DYNAMIC NETWORK OF CONCEPTS FROM WEB-PUBLICATIONS
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1 DYNAMIC NETWORK OF CONCEPTS FROM WEB-PUBLICATIONS Lande D.V. IC «ELVISTI», NTUU «KPI» Snarsk A.A. NTUU «KPI» The network, the nodes of whch are concepts (people's names, companes' names, etc.), extracted from web-publcatons, s consdered. A workng algorthm of extractng such concepts s presented. Edges of the network under consderaton refer to the reference frequency whch depends on the fact how many tmes the concepts, whch correspond to the nodes, are mentoned n the same documents. Web-documents beng publshed wthn a perod of tme together form an nformaton flow, whch defnes the dynamcs of the network studed. The phenomenon of ts structure stablty, when the number of webpublcatons, consttutng ts formaton bases, ncreases, s dscussed. Key words: complex network, network of concepts, dynamc network, extracton of concepts, nternet-content The analyss of complex networks havng a socal nature s a topc of present nterest n the research. Recently, a separate branch of dscrete mathematcs, whch s called the theory of complex networks, has been formed; t studes network characterstcs takng nto account not only ther topology, but also the dstrbuton of reference frequency of ndvdual nodes [1]. Today ths s a very actual theory n dentfyng and vsualzng varous communtes, ther nternal correlatons. A fast development of the Internet content made a great mpetus on the development of theoretcal and appled ssues of the theory of complex networks. Ths research s devoted to the analyss of the network relatons of the concepts (people's names), extracted from the nonstructured texts. Document fles, scanned from the Internet usng the InfoStream system of content-montorng, were used as an example [2]. Whle developng the network of concepts, algorthms of automated extracton of concepts from non-structured texts were used. Many works were devoted to these technologes (see, for example [3, 4]). It s worth mentonng that the approaches to the extracton of varous types of concepts from the texts dffer consderably both by ther presentaton context and structural features. To dentfy the document's belongng to a thematc column, requests made n a specal way and n nformaton-retreval languages, ncludng logc and context operators, parentheses, etc., can be used. To dentfy geographcal names mples the use of tables, where, except for spellng templates of these names, country codes, regon and town names are used. As an example, we can gve a bref descrpton of algorthm dentfcaton of company names n document texts. A document comes n the system entrance; t s analyzed n the process of sequent scannng. The document text s compared wth templates, correspondng names of well-known frms, and n case of ther exstence, they are placed n a specal table "document-frm". In addton, the extracton system of photographs envsages the dentfcaton of prmarly unknown companes' names based on both templates and structural studyng of the text. In partcular, a table of suffx of the companes' names, contanng such elements as "Inc", "Corp.", "Ltd", "Company" and others, s used. Another knd of concepts, such as "persons", s extracted from texts based on the rules whch consder tables of allowable names and surnames, ntal templates, possble varants of jont spellng of ntals/names and surnames. It s mportant to state that the above-mentoned InfoStream system contans means of concept extracton, and presents them to the users n the form of "nformaton portrats", whch have such concepts as key words, geographcal names, surnames of people, names of the companes etc. The propertes of the networks, formed wth concepts, whch are connected wth each other by beng mentoned n the same documents, are descrbed n ths work. The network formed wth people's names, extracted from Internet-meda text fles accordng to common poltcal topcs durng 1
2 1 (one) month and n 55 thousand documents, was studed more thoroughly. Over 19 thousand persons were mentoned n the texts. As t has been found out n the framework of ths research, the dstrbuton of reference frequency of persons n the text fle under consderaton corresponds to Tsypfa law [3] (Fg. 1). The network of concepts, whose nodes are persons, and edges connectng the nodes correspond to the number of references of the persons n the same documents, s researched. The network formed wth concepts, extracted from text flows, s not statc, and t depends on new documents whch appear constantly, and correspondng concepts are extracted from them. Thus, to understand the structure of such network, t s necessary to take nto account ts evoluton [6]. Let us look at some