A Novel Algorithm for Criminal Statistical Processing

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1 d Iteratoal Coferece o Electrcal, Computer Egeerg ad Electrocs (ICECEE 05) A Novel Algorthm for Crmal Statstcal Processg LIN Jahu, a *, Che J,b Departmet of Iformato Techology, Hube Uversty of Polce, P.R. Cha Adult educato offce, Hube Uversty of Polce, P.R. Cha a ljh_es@6.com, b 855@hbpa.edu.cl * Correspodg author Keywords: Socal order tred; Crmal statstcal data; proflg vector; Aomaly value Abstract. Socal order tedecy aalyss s studed based o tesve probe to preset crmal formato research jobs. The pheomeo of route fluctuato ad warg fluctuato the feld of socal publc order s extesvely studed. A urba crme dstrbuto vector geerato algorthm, whch based o expoetal atteuato, s geerated by combg the hstorc statstc data ad wth the preset oe. a Composte Statstc Proflg-Vector Hypothess-test Algorthm, cosst of a system aomaly testg expresso ad a correspodg refereced aomaly testg expresso, s preseted to exam the preset statstcs value set, thus socal system aomaly dex s obta. Prototype system ad expermet results show ts precso ad credblty. Itroducto As the developmets ad chages of poltcs, ecoomcs ad culture a certa huma socety, socal order tedecy fluctuates correspodgly. To be objectvely, chage s eteral; however the chages of socal order surely affect the socal stablty ad socal lfe. Therefore, how to dstgush the warg chages from route chages s becomg evet mportat for us []. Geerally, crme tedecy ca be abstracted from the comprehesve processg toward may relevat factors, whch volve socal status, populato fluctuato, poltcal reformato, crme quatty, crme type, crme structure, etc []. I hstorcal researches, tme seres aalyss algorthm, regresso aalyss, SVM, Bayes aalyss ad Markov cha algorthm are used to calculate or forecast the tred of socal crme [3]. Though may researches o crmal tred have bee acheved, we stll fd that rare algorthm ca effectvely process the socal order tred for decso makers to formulate the comprehesve method to decrease the crmal rate [4]. I ths paper we maly deal wth a ovel algorthm whch aalyze socal order tred from crmal statstcal data. Atteuato Based Profle Vector I terms of dvdual, each occurrece of a crme s certaly a (p, -p) bary evet, whch s a commo probablty evet realty [5]. I addto, geerally f a certa evet possesses a characterstc that ts occurrece s rare, a Posso stream may be used to approxmate t [6]. Thus, we ca verfy that geeral crme evets observe Posso dstrbuto ad urba crmal evet observes same dstrbuto, the we may use some values derved from dstrbuto property to depct the urba publc order status. Composte dstrbuto. Cosderg the great dversty of crme types, we have to aggregate some crme types order to obta a better statstcs dstrbuto. Sce that the sum of a seres Posso dstrbuto also observes a Posso dstrbuto [7], we attempt to use Posso dstrbuto meas to represet the urba crme occurrece property. Nevertheless, as a profle value whch ca dcate the mplct rule of urba crme, t must represet the fluctuato rule of preset status as well as the affecto of hstorc statstc data [8].Hece, for each compoet of profle vector, we process t as follows. 05. The authors - Publshed by Atlats Press 5

2 At the frst tme, we collect the mea value of a certa crme. We ote t as w ad draw a drected segmet to represet t. After a specfed tme spa whch s defed advace, we whrl the prevous segmet couterclockwse wth agle a, the project of t o ts orgal drecto s: w ' w cos( ). Whe secod measure comes, rotates the hstorc vector ad projects t, combe wth the preset statstcs data to geerate ew profle vector. j ζ w P j () j ( + ζ ) Wth t, ζ s system atteuato factor. O codto that system statstc terval s d (day), we set s (day) as the sem-atteuato crcle, the atteuato factor s: ζ The a ew status compoet s geerated. After a certa umber of tme spa passed, we get a profle vector compoet cota eough hstorc vector compoet. Certaly, to the extreme t ca represet the property of preset statstc measure ad ratoally cosder the effect of hstorc measure [8]. Fally, we ca defe: e d (l 0.5) s P x) ( P, P,, P ( ( x as the system profle vector. Expermets ad Results. Accordg the algorthm model above, we desg a seres of expermet o the urba crme evet: () For every 5 days, execute a Ch-square testg [9] o ear 30 days statstcs date to obta ts dstrbuto mea. ()At the bass of 30 days, execute a Ch-square testg o ear 30 days statstc date to obta ts dstrbuto mea, every ew testg spa slde the tme wdow wth 0 days. We make expermets o the profle vector algorthm, expermets results are show Fg.. Certa le 3 ca better represet the hstorc effect ad be ot sestve to preset statstc data. Occurreces s Tme spa t/week Hstorc data. 30 days statstcs data 3. Profle vector Fg. Three classes of meas. Le s hstorc accumulatve data, le s 30 days statstcs data, le 3 s profle vector. Cosequetly, we ca draw a cocluso that we ca use a seres of atteuated hstorc profle vector ad preset statstcs combe to a ew profle vector. The vector ca better represet the socal publc order status ad s ot sestve to preset statstc data, towards may type of crme we classfy raw data to optmzed based o Posso dstrbuto. System detecto algorthm I ths secto, how to depct the comprehesve status of socal publc order s the frst problem we have to solve. We propose a flow process as follows: System talzato phase 6 ))

