---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20293'
abstract:
- lang: eng
text: Motivated by questions arising at the intersection of information theory and
geometry, we compare two dissimilarity measures between finite categorical distributions.
One is the well-known Jensen–Shannon divergence, which is easy to compute and
whose square root is a proper metric. The other is what we call the minmax divergence,
which is harder to compute. Just like the Jensen–Shannon divergence, it arises
naturally from the Kullback–Leibler divergence. The main contribution of this
paper is a proof showing that the minmax divergence can be tightly approximated
by the Jensen–Shannon divergence. The bounds suggest that the square root of the
minmax divergence is a metric, and we prove that this is indeed true in the one-dimensional
case. The general case remains open. Finally, we consider analogous questions
in the context of another Bregman divergence and the corresponding Burbea–Rao
(Jensen–Bregman) divergence.
acknowledgement: "This research received partial funding from the European Research
Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation
programme, grant no. 788183, the\r\nWittgenstein Prize, Austrian Science Fund (FWF),
grant no. Z 342-N31, the DFG Collaborative\r\nResearch Center TRR 109, ‘Discretization
in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35, and
the 2022 Google Research Scholar Award for project ‘Algorithms for Topological Analysis
of Neural Networks’. The APC was waived."
article_number: '854'
article_processing_charge: Yes
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
citation:
ama: Akopyan A, Edelsbrunner H, Virk Z, Wagner H. Tight bounds between the Jensen–Shannon
divergence and the minmax divergence. Entropy. 2025;27(8). doi:10.3390/e27080854
apa: Akopyan, A., Edelsbrunner, H., Virk, Z., & Wagner, H. (2025). Tight bounds
between the Jensen–Shannon divergence and the minmax divergence. Entropy.
MDPI. https://doi.org/10.3390/e27080854
chicago: Akopyan, Arseniy, Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. “Tight
Bounds between the Jensen–Shannon Divergence and the Minmax Divergence.” Entropy.
MDPI, 2025. https://doi.org/10.3390/e27080854.
ieee: A. Akopyan, H. Edelsbrunner, Z. Virk, and H. Wagner, “Tight bounds between
the Jensen–Shannon divergence and the minmax divergence,” Entropy, vol.
27, no. 8. MDPI, 2025.
ista: Akopyan A, Edelsbrunner H, Virk Z, Wagner H. 2025. Tight bounds between the
Jensen–Shannon divergence and the minmax divergence. Entropy. 27(8), 854.
mla: Akopyan, Arseniy, et al. “Tight Bounds between the Jensen–Shannon Divergence
and the Minmax Divergence.” Entropy, vol. 27, no. 8, 854, MDPI, 2025, doi:10.3390/e27080854.
short: A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025).
corr_author: '1'
date_created: 2025-09-07T22:01:33Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-09-30T14:32:31Z
day: '01'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.3390/e27080854
ec_funded: 1
external_id:
isi:
- '001557476000001'
pmid:
- '40870326'
file:
- access_level: open_access
checksum: 65c5399c4015d9c8abb8c7a96f3d7836
content_type: application/pdf
creator: dernst
date_created: 2025-09-08T07:55:48Z
date_updated: 2025-09-08T07:55:48Z
file_id: '20309'
file_name: 2025_Entropy_Akopyan.pdf
file_size: 379340
relation: main_file
success: 1
file_date_updated: 2025-09-08T07:55:48Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
issue: '8'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z00342
name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Entropy
publication_identifier:
eissn:
- 1099-4300
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tight bounds between the Jensen–Shannon divergence and the minmax divergence
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 27
year: '2025'
...
---
_id: '9630'
abstract:
- lang: eng
text: Various kinds of data are routinely represented as discrete probability distributions.
