On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space
The probability that an entity in a set of entities uniformly distributed in space is the nearest neighbor of its nearest neighbor is evaluated for generic distances in a multidimensional environment. Such an expression is then specialized for systems with norm-based distances and for systems with q...
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| Veröffentlicht in: | IEEE transactions on information theory 2008-09, Vol.54 (9), p.4069-4080 |
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| container_title | IEEE transactions on information theory |
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| creator | Rovatti, R. Mazzini, G. |
| description | The probability that an entity in a set of entities uniformly distributed in space is the nearest neighbor of its nearest neighbor is evaluated for generic distances in a multidimensional environment. Such an expression is then specialized for systems with norm-based distances and for systems with quantized norm- based distance. Examples for scalar products and sup-norm are derived. When applicable, invariances with respect to the underlying distance and entities density are highlighted. Dimensionality effects are investigated. |
| doi_str_mv | 10.1109/TIT.2008.928246 |
| format | Article |
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Such an expression is then specialized for systems with norm-based distances and for systems with quantized norm- based distance. Examples for scalar products and sup-norm are derived. When applicable, invariances with respect to the underlying distance and entities density are highlighted. 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Dimensionality effects are investigated.</description><subject>Applied sciences</subject><subject>Biological system modeling</subject><subject>Biomedical signal processing</subject><subject>Density</subject><subject>Dimensionality effect</subject><subject>Euclidean distances</subject><subject>Exact sciences and technology</subject><subject>Extraterrestrial measurements</subject><subject>Extraterrestrial phenomena</subject><subject>Information processing</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Interference</subject><subject>Multidimensional signal processing</subject><subject>Multidimensional systems</subject><subject>nearest neighbor</subject><subject>Nearest neighbor searches</subject><subject>Poisson point processes</subject><subject>Probability</subject><subject>quantized distances</subject><subject>Routing</subject><subject>Scalars</subject><subject>Studies</subject><subject>Telecommunications and information theory</subject><subject>Wireless communication</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kctLAzEQxoMoWKtnD14WQfGyNe_HUYqPgg_Eel6y2URTttma7B70rzel0oOIp2Fmft_wDR8AxwhOEILqcj6bTzCEcqKwxJTvgBFiTJSKM7oLRhAiWSpK5T44SGmRW8oQHoH6KRT9uy0erY429bn6t_e6i0Xn_p77UDwMbe8bv7Qh-S7otph2ofdh6IZU6NAUz4PO_ZdtipeVNvYQ7DndJnv0U8fg9eZ6Pr0r759uZ9Or-9IQwvuSCKwMUY7UVkuGOEO6IcwJYRslaiKFgVrWBDkrlHYNcYhRyRmnBuZ17cgYnG_urmL3MWTT1dInY9tWB5utVYRyiinlGbz4F0RcICyIYGv09Be66IaYf86UYgozRnCGLjeQiV1K0bpqFf1Sx88KwWqdTZWzqdbZVJtssuLs56xORrcu6mB82sow5IgJSjN3suG8tXa7phxKpRD5Bmvelqo</recordid><startdate>20080901</startdate><enddate>20080901</enddate><creator>Rovatti, R.</creator><creator>Mazzini, G.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Such an expression is then specialized for systems with norm-based distances and for systems with quantized norm- based distance. Examples for scalar products and sup-norm are derived. When applicable, invariances with respect to the underlying distance and entities density are highlighted. Dimensionality effects are investigated.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2008.928246</doi><tpages>12</tpages></addata></record> |
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| ispartof | IEEE transactions on information theory, 2008-09, Vol.54 (9), p.4069-4080 |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Biological system modeling Biomedical signal processing Density Dimensionality effect Euclidean distances Exact sciences and technology Extraterrestrial measurements Extraterrestrial phenomena Information processing Information theory Information, signal and communications theory Interference Multidimensional signal processing Multidimensional systems nearest neighbor Nearest neighbor searches Poisson point processes Probability quantized distances Routing Scalars Studies Telecommunications and information theory Wireless communication |
| title | On the Nearest Neighbor of the Nearest Neighbor in Multidimensional Continuous and Quantized Space |
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