ACMD Seminar: Landscapes for Labeled Point Clouds

Evgeniya Lagoda
Ph.D. Candidate, Institute of Mathematics, Freie Universität Berlin

Tuesday, July 1, 2025, 3:00-4:00 PM ET (1:00-2:00 PM MT)

In-person at Bldg. 101 LR-C* with VTC to Boulder 1-4072
Online at: Zoom Gov (email seminar chairs for link to talk)

Abstract: Topological Data Analysis (TDA) is a rapidly developing field that studies the shape of data by identifying and quantifying topological features such as connected components, loops, and higher-dimensional holes. A common step in TDA involves constructing a one-parameter family of simplicial complexes and summarizing their evolving topology via persistence barcodes. Persistence landscapes offer a convenient vectorized representation of these barcodes for use in statistical and machine learning tasks. However, in many real-world settings, data is labeled or partitioned into meaningful subsets, introducing additional structure that standard landscapes do not account for. In this work, we propose a generalization of persistence landscapes that incorporates such subset-based parameterizations. We analyze the theoretical properties of this new invariant and discuss its computational aspects and practical utility through numerical experiments.

Bio: Evgeniya Lagoda has training in classical algebraic topology and is broadly interested in applied topology, in particular in machine learning applications. In the current projects, she is working on topics in metric geometry and topological data analysis. Evgeniya Lagoda recently completed her PhD in Mathematics at Freie Universität Berlin, Germany, as part of the Berlin Mathematical School. Before that, she received her MS from Freie Universität Berlin and BS in Mathematics from California State University, Northridge.

Host: Anthony Kearsley

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

*Safety Precaution: The hallway leading from the Courtyard to the exit closest to B-111 and B-113 will be used by contractors to move debris, machinery, and other supplies, as well as will be heavily trafficked by the contractors throughout the process. Be aware of the safety precautions posted during this time.

Note: Visitors from outside NIST must contact Meliza Lane at least 24 hours in advance.