TAG in Pattern Recognition with Applications
A workshop at the Computer Vision and Pattern Recognition (CVPR) in Vancouver, Canada on June 18th, 2023.
Call for Papers
Much of the data that is fueling the current rapid advances in mainstream data science, computer vision, and pattern recognition is high-dimensional, abundant, and relatively noise-free. However, this poses challenges in many application domains in terms of building algorithms that can capture meaningful structure from limited data and also building analytical techniques that help to understand what that structure means. Mathematicians working in topology, algebra, and geometry have more than a century’s worth of finely-developed machinery whose purpose is to give structure to, help build intuition about, and generally better understand patterns in complex data. We welcome submissions that utilize frameworks, techniques, and concepts rooted in one or more of topology, algebra, and geometry that consider a pattern recognition challenge faced in an application domain. All submitted works should include at least one real-world use-case. This session is an opportunity for researchers building robust, mathematically principled methods to present and publish work on real-world problems in pattern recognition for which standard off-the-shelf techniques do not work.
Dr. Nina Miolane
University of California Santa Barbara
A Survey of Topological Neural Networks
Topological Neural Networks (TNNs) are deep learning architectures that process signals defined on topological domains, such as hypergraphs and cellular complexes -- hence generalizing Graph Neural Networks. The additional flexibility and expressivity of TNN architectures permits the representation and processing of complex natural systems such as proteins, neural activity, and many-body physical systems. This talk synthesizes the recent TNN literature using a single unifying notation and graphical summaries and sheds light on existing challenges and exciting opportunities for future development.
Nina Miolane is an Assistant Professor at UCSB. She received her Ph.D. in Computer Science from INRIA (France) in collaboration with Stanford University. Nina worked as a postdoc at Stanford, and as a software engineer in the Silicon Valley. At UCSB, Nina’s research focuses on AI for biological shape analysis: she investigates how the shapes of proteins, cells, and organs relate to their biological functions, and how abnormal shape changes correlate with pathologies. Her team also co-develops Geomstats, an open-source software of geometric machine learning. Research fundings include a NIH R01 grant, the NSF SCALE MoDL. Nina was the recipient of the L'Oréal-Unesco for Women in Science Award and a winner of the C3.ai grand Covid-19 challenge.
Dr. Vitaliy Kurlin
Materials Inovation Factory
Recognizing Rigid Patterns of Unlabeled Point Clouds
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry that maintains all inter-point distances. Rigid patterns of point clouds can be fully identified only by complete isometry invariants (also called equivariant descriptors) that should have no false negatives (isometric clouds having different descriptions) and no false positives (non-isometric clouds with the same description). Noise in data motivates a search for invariants that are continuous under perturbations of points in a suitable metric. We propose a continuous and complete invariant for finite clouds of unlabeled points in any Euclidean space. For a fixed dimension, a new metric for this invariant is computable in a polynomial time in the number of points. The talk is based on the CVPR 2023 paper with Daniel Widdowson.
Prof Vitaliy Kurlin is a universal scientist, a mathematician by training, now leading the Data Science Theory and Applications group in the Materials Innovation Factory, Liverpool, UK. He completed a PhD in Geometry and Topology at Moscow State University in 2003 and held a Marie Curie International Incoming Fellowship in 2005-2007 and a Royal Academy of Engineering Industry Fellowship in 2021-2023. His group is developing a new area of Geometric Data Science whose key results include the Crystal Isometry Principle (NeurIPS 2022) and complete invariants of finite clouds of unlabeled points under Euclidean isometry (CVPR 2023), see details.
Dr. Tegan Emerson
Tegan Emerson received her PhD in Mathematics from Colorado State University. She was a Jerome and Isabella Karle Distinguished Scholar Fellow in optical sciences at the Naval Research Laboratory from 2017-2019. In 2014 she had the honor of being a member of the American delegation at the Heidelberg Laureate Forum. Dr. Emerson is now a Senior Data Scientist and Team Leader in the Data Sciences and Analytics Group at Pacific Northwest Laboratory. In addition to her role at Pacific Northwest National Laboratories, Dr. Emerson also holds Joint Appointments as Affiliate Faculty in the Departments of Mathematics at Colorado State University and the University of Texas, El Paso. Her research interests include geometric and topological data analysis, dimensionality reduction, algorithms for image processing and materials science, deep learning, and optimization.
Dr. Henry Kvinge
Henry Kvinge received his PhD in Mathematics from UC Davis where his research focused on the intersection of representation theory, algebraic combinatorics, and category theory. After two years as a postdoc in the Department of Mathematics at Colorado State University where he worked on the compressive sensing-based algorithms underlying single-pixel cameras, he joined PNNL as a senior data scientist. These days his work focuses on leveraging ideas from geometry, and representation theory to build more robust and adaptive deep learning models and frameworks.
Dr. Tim Doster
Pacific Northwest National Laboratory
Tim Doster is a Senior Data Scientist at the Pacific Northwest National Laboratory. He received the B.S. degree in computational mathematics from the Rochester Institute of Technology in 2008 and the Ph.D. degree in applied mathematics and scientific computing from the University of Maryland, College Park, in 2014. From 2014 to 2016, he was a Jerome and Isabella Karle Distinguished Scholar Fellow before becoming a Permanent Research Scientist in the Applied Optics division with the U.S. Naval Research Laboratory. During his time with the U.S. Naval Research Laboratory he won the prestigious DoD Laboratory University Collaboration Initiative (LUCI) grant. His research interests include machine learning, harmonic analysis, manifold learning, remote sensing, few-shot learning, and adversarial machine learning.
Dr. Bastian Rieck
Bastian Rieck, M.Sc., Ph.D. is the Principal Investigator of the AIDOS Lab at the Institute of AI for Health at Helmholtz Munich, focusing on topology-driven machine learning methods in biomedicine. Bastian is also a faculty member of TUM, the Technical University of Munich, and a member of ELLIS, the European Laboratory for Learning and Intelligent Systems. Wearing yet another hat, he serves as the co-director of the Applied Algebraic Topology Research Network. Bastian received his M.Sc. degree in mathematics, as well as his Ph.D. in computer science, from Heidelberg University in Germany. He is a big proponent of scientific outreach and enjoys blogging about his research, academia in general, and software development.
Dr. Alex Cloninger
University of California, San Diego
Halıcıoğlu Data Science Institute
Alex Cloninger is an Associate Professor in Mathematics and the Halıcıoğlu Data Science Institute at UC San Diego. He received his PhD in Applied Mathematics and Scientific Computation from the University of Maryland in 2014, and was then an NSF Postdoc and Gibbs Assistant Professor of Mathematics at Yale University until 2017, when he joined UCSD. Alex researches problems in the area of geometric data analysis and applied harmonic analysis. He focuses on approaches that model the data as being locally lower dimensional, including data concentrated near manifolds or subspaces. These types of problems arise in a number of scientific disciplines, including imaging, medicine, and artificial intelligence, and the techniques developed relate to a number of machine learning and statistical algorithms, including deep learning, network analysis, and measuring distances between probability distributions.
Dr. Sarah Tymochko
University of California, Los Angles
Dr. Sarah Tymochko received her PhD in mathematics in 2022 from the Michigan State University in the Department of Computational Mathematics, Science, and Engineering under the advisorship of Dr. Liz Munch. Her dissertation research focuses on topological tools for time series analysis. In 2017 she recieved a B.A. in mathematics from College of the Holy Cross in Worcester, MA. Her research interests include topological data analysis, dynamical systems, time series analysis, network science, and machine learning.