Group-Invariant Max Filtering.
Saved in:
| Title: | Group-Invariant Max Filtering. |
|---|---|
| Authors: | Cahill, Jameson1 (AUTHOR), Iverson, Joseph W.2 (AUTHOR), Mixon, Dustin G.3,4 (AUTHOR) mixon.23@osu.edu, Packer, Daniel3 (AUTHOR) |
| Source: | Foundations of Computational Mathematics. Jun2025, Vol. 25 Issue 3, p1047-1084. 38p. |
| Subjects: | Inner product spaces, Real variables, Filter banks, Orbits (Astronomy), Machine learning |
| Abstract: | Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where V = L 2 (R d) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice. [ABSTRACT FROM AUTHOR] |
| Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Text: Availability: 1 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 185351220 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Group-Invariant Max Filtering. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cahill%2C+Jameson%22">Cahill, Jameson</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Iverson%2C+Joseph+W%2E%22">Iverson, Joseph W.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mixon%2C+Dustin+G%2E%22">Mixon, Dustin G.</searchLink><relatesTo>3,4</relatesTo> (AUTHOR)<i> mixon.23@osu.edu</i><br /><searchLink fieldCode="AR" term="%22Packer%2C+Daniel%22">Packer, Daniel</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Foundations+of+Computational+Mathematics%22">Foundations of Computational Mathematics</searchLink>. Jun2025, Vol. 25 Issue 3, p1047-1084. 38p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Inner+product+spaces%22">Inner product spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Real+variables%22">Real variables</searchLink><br /><searchLink fieldCode="DE" term="%22Filter+banks%22">Filter banks</searchLink><br /><searchLink fieldCode="DE" term="%22Orbits+%28Astronomy%29%22">Orbits (Astronomy)</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where V = L 2 (R d) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=185351220 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10208-024-09656-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 1047 Subjects: – SubjectFull: Inner product spaces Type: general – SubjectFull: Real variables Type: general – SubjectFull: Filter banks Type: general – SubjectFull: Orbits (Astronomy) Type: general – SubjectFull: Machine learning Type: general Titles: – TitleFull: Group-Invariant Max Filtering. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cahill, Jameson – PersonEntity: Name: NameFull: Iverson, Joseph W. – PersonEntity: Name: NameFull: Mixon, Dustin G. – PersonEntity: Name: NameFull: Packer, Daniel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 16153375 Numbering: – Type: volume Value: 25 – Type: issue Value: 3 Titles: – TitleFull: Foundations of Computational Mathematics Type: main |
| ResultId | 1 |