mportant characterstcs from the theory of complex networks, whch are consdered n the context of ths work. Fg. 1. Plot of dstrbuton of reference frequency of persons n a logarthmc scale The dstance between nodes can be defned as a quantty of steps to be taken to get from one node to the other. Naturally, nodes can be connected drectly or ndrectly. It s possble to ntroduce a concept of an average dstance for the whole system,.e., the shortest way between pars of nodes. But some networks can be unbound (a network of persons, for example), t means that there mght be nodes wth an nfnte dstance between them. Correspondngly, an average dstance may appear to be nfnte as well. To keep record of such cases, we ntroduce a concept of an average nverse dstance between nodes, whch s calculated as follows: 2 1 l =, n( n 1) > j d j where dj the shortest dstance between nodes and j. The edges of the ntal network are gven weght meanngs, equal to the number of documents (a document flow from Internet-meda s analyzed), n whch persons of correspondng nodes are mentoned. To prevent "nose", edges wth the weght less than 2, were gnored. Developng the network wth a fxed number of persons (e.g., n Fg. 2 a network wth 50 persons s consdered), whch s realzed through the ncrease of the number of documents under consderaton, an average nverse dstance between nodes ncreases reachng ts logcal saturaton. 2
3 Fg. 2. Dynamcs of changng an average nverse dstance (Y-axs) when the number of documents ncreases (X-axs) The coeffcent of clusterng [6] characterzes the tendency to the development of groups of nterconnected nodes, so-called clques. For a separate node of the network, havng a degree k,.e., whch k edges come from, connectng t wth other k nodes (so-called the nearest neghbors), ths parameter s defned as the rato between a real quantty of edges, connectng the nearest neghbors among themselves, and a maxmum possble one. If to assume that the nearest neghbors are connected drectly wth each other, the quantty of edges between them would be 1 ( 1). 2 k k Hence, clusterng coeffcent s the number that corresponds to a maxmum possble number of edges whch could connect the nearest neghbors of a chosen node. The level of clusterng for the whole network s defned as a rated sum (based on the quantty of nodes) of correspondng coeffcents of ndvdual nodes. Naturally, when the network under consderaton (consstng of a fxed quantty of concepts) s developed, and the number of analyzed documents ncreases, the quantty of edges ncreases constantly and clusterng coeffcent can reach meanngs whch are close to one (Fg. 3). Fg. 3. Dynamcs of changng clusterng coeffcent (Y-axs) when the number of documents ncreases (X-axs). 3
4 One of the man characterstcs of the network nodes s betweenness, whch s smlar to load, a term used n lterary sources sometmes. Ths feature expresses the role of the node n establshng connectons n the network and shows how many shortest ways come through t; t s also tradtonal for socology where persons wth a hgh level of betweenness play a leadng role n establshng contacts wth other persons. Obvously, betweenness coeffcent ( b ) s complementary to clusterng. One of the results receved n the context of ths research s the establshment of the fact that nodes of the person network under consderaton wth a maxmum quantty of edges (a degree) possess the hghest level of betweenness n most cases (Fg.4); ths s the reason why they can rather be vewed as the elements whch connect separate person groups than as the bass for developng clusters under automated groupng. Fg. 4. Coeffcents b (Y-axs) for nodes, ranged by a degree An mportant characterstc of the network s the dstrbuton of node degrees P( k ), whch s defned as probablty that the node has a degree k = k. The networks, characterzed by varous P( k), demonstrate dfferent behavor. In some cases P( k ) can be Posson dstrbuton, exponental or degree dstrbuton. The networks wth exponental dstrbuton of node degrees are called scalefree. It s scale-free dstrbutons that are observed n really exstng complex networks. The exstence of nodes wth a very hgh degree s possble n degree dstrbuton; n fact they do not occur n the networks wth Posson or exponental dstrbutons. In a developng network under consderaton wth a fxed quantty of nodes correspondng to persons and an ncreasng number of documents, at frst the dstrbuton appeared to be close to a degree dstrbuton and then to a Posson dstrbuton (Fg. 5). Ths s explaned by the fact that at frst node degrees have a systematc nature correspondng to real connectons, and then due to a large quantty of "occasonal contacts" whch occur wth large number of documents, the network becomes closer to an occasonal one n whch a great number of nodes are connected wth numerous other ones (Fd. 6, 7). 4
