Computation and Applications of Euclidean and Normed Representations of Massive Data
Abstract
This thesis investigates Euclidean-space and ℓp-norm representations of different forms of data, with a focus on efficient algorithms for computing these representations in settings where the amount of data is very large. The applications of such representations are also discussed: they may be used to summarize the data in a more compact form for downstream tasks while preserving its most salient properties; and further, they may also be used to extract insights about the data that may not be apparent in its original form. This thesis presents novel algorithms for computing Euclidean representations in the case where the data comes with linear structure, as well as in the case where the data comes only with metric, or distance structure. In addition, we give algorithms for computing ℓp-norm representations in linear structured cases. The analyses of these algorithms use tools from geometry, probability, and optimization, and these tools are used to illuminate other algorithms for similar problems.
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BibTeX
@misc{ovsiankin2026computation,
title = {{Computation and Applications of Euclidean and Normed Representations of Massive Data}},
author = {Max Ovsiankin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06329},
eprint = {2609.06329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06329},
}
RIS
TY - UNPB
TI - Computation and Applications of Euclidean and Normed Representations of Massive Data
AU - Max Ovsiankin
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06329
UR - https://arxiv.org/abs/2609.06329
AB - This thesis investigates Euclidean-space and ℓ_p-norm representations of different forms of data, with a focus on efficient algorithms for computing these representations in settings where the amount of data is very large. The applications of such representations are also discussed: they may be used to summarize the data in a more compact form for downstream tasks while preserving its most salient properties; and further, they may also be used to extract insights about the data that may not be apparent in its original form. This thesis presents novel algorithms for computing Euclidean representations in the case where the data comes with linear structure, as well as in the case where the data comes only with metric, or distance structure. In addition, we give algorithms for computing ℓ_p-norm representations in linear structured cases. The analyses of these algorithms use tools from geometry, probability, and optimization, and these tools are used to illuminate other algorithms for similar problems.
ER -