The measurement of similarity in stock data documents collections

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1 The measuremet of similarity i stock data documets collectios Nikitas N. Karaikolas 1 1 Departmet of Iformatics, Techological Educatioal Istitute of Athes, Athes, Greece Tel: , Fax: , k@teiath.gr I this paper we focused o the similarity of documets, stored i a documets collectio, agaist a submitted query. This topic is also kow as Documet versus Query similarity or Nearest Neighbors method. The aalysis of experimetal queries coducted to a collectio of 4984 fiacial documets (related to stock data ad varyig i size from few words to a lot of pages) give us a idicatio that the Nearest Neighbor method presets a "preferece" to short documets agaist loger oes. A ew calculatio of the similarity measure is proposed ad some experimetatio with the ew measure is discussed. 1. Itroductio Iformatio Retrieval Systems (Kowalski G., 1997) have bee used for the retrieval of documets / iformatio relevat to a submitted query. The queries are submitted either i Natural Laguage or i a Commad Laguage. Moder Iformatio Retrieval systems usually preset the retrieved documets i decreasig order accordig to their similarity to the submitted query. 1.1 The measuremet of similarity The earest eighbor problem The problem of similarity for a documet agaist a submitted query, also kow as Documet versus Query similarity or earest eighbors has bee the field of cotiuig research for more tha 20 years (Smeato A.F. & va Reijsberge C.J., 1981). May similarity fuctios / measures, ad algorithms elimiatig the querydocumet comparisos have bee proposed (e.g. (Betley J.L. et al, 1980), (Lucarella D., 1988), (Borlud & Igwere, 1998)). 1.2 The vector space model I the popular vector space model a data set of uique terms is specified, called the idex terms (or keywords) of the documet collectio, ad every documet ca be represeted by a vector, (T 1, T 2,, T ) where T i =1, if the idex term i is preset i the documet, ad 0 otherwise. A query ca be represeted i the same maer. The documet ad query vectors ca be evisioed as a -dimesioal vector space. A vector matchig operatio, based o the cosie correlatio used to measure the cosie of the agle betwee

2 vectors ca be used to compute the similarity. Hece, the followig equatio (e.g. (Lucarella D., 1988)) gives us a well-kow method to measure the similarity of documet D i agaist query Q: q t j ij j= 1 j= q j tij j= 1 j 1 Q q j t ij S( Di, Q) = = (1) L L D i where is the umber of idex terms used i the collectio, t ij is the weight of term j i documet D i ad q j is the weight of term j i the query. The followig two equatios ca be used to measure the terms t ij ad q j : t ij = F ij maxf i (2) q j N = log 2 DOCFREQ (3) j where F ij is the frequecy of term j i documet D i, maxf i is the maximum frequecy of the terms i documet D i, N is the umber of documets i the collectio ad DOCFREQ j is the umber of documets that iclude the idex term j. Accordig to (1) some kid of the documet legth is give by: L D i = 2 j 1 t ij (4) 2. A ew calculatio of the similarity measure The Computer Assisted Iformatio Resources Navigatio (CAIRN) system (Karaikolas N.N., 2007) is a geeral purpose Iformatio Retrieval system based o the popular Vector Space Model (VSM) (Smeato A.F. & va Reijsberge C.J., 1981). CAIRN uses stems for automatic idexig of Greek, Lati ad Multiligual texts. The queries are submitted i Natural Laguage ad the retrieved documets are preseted i decreasig order of similarity. Two earest eighbor algorithms, based o Lucarella (Lucarella D., 1988), were implemeted optimizig both the umber of documets to be evaluated ad the umber of iverted lists to be ispected. The use of the system gave us a idicatio that the Nearest Neighbour Method (ad the related similarity measure) used i CAIRN system presets a preferece to short documets agaist loger oes. Hece, a ew calculatio of the similarity measure was proposed i a previous work related to medical data (Karaikolas N.N. & Skourlas C., 2000). To tackle the problem of "preferece" of short documets agaist loger oes we decreased L D for loger documets suggestig that for the measuremet of the similarity (see equatio 1) is better to use equatio (5) istead of the equatio (4):

