DECISION HELP SYSTEM SUPPORTED DATA-MINING METHOD

Transcription

1 DECISION HELP SYSTEM SUPPORTED DATA-MINING METHOD Péter Tamás, Norbert Szakály Budapest Unversty of Technology and Economcs Mechancal engneerng Faculty Department of Mechatroncs, Optcs and Engneerng Informatcs Abstract Database of scoloss examnaton stores a lot of data of patents. The exact numbers and the wrtten opnon of doctors are useable n decson about the resoluton of screenng process. The moré method and results of depth scannng are pctures. The conclusons are subjectve. The paper s about a data mnng based method for qualfcaton of case to help of dagnoss. Keywords: scoloss, screenng, moré method, POTSI, computer aded decson 1. Introducton The am of the project was to develop a teachable system whch s able to store all data of examnatons and t s able to suggest a concluson or a dagnoss to doctors based on the database stored cases. 2. Methods The heart of the system a database and selecton of the nearest data and the nterpolaton. 2.1 Database of the system The method of decson makng s the known data mnng method named n-nearest neghbor 1 and the nterpolaton techncs. 2 Data of examnaton s stored n database and upon the vector of actual parameters of examnaton s compared wth all of the stored exams data vector and select the k nearest examnatons. The nearest examnaton that where the dfference between the stored data vectors and the actual data vector s the mnmal one. Concluson can be defned on the subset wth k element, where the known conclusons nterpolated wth a polynomal as the functon of the known parameters. The actual parameters are substtuted nto the nterpolated functon value wll be the suggested concluson. There s a frame system teachable wth measured data and accepted decsons. The am to fnd the closest cases to actual examnaton data set (green n the Fgure 1.). Based ths data the system evaluates the concluson upon the known cases (red n Fgure 1.). 119

2 Data Concl Fgure 1. Schema of the system 2.2 Workng of the system The data of all examnaton are stored n numercal form n database. Concluded data are numercal too. The appled method s a multdmensonal nterpolaton. The frst step s to defne the set of closest data wth help of a query. Let us magne the decson data of the known cases as the multdmensonal functon of the known data! 2.3 The developed mathematcal background Data of examnatons are defned as elements of ntervals. Lmts of ntervals defned by the possble maxmum and mnmum of these values [x mn,x max ] where =1,...N and N s the number of known and accepted cases. That means data are n an nterval of N dmenson. [x 1 mn, x 1 max ] x [x 2 mn, x 2 max ]x...x[x N mn, x N max ] = X (1) Smlarly the accepted conclusons are n an nterval of P dmenson. [y 1 mn, y 1 max ]x[y 2 mn, y 2 max ]x...x[y P mn, y P max ] = Y (2) The bass of work s to fnd the functon ф mappng the known data to known conclusons. Ф : X Y ; Ф(x) = y; x Є X and y Є Y (3) 120

3 If ф functon s known we can substtute the questonable examnaton data n t and the suggeston wll be the functon values. Because of numercal stablty t s worth to project all nterval nto [0,1]. Let the I and j the normalzer functons. : [x mn,x max] [0,1] ; (x) = ξ ; j : [y j mn,y j max] [0,1] ; j(y) = η ; =1 N and j=1 P x Є X and y Є Y ξ Є [0,1] N and η Є [0,1] P (4) Usng the normalzed data we search for the ф functon. It can be computed from (3) and (4). ф : [0,1] N [0,1] P ; ф ( ξ) = η ; ξ Є [0,1] N and η Є [0,1] P (5) The followng shows the defnton of ф functon. In the frst step we search for the functon n thrd order: N 3 2 j ( x ) (a b c d 1 ) j 1...P (6) We can select the 4N closest records to the questonable one based on the Eucldan norm. The nterpolaton functon of ф s defned wth the 4N equatons for 4N unknown a,,j, b, c, d coeffcent. If the equaton system s solvable then we are ready. We can substtute the questonable data end we get the suggestons. If t s not possble to solve the equaton system (there s no enough data or there s a sngularty), than the ф functon can be searched for the followng form N 2 j ( x ) (a b c 1 ) j 1...P (7) In ths case we have to select the closest 3N records from the database. If the nterpolaton ф functon n second order successful, the coeffcents a.,j, b.j, c can be defned we are ready and ф functon s defned. If t was not successful because of there s no enough data or there s a sngularty, than we search for the ф functon upon the 2N closest records n form of (8). 121

4 N j ( x ) (a b 1 ) j 1...P (8) When there are 2N closest records and t s successful to compute a,,j, b coeffcents (=1...N), then ф defnes ф. If t was unsuccessful then t s enough to search the closest record to the actual data. The concluson part of t wll defne ф functon and the ф functon and the suggeston. 3. Used data There are two specal examnaton ncluded n the system. 3.1 A POTSI (POsteror TrunkSymmetry Index) Upon POTSI - posteror trunk symmetry ndex 3 we are able to conclude the deformty of back surface and so the curvature of vertebral n the vertcal plane. There are eght ponts on the back we have to defne. It s easy to do however on a photo or on the moré pcture. In a symmetrc back surface the POTSI ndex s zero. The hgher POTSI ndex s the worse. The ndex under 27.5 t s normal. Upon the experences POTSI classfcaton s good for asymmetry, but t show a lot of cases of the scoloss to be healthy. The experences shows that the POTSI s the functon of Cobb angle n 44.6% and the rotaton n 26.8%. The POTSI s defned by equaton of (9) based on Fgure 2. POTSI = FAI + HAI (9) where defntons of FAI: s the Frontal Asymmetry Index and HAI: Heght Asymmetry Index There are the follows: Fgure 2. Defnton of POTSI The eght anatomc ponts are: 1. C7 vertebra 2. upon pont of back-end 3. ntersecton pont of tangent of left shoulder and tangent of left hand 4. ntersecton pont of tangent of rght shoulder and tangent of rght hand 5. left armpt 6. rght armpt 7. left wast pont 8. rght wast pont 122

