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In the case where <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$V={\\mathbb {R}}^d$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:msup>\n                      <mml:mrow>\n                        <mml:mi>R<\/mml:mi>\n                      <\/mml:mrow>\n                      <mml:mi>d<\/mml:mi>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and <jats:italic>G<\/jats:italic> is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$V=L^2({\\mathbb {R}}^d)$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>V<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:msup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:msup>\n                        <mml:mrow>\n                          <mml:mi>R<\/mml:mi>\n                        <\/mml:mrow>\n                        <mml:mi>d<\/mml:mi>\n                      <\/mml:msup>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and <jats:italic>G<\/jats:italic> 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.<\/jats:p>","DOI":"10.1007\/s10208-024-09656-9","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T20:18:20Z","timestamp":1715977100000},"page":"1047-1084","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Group-Invariant Max Filtering"],"prefix":"10.1007","volume":"25","author":[{"given":"Jameson","family":"Cahill","sequence":"first","affiliation":[]},{"given":"Joseph W.","family":"Iverson","sequence":"additional","affiliation":[]},{"given":"Dustin G.","family":"Mixon","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Packer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,17]]},"reference":[{"key":"9656_CR1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/12089939X","volume":"7","author":"B Alexeev","year":"2014","unstructured":"B. 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