Examples include text documents summarized by histograms of word occurrences and
images represented as histograms of oriented gradients. Viewing a discrete probability
distribution as a point in the standard simplex of the appropriate dimension,
we can understand collections of such objects in geometric and topological terms. Importantly,
instead of using the standard Euclidean distance, we look into dissimilarity measures
with information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable the usage of existing computational topology software
in this context.
acknowledgement: This research is partially supported by the Office of Naval Research,
through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR
109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of
the Austrian Science Fund (FWF).
article_processing_charge: Yes
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Hubert
full_name: Wagner, Hubert
id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0009-0009-9111-8429
citation:
ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information
space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7
apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis
in information space. Journal of Computational Geometry. Carleton University.
https://doi.org/10.20382/jocg.v11i2a7
chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data
Analysis in Information Space.” Journal of Computational Geometry. Carleton
University, 2020. https://doi.org/10.20382/jocg.v11i2a7.
ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information
space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University,
pp. 162–182, 2020.
ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information
space. Journal of Computational Geometry. 11(2), 162–182.
mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.”
Journal of Computational Geometry, vol. 11, no. 2, Carleton University,
2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.
short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11
(2020) 162–182.
corr_author: '1'
date_created: 2021-07-04T22:01:26Z
date_published: 2020-12-14T00:00:00Z
date_updated: 2026-04-02T14:35:31Z
day: '14'
ddc:
- '510'
- '000'
department:
- _id: HeEd
doi: 10.20382/jocg.v11i2a7
file:
- access_level: open_access
checksum: f02d0b2b3838e7891a6c417fc34ffdcd
content_type: application/pdf
creator: asandaue
date_created: 2021-08-11T11:55:11Z
date_updated: 2021-08-11T11:55:11Z
file_id: '9882'
file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf
file_size: 1449234
relation: main_file
success: 1
file_date_updated: 2021-08-11T11:55:11Z
has_accepted_license: '1'
intvolume: ' 11'
issue: '2'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 162-182
project:
- _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316
grant_number: I4887
name: Persistent Homology, Algorithms and Stochastic Geometry
publication: Journal of Computational Geometry
publication_identifier:
eissn:
- 1920-180X
publication_status: published
publisher: Carleton University
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological data analysis in information space
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode
name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
short: CC BY (3.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 11
year: '2020'
...
---
_id: '521'
abstract:
- lang: eng
text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y
induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful
in showing that the classical dimension raising theorems hold in large scale;
that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and
Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely
n-to-1 maps, which include the natural quotient maps via a finite group action,
and prove that they preserve the asymptotic dimension.
article_processing_charge: No
arxiv: 1
author:
- first_name: Kyle
full_name: Austin, Kyle
last_name: Austin
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
citation:
ama: Austin K, Virk Z. Higson compactification and dimension raising. Topology
and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005
chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.
ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology
and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.
ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology
and its Applications. 215, 45–57.
mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.
short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.
corr_author: '1'
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-09-18T09:47:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
external_id:
arxiv:
- '1608.03954'
isi:
- '000390501400005'
intvolume: ' 215'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.03954
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 215
year: '2017'
...
---
_id: '737'
abstract:
- lang: eng
text: We generalize Brazas’ topology on the fundamental group to the whole universal
path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
basic properties of the new notion and provide a complete comparison of the obtained
topology with the established topologies, in particular with the Lasso topology
and the CO topology, i.e., the topology that is induced by the compact-open topology.
It turns out that the new topology is the finest topology contained in the CO
topology, for which the action of the fundamental group on the universal path
space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
full_name: Virk, Ziga
id: 2E36B656-F248-11E8-B48F-1D18A9856A87
last_name: Virk
- first_name: Andreas
full_name: Zastrow, Andreas
last_name: Zastrow
citation:
ama: Virk Z, Zastrow A. A new topology on the universal path space. Topology
and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
apa: Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015
chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.
ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology
and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.
ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
and its Applications. 231, 186–196.
mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.
short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
corr_author: '1'
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2026-04-16T10:04:39Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
isi:
- '000413889100012'
intvolume: ' 231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 231
year: '2017'
...