5 Upon these I: dstance between 1. and 2. ponts A: length of vertcal projecton of I (ths s the reference lne of followng calculatons. B: dstance of pont 5. from A secton C: dstance of pont 6. from A secton D: dstance of pont 7. from A secton E: dstance of pont 8. from A secton F: vertcal projecton of dstance from 3. to 4. G: vertcal projecton of dstance from 5. to 6. H: vertcal projecton of dstance from 7. to 8. From these FAI=FAI C7 +FAI armpt +FAI wast (10) where and and and where FAI C7 =A100/I (11) FAI armpt = B-C 100/I (12) FAI wast = D-E 100/I (13) HAI=HAI shoulder +HAI armpt +HAI wast (14) HAI shoulder =F100/I (15) HAI armpt =G100/I (16) HAI wast =H100/I (17) 3.2 Predag method There was a survey made n frame of Gernco2 project wth more than 300 examnatons of students. Upon the test doctors created a new estmaton method named predag

6 Fgure 3. The estmaton data On Fgure 3 the defntons of estmaton data are shown. The man contour ponts are sgned wth four sded yellow starts. KFT KNYB, KNYJ KVB, KVJ KHB, KHJ KDB, KDJ KTB, KTJ maxmum heght of head, contour ponts on the neck, contour on the shoulder, contour ponts on the armpts, contour ponts on the wast, contour ponts on the hams. The specal man ponts are sgned by red pentangular. C7 vertebra C7 S1 spnal process of vertebra L the lower pont of the lumbal sector Other pont on the moré pcture sgned by yellow trangle ISOTHPB, ISOTHPJ proxmal so-lnes on left and rght thoracc regon ISOTHDB, ISOTHDJ dstal so-lnes on left and rght thoracc regon ISOLPB, ISOLPJ proxmal so-lnes on left and rght lumbar regon Estmated centrum ponts of so curves are sgned by orange rectangles. t BDC Left dorsal centrum JDC Rght dorsal centrum LC Lumbar centrum 124

7 BGC Left gluteal centrum JGC Rght gluteal centrum (same as L) From the above mentoned the healthy case when the C7-S1 lne s the same than the VL - vertcal lne (the sagttal plane) (Vertcal Lne) and the KTB-KTJ lne s the same as the (HLhorzontal lne). The measure of compensaton s the angle of C7-S1 and the vertcal lne. 4. Results, Processng of moré pcture In the software system there s a panel of more pcture (Fgure 4). On the panel we are able to show and to analyze the stored more pcture. Moré pcture uploadng and analyss Fgure 4. Moré panel If we have a new examnaton or we want to modfy an old one we show the dalog of more examnaton (Fgure 4.). There s the possblty to zoom and re-zoom the pcture by buttons. Wth button we select the POTSI examnaton. After selecton the button and the selecton one element on lst of Fgure 5. (Hungaran software) we can select a dstance to defne n the pcture Fgure 6. Fgure 5. Selecton of the POTSI dstance After defnng the POTSI panel shows the POTSI value. 125

8 Fgure 6. The POTSI panel If we choose the button we wll get the Predag dalog (Fgure 7.) Fgure 7. The Predag panel Lke n the case demonstrated above we can choose a dstance by a lst shown n Fgure

9 Fgure 8. The dstances of Predag In the case of new examnaton or modfed examnaton n the rght scrollbar of the panel doctor s able to qualfy the patent. The healthy case s colored green, the problematc s yellow and the dangerous s red. The system helps to decde n way wrtten n 2. In the case of old examnatons the system automatcally shows the qualfcaton of the case. 5. Dscusson The presented method worked well n test phase. The next step s the verfcaton n real screenng processes. Tunng of settng parameters can be made after the processng of results. REFERENCES 1. Abony J. Adatbányászat a hatékonyság eszköze, ComputerBooks Kadó Budapest Dr. Bajcsay P. Numerkus analízs, Tankönyvkadó, Budapest, Mnguez MF, Buenda M, Cbrán RM, Salvador R, Lagua M, Martn A, Gomar F. Quantfer varables of the back surface deformty obtaned wth a nonnvasve structured lght method: evaluaton of ther usefulness n dopathc scoloss dagnoss. Eur Spne J 2007;16: Report of Gernco2 project Natonal Offce for Research and Technology (NKTH) of Hungaran Government for ther support snce ths study has been carred out commonly as part of the project GERINCO2 TECH_08-A1/