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In the past decade, topological data analysis has emerged as a powerful algebraic topology approach in data science. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a paradigm that incorporates curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale and offers a multiscale geometric topology approach to capture the local structures and connectivities in data. By integration with machine learning or deep learning, the proposed mGLI significantly outperforms other state-of-the-art methods across various benchmark problems in 13 intricately complex biological datasets, including protein flexibility analysis, protein–ligand interactions, human Ether-à-go-go-Related Gene potassium channel blockade screening, and quantitative toxicity assessment. Our KDA opens a research area—knot deep learning—in data science.
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Spatially weighted structural similarity index: a multiscale comparison tool for diverse sources of mobility data
Data collected about routine human activity and mobility is used in diverse applications to improve our society. Robust models are needed to address the challenges of our increasingly interconnected world. Methods capable of portraying the dynamic properties of complex human systems, such as simulation modeling, must comply to rigorous data requirements. Modern data sources, like SafeGraph, provide aggregate data collected from location aware technologies. Opportunities and challenges arise to incorporate the new data into existing analysis and modeling methods. Our research employs a multiscale spatial similarity index to compare diverse origin-destination mobility datasets. Established distance ranges accommodate spatial variability in the model’s datasets. This paper explores how similarity scores change with different aggregations to address discrepancies in the source data’s temporal granularity. We suggest possible explanations for variations in the similarity scores and extract characteristics of human mobility for the study area. The multiscale spatial similarity index may be integrated into a vast array of analysis and modeling workflows, either during preliminary analysis or later evaluation phases as a method of data validation (e.g., agent-based models). We propose that the demonstrated tool has potential to enhance mobility modeling methods in the context of complex human systems.
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- Award ID(s):
- 2031407
- PAR ID:
- 10381900
- Editor(s):
- Ossi, Federico; Hachem, Fatima; Robira, Benjamin; Ellis Soto, Diego; Rutz, Christian; Dodge, Somayeh; Cagnacci, Francesca; Damiani, Maria Luisa
- Date Published:
- Journal Name:
- Proceedings of the 2nd ACM SIGSPATIAL International Workshop on Animal Movement Ecology and Human Mobility
- Page Range / eLocation ID:
- 19 to 22
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3557921.3565542