3 2 LD = l( tij + e 1) i j= 1 (5) As test base was selected a small collectio (1033 medical documets, 30 queries, ad the file of the relevace assessmets) accessible through the IDOMENEUS techology trasfer server at the Uiversity of Glasgow / Departmet of Computig Sciece (IDOMENEUS server). The experimetatio with the two versios of the system cofirmed our cojecture for the preferece of the first calculatio of the similarity measure to short documets agaist larger oes ad that the proposed calculatio of the measure improves the whole situatio. 3. Results ad discussio 3.1 A outlie of the problem Example Let us cosider the case of the followig query (i Greek) submitted to the CAIRN system: Συγχώνευση Πλαστικών Μακεδονίας και Ομίλου Πετζετάκι The list of relevat documets retrieved by the CAIRN system versio usig the Lucarella measure cotais a short documet ad a loger oe. Short Documet has four terms i commo with the query, while loger documet has five terms i commo with the query. These documets follow: Short Documet: Loger Documet: Συμφωνία υπέγραψε ο όμιλος Πετζετάκι και πιο συγκεκριμένα η θυγατρική του εταιρία Πλαστικά Μακεδονίας με τη Δημόσια Επιχείρηση Αερίου (ΔΕΠΑ) Α.Ε. Ειδικότερα, υπεγράφη σύμβαση για την προμήθεια της Δημόσιας Επιχείρησης Αερίου με σωλήνες πολυαιθυλενίου για το δίκτυο διανομής φυσικού αερίον, ύψους περίπου 1 δισ. δραχμές.τη σύμβαση υπέγραψε ο διευθύνων σύμβουλος της "Πλαστικά Μακεδονίας" κ. Σταύρος Πλακαντωνάκτης παρουσία του υποδιευθυντού τεχνικών προμηθειών της ΔΕΠΑ κ. Στέφανου Οικονομίδη. Μέχρι το τέλος της τρέχουσας χρήσης αναμένεται να ολοκληρωθεί η συγχώνευση της θυγατρικής εταιρίας Πλαστικά Μακεδονίας. του ομίλου Πετζετάκι με τη μητρική Α.Γ. Πετζετάκις ενώ παράλληλα θα προχωρήσει η αξιοποίηση της ακίνητης περιουσίας της θυγατρικής Πλαστικά Καβάλας. Τα παραπάνω ανέφερε ο κ.γ. Πετζετάκις, πρόεδρος και διευθύνων σύμβουλος του ομίλου Πετζετάκι, στην Ένωση Θεσμικών Επενδυτών. Σε ό,τι αφορά τα οικονομικά αποτελέσματα της μητρικής εταιρίας, το 1996, τα κέρδη προφορών κινήθηκαν με ρυθμό αύξησης 41,09%, φθάνοντας τα 312,1 εκατ. δρχ. από 221,2 εκατ. δρχ. το Ο κύκλος εργασιών της εταιρίας εκτιμάται ότι θα ανέλθει σε 16,71 δισ. δρχ., παρουσιάζοντας αύξηση 26,2% από 13,24 δις. δρχ. το Οι συνθήκες ανταγωνισμού που επικρατούν στην αγορά έχουν οδηγήσει στη συμπίεση των περιθωρίων κέρδους και η κατάσταση αυτή αναμένεται να διαφοροποιηθεί μετά το β' εξάμηνο του Η διοίκηση εκτιμά ότι το 1997 τα κέρδη θα διπλασιαστούν και θα φθάσουν τα 640 εκατ. δρχ. ενώ ο κύκλος εργασιών θα προσεγγίσεί τα 20 δις. δραχμές. Ο όμιλος Πετζετάκι προχώρησε στη διετία πρόγραμμα αναδιάρθρωσης με στόχο τη μείωση του κόστους παραγωγής και τη δημιουργία συνθηκών μακροχρόνιας ανάπτυξης. Το πρόγραμμα περιελάμβανε τη διακοπή των ζημιογόνων θυγατρικών (Πλαστικά Καβάλας), την υλοποίηση επενδυτικού προγράμματος με την εγκατάσταση του εργοστασίου των Αθηνών στη Θήβα, τον εκσυγχρονισμό του εργοστασίου των Θηβών και την έντονη δραστηριοποίηση στο κλάδο των πολυολεφινών. Η άλλη θυγατρική εταιρία του

4 ομίλου Πετζετάκι. που είναι εισηγμένη στο ΧΑΑ, τα Πλαστικά Μακεδονίας, παρουσίασαν το 1996 κύκλο εργασιών 6,4 δις. δρχ. από 5,7 δις. δρχ. το 1995 ενώ τα κέρδη προ φόρων μειώθηκαν σε 155 εκατ. δρχ. από 192 εκατ. δρχ. το 1995 The same query also submitted to the versio of CAIRN with the ew calculatio of the similarity measure. The followig table presets the relative positio of these two documets accordig to both algorithms: Documet Positio of Documet accordig to the classic similarity measure Short 1 2 Log 2 1 Positio of Documet accordig to the ew versio of similarity measure Table 1: Order of documets accordig to the classic similarity measure ad our proposal The followig tables 2, 3 also preset the comparative results for aother simple query. Query: Είσοδος του ΟΤΕ στο χρηματιστήριο Etrace of Greek Telecommuicatio Orgaizatio (GTO) i Stock Exchagig Repetitios of Query Terms i documets Documet umber Measuremet of similarity usig (5) Fmax Είσοδος (Etrace) ΟΤΕ (GTO) χρηματιστήριο (Stock Exchagig) Documet's physical size (lies) Table 2: Order of documets accordig to our similarity measure proposal

