Function approximation on non-Euclidean spaces
This paper presents a family of layered feed-forward networks that is able to uniformly approximate functions on any metric space, and also on a wide variety of non-metric spaces. Non-Euclidean input spaces are frequently encountered in practice, while usual approximation schemes are guaranteed to w...
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| Veröffentlicht in: | Neural networks 2005, Vol.18 (1), p.91-102 |
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| container_title | Neural networks |
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| creator | Courrieu, Pierre |
| description | This paper presents a family of layered feed-forward networks that is able to uniformly approximate functions on any metric space, and also on a wide variety of non-metric spaces. Non-Euclidean input spaces are frequently encountered in practice, while usual approximation schemes are guaranteed to work only on Euclidean metric spaces. Theoretical foundations are provided, as well as practical algorithms and illustrative examples. This tool potentially constitutes a significant extension of the common notion of ‘universal approximation capability’. |
| doi_str_mv | 10.1016/j.neunet.2004.09.003 |
| format | Article |
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Neural networks</subject><subject>Exact sciences and technology</subject><subject>Feed-forward neural networks</subject><subject>Function approximation</subject><subject>Invariants</subject><subject>Least-Squares Analysis</subject><subject>Neural Networks (Computer)</subject><subject>Non-metric spaces</subject><subject>Pattern Recognition, Automated</subject><subject>Regularization</subject><subject>Space Perception - physiology</subject><subject>Synapses - physiology</subject><issn>0893-6080</issn><issn>1879-2782</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kFFLwzAQx4Mobk6_gche9K31kmZp8yLIcCoMfNHnkF6vkNGls2lFv72ZHexNODgOfv_j7sfYNYeUA1f3m9TT4KlPBYBMQacA2Qmb8iLXicgLccqmUOgsUVDAhF2EsAEAVcjsnE34QkmtlJyydDV47F3r53a369pvt7V_Uyzf-uRpwMZVZP087CxSuGRntW0CXR36jH2snt6XL8n67fl1-bhOUHLdJ6rSmqMCBJ0tVCa1QME1QQWKF2SVrGqCEqWQyAsoRKmRa1HmeSl4XaPIZuxu3Btv-hwo9GbrAlLTWE_tEIzKs5zLXEVQjiB2bQgd1WbXxR-6H8PB7D2ZjRk9mb0nA9pETzF2c9g_lFuqjqGDmAjcHgAb0DZ1Zz26cOSUFAut88g9jBxFG1-OOhPQkUeqXEfYm6p1_1_yC1rihtg</recordid><startdate>2005</startdate><enddate>2005</enddate><creator>Courrieu, Pierre</creator><general>Elsevier Ltd</general><general>Elsevier Science</general><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>2005</creationdate><title>Function approximation on non-Euclidean spaces</title><author>Courrieu, Pierre</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c419t-6d991c60c093563492c219e0d0618ea64dfe0bc424c18082b9c192b77b21ffc23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Connectionism. 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| ispartof | Neural networks, 2005, Vol.18 (1), p.91-102 |
| issn | 0893-6080 1879-2782 |
| language | eng |
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| source | MEDLINE; Access via ScienceDirect (Elsevier) |
| subjects | Algorithms Applied sciences Artificial intelligence Computer science control theory systems Connectionism. Neural networks Exact sciences and technology Feed-forward neural networks Function approximation Invariants Least-Squares Analysis Neural Networks (Computer) Non-metric spaces Pattern Recognition, Automated Regularization Space Perception - physiology Synapses - physiology |
| title | Function approximation on non-Euclidean spaces |
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