On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification
Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the ma...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Torshin, I. Yu. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Pattern recognition and image analysis - Moscow : MAIK Nauka/Interperiodica Publ., 1996, 25(2015), 4 vom: Okt., Seite 577-587 |
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| Übergeordnetes Werk: |
volume:25 ; year:2015 ; number:4 ; month:10 ; pages:577-587 |
| Links: |
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| DOI / URN: |
10.1134/S1054661815040252 |
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| Katalog-ID: |
SPR020180047 |
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| 100 | 1 | |a Torshin, I. Yu. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
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| 520 | |a Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. | ||
| 650 | 4 | |a algebraic approach |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a metric analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a the theory of classification of feature values |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a metric condensations |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a combinatorial theory of solvability |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Rudakov, K. V. |4 aut | |
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10.1134/S1054661815040252 doi (DE-627)SPR020180047 (SPR)S1054661815040252-e DE-627 ger DE-627 rakwb eng Torshin, I. Yu. verfasserin aut On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 Rudakov, K. V. aut Enthalten in Pattern recognition and image analysis Moscow : MAIK Nauka/Interperiodica Publ., 1996 25(2015), 4 vom: Okt., Seite 577-587 (DE-627)327148179 (DE-600)2044032-7 1555-6212 nnns volume:25 year:2015 number:4 month:10 pages:577-587 https://dx.doi.org/10.1134/S1054661815040252 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 10 577-587 |
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10.1134/S1054661815040252 doi (DE-627)SPR020180047 (SPR)S1054661815040252-e DE-627 ger DE-627 rakwb eng Torshin, I. Yu. verfasserin aut On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 Rudakov, K. V. aut Enthalten in Pattern recognition and image analysis Moscow : MAIK Nauka/Interperiodica Publ., 1996 25(2015), 4 vom: Okt., Seite 577-587 (DE-627)327148179 (DE-600)2044032-7 1555-6212 nnns volume:25 year:2015 number:4 month:10 pages:577-587 https://dx.doi.org/10.1134/S1054661815040252 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 10 577-587 |
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10.1134/S1054661815040252 doi (DE-627)SPR020180047 (SPR)S1054661815040252-e DE-627 ger DE-627 rakwb eng Torshin, I. Yu. verfasserin aut On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 Rudakov, K. V. aut Enthalten in Pattern recognition and image analysis Moscow : MAIK Nauka/Interperiodica Publ., 1996 25(2015), 4 vom: Okt., Seite 577-587 (DE-627)327148179 (DE-600)2044032-7 1555-6212 nnns volume:25 year:2015 number:4 month:10 pages:577-587 https://dx.doi.org/10.1134/S1054661815040252 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 10 577-587 |
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10.1134/S1054661815040252 doi (DE-627)SPR020180047 (SPR)S1054661815040252-e DE-627 ger DE-627 rakwb eng Torshin, I. Yu. verfasserin aut On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 Rudakov, K. V. aut Enthalten in Pattern recognition and image analysis Moscow : MAIK Nauka/Interperiodica Publ., 1996 25(2015), 4 vom: Okt., Seite 577-587 (DE-627)327148179 (DE-600)2044032-7 1555-6212 nnns volume:25 year:2015 number:4 month:10 pages:577-587 https://dx.doi.org/10.1134/S1054661815040252 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 10 577-587 |
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10.1134/S1054661815040252 doi (DE-627)SPR020180047 (SPR)S1054661815040252-e DE-627 ger DE-627 rakwb eng Torshin, I. Yu. verfasserin aut On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2015 Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 Rudakov, K. V. aut Enthalten in Pattern recognition and image analysis Moscow : MAIK Nauka/Interperiodica Publ., 1996 25(2015), 4 vom: Okt., Seite 577-587 (DE-627)327148179 (DE-600)2044032-7 1555-6212 nnns volume:25 year:2015 number:4 month:10 pages:577-587 https://dx.doi.org/10.1134/S1054661815040252 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 25 2015 4 10 577-587 |
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Torshin, I. Yu. |
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Torshin, I. Yu. misc algebraic approach misc metric analysis misc the theory of classification of feature values misc metric condensations misc combinatorial theory of solvability On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
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On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification algebraic approach (dpeaa)DE-He213 metric analysis (dpeaa)DE-He213 the theory of classification of feature values (dpeaa)DE-He213 metric condensations (dpeaa)DE-He213 combinatorial theory of solvability (dpeaa)DE-He213 |
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On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
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on the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
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On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
| abstract |
Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. © Pleiades Publishing, Ltd. 2015 |
| abstractGer |
Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. © Pleiades Publishing, Ltd. 2015 |
| abstract_unstemmed |
Abstract In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions. © Pleiades Publishing, Ltd. 2015 |
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On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification |
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https://dx.doi.org/10.1134/S1054661815040252 |
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Rudakov, K. V. |
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10.1134/S1054661815040252 |
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2024-07-03T14:23:38.838Z |
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