

The information contained across many data sets is often highly correlated. Such connections and correlations can arise because the data captured comes from the same or similar objects, or because of particular repetitions, symmetries or other relations and self-relations that the data sources satisfy. This is particularly true for data sets of a geometric character, such as 1D GPS traces, 2D images or videos, 3D scans or models, etc.

It is important to develop rigorous mathematical and computational tools for making such relationships or correspondences between data sets first-class citizens -- so that the relationships themselves become explicit, algebraic, storable and searchable objects. Networks of such relations can interconnect data sets into societies where the "wisdom of the collection" can be exploited in performing operations on individual data sets better, or in further assessing relationships between them. Examples include entity extraction from images or videos, 3D segmentation, the propagation of annotations and labels among images/videos/3D models, variability analysis in a collection of shapes, etc. We discuss mathematical and algorithmic issues on how to represent and compute relationships or mappings between data sets at multiple levels of detail. We also show how to analyze and leverage networks of maps, small and large, between inter-related data.

This "functorial" view of data puts the spotlight on consistent, shared relations and maps as the key to understanding structure in data. It is a little different from the current dominant paradigm of extracting supervised or unsupervised feature sets, defining distance or similarity metrics, and doing regression or classification -- though sparsity still plays an important role. The inspiration is more from ideas in homological algebra or algebraic topology, exploiting the algebraic structure of data relationships or maps in an effort to disentangle dependencies and assign importance to the vast web of all possible relationships among multiple data sets.

These ideas are further elaborated in the Forum workshop on Wednesday, April 16, titled "Networks of Shapes, Images, and Programs: The Power of Joint Data Analysis".

Leonidas Guibas obtained his Ph.D. from Stanford under the supervision of Donald Knuth. His main subsequent employers were Xerox PARC, DEC/SRC, MIT, and Stanford. He is currently the Paul Pigott Professor of Computer Science (and by courtesy, Electrical Engineering) at Stanford University. He heads the Geometric Computation group and is part of the Graphics Laboratory, the AI Laboratory, the Bio-X Program, and the Institute for Computational and Mathematical Engineering. Professor Guibas' interests span geometric data analysis, computational geometry, geometric modeling, computer graphics, computer vision, robotics, ad hoc communication and sensor networks, and discrete algorithms. Some well-known past accomplishments include the analysis of double hashing, red-black trees, the quad-edge data structure, Voronoi-Delaunay algorithms, the Earth Mover's distance, Kinetic Data Structures (KDS), Metropolis light transport, and the Heat-Kernel Signature. Professor Guibas is an ACM Fellow, an IEEE Fellow and winner of the ACM Allen Newell award.