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- research-articleJune 2024
Topological Interpretability for Deep Learning
PASC '24: Proceedings of the Platform for Advanced Scientific Computing ConferenceArticle No.: 21, Pages 1–11https://doi.org/10.1145/3659914.3659935With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is ...
- ArticleJuly 2024
Mapper-Based Rough Sets
AbstractThis paper presents a new approach to analyzing numerical data sets using covering-based rough sets based on the Mapper algorithm, a fundamental tool of topological data analysis (TDA). Specifically, by varying the parameters of Mapper, our ...
- research-articleAugust 2024
Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites
It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of ...
- posterNovember 2023
Poster: Computing the Persistent Homology of Encrypted Data
CCS '23: Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications SecurityPages 3546–3548https://doi.org/10.1145/3576915.3624406Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features of high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. Persistent homology (PH) transforms ...
- research-articleOctober 2023
Curiosity as filling, compressing, and reconfiguring knowledge networks
- Shubhankar P Patankar,
- Dale Zhou,
- Christopher W Lynn,
- Jason Z Kim,
- Mathieu Ouellet,
- Harang Ju,
- Perry Zurn,
- David M Lydon-Staley,
- Dani S Bassett
Theoretical constructs, such as the information gap theory and compression progress theory, seek to explain how humans practice curiosity. According to the former, curiosity is the drive to acquire information missing from our understanding of the world. ...
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- research-articleJune 2023
Detection of Fibrillatory Episodes in Atrial Fibrillation Rhythms via Topology-informed Machine Learning
ICMVA '23: Proceedings of the 2023 6th International Conference on Machine Vision and ApplicationsPages 22–27https://doi.org/10.1145/3589572.3589576Effective and efficient methods for diagnosing cardiac conditions remain of significant importance and relevance in clinical cardiology. As such, advances in machine- and deep-learning technologies pave the way to high throughput approaches to ...
- research-articleMarch 2024
Limits of dense simplicial complexes
The Journal of Machine Learning Research (JMLR), Volume 24, Issue 1Article No.: 225, Pages 10640–10681We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0, 1]-valued functions on ...
- research-articleMarch 2024
Intrinsic persistent homology via density-based metric learning
The Journal of Machine Learning Research (JMLR), Volume 24, Issue 1Article No.: 75, Pages 3341–3382We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with a sample ...
- research-articleMarch 2024
Topological convolutional layers for deep learning
The Journal of Machine Learning Research (JMLR), Volume 24, Issue 1Article No.: 59, Pages 2544–2578This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used as ...
- research-articleOctober 2022
Smart Contract Scams Detection with Topological Data Analysis on Account Interaction
CIKM '22: Proceedings of the 31st ACM International Conference on Information & Knowledge ManagementPages 468–477https://doi.org/10.1145/3511808.3557454The skyrocketing market value of cryptocurrencies has prompted more investors to pour funds into cryptocurrencies to seek asset hedging. However, the anonymity of blockchain makes cryptocurrency naturally a tool of choice for criminals to commit smart ...
- short-paperJuly 2022
Topological Analysis of Contradictions in Text
SIGIR '22: Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information RetrievalPages 2478–2483https://doi.org/10.1145/3477495.3531881Automatically finding contradictions from text is a fundamental yet under-studied problem in natural language understanding and information retrieval. Recently, topology, a branch of mathematics concerned with the properties of geometric shapes, has ...
- research-articleJanuary 2022
A computationally efficient framework for vector representation of persistence diagrams
The Journal of Machine Learning Research (JMLR), Volume 23, Issue 1Article No.: 268, Pages 12281–12313In Topological Data Analysis, a common way of quantifying the shape of data is to use a persistence diagram (PD). PDs are multisets of points in R2 computed using tools of algebraic topology. However, this multi-set structure limits the utility of PDs in ...
- research-articleJanuary 2022
Risk analysis of China’s stock markets based on topological data structures
Procedia Computer Science (PROCS), Volume 202, Issue CPages 203–216https://doi.org/10.1016/j.procs.2022.04.028AbstractWe choose 100 stocks from China’s markets and use their daily returns from January 3, 2013 to August 31, 2020 to investigate the risk situation in China’s stock markets by exploring their correlations in the sample period. We build complexes and ...
- research-articleAugust 2021
Pheno-mapper: an interactive toolbox for the visual exploration of phenomics data
BCB '21: Proceedings of the 12th ACM Conference on Bioinformatics, Computational Biology, and Health InformaticsArticle No.: 20, Pages 1–10https://doi.org/10.1145/3459930.3469511High-throughput technologies to collect field data have made observations possible at scale in several branches of life sciences. The data collected can range from the molecular level (genotypes) to physiological (phenotypic traits) and environmental ...
- invited-talkMay 2021
Scalable topological data analysis for life science applications
CF '21: Proceedings of the 18th ACM International Conference on Computing FrontiersPage 208https://doi.org/10.1145/3457388.3459983Enabling discoveries and foundational understanding in modern day life sciences have largely become centered on our ability to effectively analyze large swathes of complex data from a diverse range of sources, capturing complex information encapsulated ...
- research-articleJuly 2021
Analysis of Contagion Maps on a Class of Networks That Are Spatially Embedded in a Torus
SIAM Journal on Applied Mathematics (SJAM), Volume 81, Issue 4Pages 1416–1440https://doi.org/10.1137/18M1235910Spreading processes on networks with some underlying spatial structure can be influenced by that structure, and it is insightful to study the extent to which a spreading process follows a network's underlying geometry. We consider a threshold contagion ...
- research-articleJanuary 2021
giotto-tda: a topological data analysis toolkit for machine learning and data exploration
- Guillaume Tauzin,
- Umberto Lupo,
- Lewis Tunstall,
- Julian Burella Pérez,
- Matteo Caorsi,
- Anibal M. Medina-Mardones,
- Alberto Dassatti,
- Kathryn Hess
The Journal of Machine Learning Research (JMLR), Volume 22, Issue 1Article No.: 39, Pages 1834–1839We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ implementations. The library's ability to handle various types of data is ...
- research-articleJanuary 2021
Persistent Homology of Geospatial Data: A Case Study with Voting
A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (which, in our case, is a simplicial complex). Software packages for computing persistent homology typically construct Vietoris--Rips ...
- research-articleAugust 2020
Voronoi Graph Traversal in High Dimensions with Applications to Topological Data Analysis and Piecewise Linear Interpolation
KDD '20: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data MiningPages 2154–2164https://doi.org/10.1145/3394486.3403266Voronoi diagrams and their dual, the Delaunay complex, are two fundamental geometric concepts that lie at the foundation of many machine learning algorithms and play a role in particular in classical piecewise linear interpolation and regression ...