5 а) b) Fg. 5. Dstrbuton of network degrees: а) Low relaton of the scope of text fles to the number of persons (1000:250); b) hgh relaton (50000:250) Fg. 6. Dynamcs of the network development when the number of documents n a text fle ncreases Fg. 7. Network, close to a degradaton condton: 50 persons, documents As t wll be shown below, when the network under consderaton s analyzed, the dstrbuton of weght meanngs of ts edges, when varous scopes of document flows are consdered and whose rank dstrbuton are shown n Fg. 8, s of great mportance. 5
6 Fg. 8. Dstrbuton of network edge weght (X-axs) wth 50 persons n a logarthmc scale (Y-axs) for web-publcaton fles wth 1000, and documents To avod the network degradaton, assocated wth the accumulaton of "occasonal contacts", let us determne a supermposed network, correspondng to the desred one, wth some rough meanngs of edge weghts, namely, wth help of the equaton: 1, v εvmax v ' = 0, v < εvmax v ' - weght of the edge of a supermposed network, v - weght of the edge of the ntal v - maxmum meanng of the edge weght, ε - coeffcent of rough estmate. where person network, max As the measurements show, weght meanngs of the network edges are dstrbuted exponentally on a larger area; t allows assumng: a r v = e +λ, where v - edge weght of a person network, correspondng to a certan number of nput documents D, a - a coeffcent, dependng on meanng D, λ - a constant, r - meanng of the edge rank (numbers of decreasng rankng of weght meanngs of edges). Let us assume that for some r < ε ) the followng s performed: a r a v e +λ ε e = = ε. = (0 1 In ths case for some quantty of nput documents followng wll be performed: v = e = e = ε e e e = ε e k r ε a +λr a a + a +λr a a a a k ε k ε k k 6 D k for the same meanng r = r ε the Thus, n accordance wth a suggested model, where ε expresses a threshold meanng n the condtons of rough estmate of a supermposed model, total meanngs of all v ' (a quantty of edges n a supermposed network) appear to be a constant quantty. The studyng of real data showed that the meanngs of an average dstance and clusterng appeared to be constant as well. The effect proves the stablty of a supermposed network and ts relatve ndependence from the scopes of n-comng documents. In partcular, for meanng ε =0.001, 50 persons and the quantty of documents rangng from 1000 to 50000, a clusterng coeffcent was 0.78 ± 0.01, and the average nverse dstance ± The emprc results receved can be useful, for example, for theoretcal descrpton and modelng of socal and technologcal processes, dentfyng and vsualzng mplct connectons of separate objects or subjects n a compettve survey..
7 The stablzaton phenomenon of a supermposed network makes t possble to practcally dentfy stable connectons, to reduce the effect of nose factors through the analyss of relatvely small document fles. Alongsde wth ths, the ssue of the estmaton of the correlaton of the receved nformaton person connectons calculated by countng document frequency, where persons are mentoned together and real nterconnectons, remans open/not studed. It s necessary to state that the stablzaton of a supermposed network was studed where ε was hgher than a threshold unt. At the same tme, n vew of an exponental nature of the dstrbuton of weght meanngs of the edges n the ntal network, probably the part of connectons, gnored by us, s as complcated as the whole network. In a concluson, the authors would lke to thank the staff members of the Informaton center ElVst, S. M. Brachevsky and A.T. Darmokhval for ther partcpaton n constructve dscussons of partcular aspects, presented n ths work, and for ther assstance n makng calculatons. Reference 1. Newman M.E.J. The structure and functon of complex networks. // SIAM Revew Vol. 45. pp Brachevsk, S.M. Lande, D.V. Urgent aspects of current nformaton flow // Scentfc and techncal nformaton processng / - Allerton press, nc. Vol 32, part P Ralph Grshman. Informaton extracton: Technques and challenges.in Informaton Extracton (Internatonal Summer School SCIE-97). Sprnger-Verlag, Lande, D., Darmokhval A., Morozov A. The approach to duplcaton detecton n news nformaton flows // In Proc. Of the 8th Russan Conference on Dgtal Lbrares RCDL 2006, Suzdal, Russa, P Avalable onlne: 5. Newman M. E. J., Barabas A. L., Watts D. J. The Structure and Dynamcs of Networks (Prnceton Unversty Press, Prnceton, New Jersey, 2006). 6. Watts, D.J. Small Worlds: The Dynamcs of Networks between Order and Randomness (Prnceton Unversty Press, Prnceton, NJ, 1999). 7
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