5 Query: Είσοδος του ΟΤΕ στο χρηματιστήριο Etrace of Greek Telecommuicatio Orgaizatio (GTO) i Stock Exchagig Repetitios of Query Terms i documets Documet umber Measuremet of similarity usig (4) Fmax Είσοδος (Etrace) ΟΤΕ (GTO) χρηματιστήριο (Stock Exchagig) Documet's physical size (lies) Table 3: Order of documets accordig the classic similarity measure 3.2 A detailed compariso As we have already metioed, the test bed for the proposed method is based o a collectio of stock data. Table 4 illustrates our collectio. Three stockbrokers aalyzed the results of their queries i the two differet versios of the system ad evaluated the results. Stockbrokers have evaluated the results of the secod versio (the oe that uses equatio 5) as better oes. The results of the submitted queries were also automatically saved for further study, i both versios of the system.

6 2 t ij j 1 Number of documets [1-10] 287 (10 20] 901 (20 30] 1076 (30 40] 1234 (40 50] 806 (50 60] 346 (60 70] 156 (70 80] 79 (80 90] 30 (90 100] 24 ( ] 19 ( ] 8 ( ] 3 ( ] 6 ( ] 3 ( ] 3 ( ] 3 2 t ij rages from 1 to , its j 1 mea value is ad its variace is Table 4: The rage of Σ i our stock exchage collectio The followig table gives us a compariso of L D measured with equatio (4) ad equatio (5): Σ 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00 15,00 20,00 30,00 40,00 50,00 70,00 90,00 100,00 l(σ+e-1) (5) 1,00 1,31 1,55 1,74 1,90 2,04 2,17 2,27 2,37 2,46 2,82 3,08 3,46 3,73 3,95 4,27 4,52 4,62 sqrt(σ) (4) 1,00 1,41 1,73 2,00 2,24 2,45 2,65 2,83 3,00 3,16 3,87 4,47 5,48 6,32 7,07 8,37 9,49 10,00 Table 5: L D measured with equatio (4) ad equatio (5) 4. Coclusio ad future work I this paper, we suggest a ew calculatio of the measuremet of a documet's legth i order to avoid the Nearest Neighbor method's preferece for the short documets. We tested our method usig a collectio of documets with Σ varyig (i most cases) from 1 to 100 ad the results were positive. CAIRN is a costatly evolvig system. Curretly we are workig to coduct some more experimetatio with the proposed, ew similarity measure to cofirm our

7 cojecture. A bigger Test Collectio will be used, to give us a more accurate evaluatio of the ew calculatio of the measure. We pla to evaluate the method usig loger documets where Σ varies from 1 to 1000 or greater values. We have also some ideas i usig other calculatios of the similarity measure for improvig the effectiveess of the system. The modular desig of the CAIRN iformatio retrieval system has allowed us a great flexibility, ad gives us the possibilities for future ehacemets. Usig modular desig has also allowed us to implemet, easily, differet versios of the system ad coduct experimetatio with alterative similarity measures. Hece, CAIRN system ca be easily modified to icorporate other similarity measures ad take advatage of user s suggested improvemets. Refereces [1] Kowalski G: Iformatio Retrieval Systems. Theory ad Implemetatio, 1st ed (Prited i the USA; Kluwer Academic Publishers), ISBN , [2] A.F. Smeato ad C.J. va Reijsberge, 1981, The Nearest Neighbour problem i Iformatio Retrieval. A algorithm usig upperbouds. ACM SIGIR Forum 16, pp [3] Betley, J. L., Weide, B.W. ad Yao, A. C., 1980, Optimal expected time algorithms for closest poit problems. ACM Tras. Math. Software, 6, pp [4] Lucarella, D., 1988, A documet retrieval system based o earest eighbor searchig. Joural of Iformatio Sciece, 14, [5] Borlud ad Igwere, 1998, Measure of relative relevace ad raked half life: performace idicators for iteractive IR. SIGIR 98, pp [6] Karaikolas N.N. ad Skourlas C., 2000, Computer assisted Iformatio resources avigatio. Medical Iformatics ad the Iteret i Medicie, vol. 25, [7] Karaikolas N.N., 2007, Low cost, cross-laguage ad cross-platform Iformatio Retrieval ad Documetatio tools. Joural of Computig ad Iformatio Techology (CIT), ISSN: , volume 15, No 1. [8] The med.all collectio at the IDOMENEUS server.