Geodesic
Hierarchical structures and combinatorial problems of information retrieval
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 97-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

We examine combinatorial objects of pyramidal structure. We consider one of the ways of representing rules in hierarchical, sequential structures: the method of decision trees, where each object corresponds to a single node that provides a solution. An algorithm for constructing a decision tree based on the generalized Pascal pyramid is suggested. Also, we propose a method for constructing a search index, which displays the proportion of relevant material and allows one to perform comparisons in the variety of terms based on the weight coefficients of terms and paths.
Keywords: hierarchical structure, partially ordered set, generalized Pascal pyramid, decision-making problem, decision tree, combinatorial algorithm. 
@article{INTO_2023_224_a11,
     author = {O. V. Kuz'min},
     title = {Hierarchical structures and combinatorial problems of information retrieval},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a11/}
}
TY  - JOUR
AU  - O. V. Kuz'min
TI  - Hierarchical structures and combinatorial problems of information retrieval
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 97
EP  - 108
VL  - 224
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_224_a11/
LA  - ru
ID  - INTO_2023_224_a11
ER  - 
%0 Journal Article
%A O. V. Kuz'min
%T Hierarchical structures and combinatorial problems of information retrieval
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 97-108
%V 224
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_224_a11/
%G ru
%F INTO_2023_224_a11
O. V. Kuz'min. Hierarchical structures and combinatorial problems of information retrieval. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 97-108. http://geodesic.mathdoc.fr/item/INTO_2023_224_a11/

[1] Alsvede V., Vegener I., Zadachi poiska, Mir, M., 1982

[2] Balagura A. A., Kuzmin O. V., “Obobschennaya piramida Paskalya i chastichno uporyadochennye mnozhestva”, Obozr. prikl. prom. mat., 14:1 (2007), 88–91

[3] Bondarenko B. A., Obobschennye treugolniki i piramidy Paskalya, ikh fraktali, grafy i prilozheniya, Fan, Tashkent, 1990

[4] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982

[5] Deit K. Dzh., Vvedenie v sistemy baz dannykh, Vilyams, M., 2001 | MR

[6] Dokin V. N., “O treugolnoi skheme razvitiya populyatsii”, Issled. geomagnet. aeronom. fiz. Solntsa., 41 (1975), 104–106

[7] Kristofides N., Teoriya grafov. Algoritmicheskii podkhod, Mir, M., 1978

[8] Kuzmin O. V., Obobschennye piramidy Paskalya i ikh prilozheniya, Nauka, Novosibirsk, 2000 | MR

[9] Kuzmin O. V., Loginov T. A., “Postroenie indeksa relevantnosti s pomoschyu obobschennykh piramid Paskalya”, Vestn. Buryat. un-ta. Ser. 13. Mat. Inform., 2006, no. 3, 40–45

[10] Kuzmin O. V., Seregina M. V., “Verkhnie otsecheniya obobschennoi piramidy Paskalya i ikh interpretatsii”, Zh. Sib. fed. un-ta. Ser. mat. fiz., 3:4 (2010), 533–543

[11] Lebedev V. B. , Fedotov E. A., “Modelirovanie dannykh informatsionnykh sistem metodami teorii reshetok”, Izv. vuzov. Povolzh. reg. Ser. tekh. nauki., 3 (2015), 104–110

[12] Mesarovich M., Mako D., Takakhara I., Teoriya ierarkhicheskikh mnogourovnevykh sistem, Mir, M., 1973

[13] Platonov M. L., Dokin V. N., “Treugolnaya skhema razvitiya populyatsii”, Issled. geomagnet. aeronom. fiz. Solntsa., 35 (1975), 26–31

[14] Saati T., Prinyatie reshenii. Metod analiza ierarkhii, Radio i svyaz, M., 1993

[15] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990

[16] Tiori T., Frai Dzh., Proektirovanie struktur baz dannykh. Kn. 1, Mir, M., 1985

[17] Balagura A. A., Kuzmin O. V., “Generalized Pascal pyramids and their reciprocals”, Discr. Math. Appl., 17 (2007), 619-628 | MR | Zbl

[18] Breiman L., Friedma J., Olshen R., Stone C., Classification and Regression Trees, Wadsworth Books, New York, 1984 | MR | Zbl

[19] Hovland C. I., “Computer simulation of thinking”, Am. Psychologist., 15:11 (1960), 687–693 | DOI

[20] Hunt E. B., Janet M., J. S. Philip J. S., Experiments in Induction, Academic Press, New York, 1966

[21] Kuzmin O. V., “Generalized Pascal's pyramids and decision trees”, Adv. Appl. Discr. Math., 34 (2022), 1–15 | MR

[22] Kuzmin O. V., Balagura A. A., Kuzmina V. V., Khudonogov I. A., “Partially ordered sets and combinatory objects of the pyramidal structure”, Adv. Appl. Discr. Math., 20:2 (2019), 219–236 | Zbl

[23] Kuzmin O. V., Khomenko A. P., Artyunin A. I., “Discrete model of static loads distribution management on lattice structures”, Adv. Appl. Discr. Math., 19:3 (2018), 183–193 | Zbl

[24] Kuzmin O. V., Khomenko A. P., Artyunin A. I., “Development of special mathematical software using combinatorial numbers and lattice structure analysis”, Adv. Appl. Discr. Math., 19:3 (2018), 229–242 | Zbl

[25] Kuzmin O. V., Seregina M. V., “Plane sections of the generalized Pascal pyramid and their interpretations”, Discr. Math. Appl., 20:4 (2010), 377–389 | MR | Zbl

[26] Lovász L., Combinatorial Problems and Exercises, Akadémiai Kiadó, Budapest, 1979 | MR | Zbl

[27] Murthy S. K., “Automatic construction of decision trees from data: A multidisciplinary survey”, Data Mining and Knowledge Discovery., 2 (1998), 345–389

[28] Quinlan J. R., “Induction of decision trees”, Machine Learning., 1 (1986), 81–106 | MR

[29] Quinlan J. R., C4.5: Programs for Machine learning, Morgan Kaufmann Publ., San Mate, 1993 | MR