3 Aomaly detecto phase Recovery phase Dervato of System detecto algorthm. Assume a certa complex system C whch cotas parameters M ( m, m,, m ) ad M ca be descrbed by a o-egatve tegral wth each fxed tme spa t, after a preset eough log tme γ : Wth t, j t( γ / t) M ( m, m,, m m ( j) c j, M ( m', m',, m' ). m () m () m ( j) m () m () m ( j) m3() m 3() m3( j) Assumg matrx ', ts factor m ' cotas q les, the the relato betwee M ad m ' ca be descrbed as follows: m' mlast _ () m' q mlast _ q+ ( x) Provded radom varable m observes Posso dstrbuto, we ca geerate N-dmesoed radom varable Mea ( mea, mea,, mea ), whch geerate a ew le whe M ' process a update: mea, j E( m j ) (3) profle ( mea' last, j ) Def. : Vector followg requremets are met: mea' k, j mea ' k, j mea s called profle vector of complex system C, f the E( m' ) k k, j j + ζ mea' ζ s a costat, ad 0.9 ζ <, Mea ' s call profle set of complex system C. Def. : N-dmesoed radom varable D s called aomaly dex f followg requremets are met: d (0), f d mea + ζ mea', k, j f > Sce every colum of D s dfferece value betwee the mea value of a Posso dstrbuto varable ad the weghted value of whch, obvously d observes a Normal dstrbuto. We ca draw a cocluso that: d ~ N(0,) σ Ad they are depedet of each other, the ( ) S ~ χ ( ) ( ) S d d / ~ t( ) σ ( ) S / Now makg a hypothess: H 0 : µ d 0 Note sample mea value ad sample varace value of d, d,, d as d,s separately, the: S d d ( d d ) k> 7

4 Now settg a small postve umber α > 0, we suppose Eq.3.5 as aomaly detectg formula of complex system C ad Eq.3.6 as refereced aomaly detectg formula. d t t / ( ) (6) s / p P( t t ( ) µ 0) (7) / d System detecto algorthm process. I geeral, the Composte Statstc Proflg-Vector Hypothess test Algorthm we supposed ca be descrbed as follows: Composte Statstc Proflg-Vector Hypothess test Algorthm Iput: atteuato perod ζ, parameter statstcal value measure, detecto segmet ds, statstcal segmet ts Output: aomaly dex of complex system C Method: whle.t. lecoutle(m); sertle(m,measure); // sert a ew le to M for each measure f le<ts wdow_start0; wdow_edle; else wdow_start+; wdow_ed+; //slde wdows edf mea_valuegetmea(m,wdow_start,wdow_ed); edfor sertle(mea,mea_value); // sert a ew le f frst_le_of_mea sertle(mea,mea_value); else mea (mea + ζ mea)/(+ ζ) ; edf for each ed_of_ts dmea-mea ; sertle(d,d); ed for svarace(d) ; //cout statstcal stadard varace daverage(d) ; tabs(d).sqrt().s sertle(t,t); //record the testg aomaly value f t>threshold_value f test_fal // refuse 0 assumpto sed_abormal(serous_alert); // serous alert else sed_abormal(warg); //warg // compute mea value 8

5 edf else sed_ormal(); edf retur t; edwhle As far as the process of aomaly value s cocered, there are two opos: () to elmate the effect system property vector upo system property value to make system property stable; () sce the system aomaly value mples the fluctuato of socal status, t should be remaed to affect ad update socal order vector tme. Cosderg the fluctuato characterstcs of socal order status agast relatvely stable status, ts value may ot be costat but chaged slowly. Ths kd of movemet derved from the aomaly status of complex system, as a result the aomaly status should rema. Of course, aomaly rses from statstcal error have to be elmated. Expermets ad coclusos I expermet evromet, we collect the statstcal data of crmal cases a certa cty of Cha 009. Cosderg that the algorthm bases upo hstorcal data, we abstract last 0 weeks data as our detecto data, the others s treated as the trag data of the model. Settg ζ0.9330, expermets results are showed as Fg.. Settg alert threshold as 0.70 ad system ca receve 3 alerts. Comparg wth tal data we collect, urba crmal statstcs data chages sharply whe alert sgal receved. Cosequetly we ca draw a cocluso that aalyss predcto results are scetfc ad accurate. Aomaly dex Tme t/week detcto tred Fg. Expermet results ad comparso. Le s the detecto result of Algorthm, Le s statstcal Crmal data tred. There are two methods to adjust the accuracy of system. Adjustg the wdth of statstcal spa ca affect the sestvty of system. Certaly the sestvty of warg aomaly detecto may slghtly decrease. To sum up, order to obta more scetfc ad accurate results, we should approprately adjust system parameters accordg hstorc collectg data ad expert advces. I addto, accordg to the character of the complex socal system, t uses may layers of olear processg uts for feature extracto ad trasformato, the processg algorthms may be supervsed or usupervsed ad applcatos clude patter recogto ad statstcal classfcato, ad t s based o the learg of multple levels of features or represetatos of the data, the optmzed algorthm based o deep learg may be appled to accurate the detecto effcecy ad alert correcto the future researchg. 9

6 Ackowledgmets Ths Work s partally supported by the humates ad socal scece research projects of Hube Provce (0G) ad the uverstes youth scece ad techology ovato team project of Hube Provce (T0). It s also supported by Cooperatve Iovato Ceter of Dgtal Data Forescs. Refereces []L Jahu, Huag Tashu. Aalyss ad realzato of a crme predcto system based o statstcs algorthm. Joural of Iformato ad Computatoal Scece. 4(007), []Chadra B, Gupta M. A multvarate tme seres clusterg approach for crme treds predcto. IEEE Iteratoal Coferece o Systems, Ma ad Cyberetcs. (008), [3]Kell Crews. Bayesa Network Modelg of Offeder Behavor for Crmal Proflg. Proceedgs of the 44th IEEE Coferece o Decso ad Cotrol, ad the Europea Cotrol Coferece. (005), [4]Plla R.K.G. Smulato of Huma Crmal Behavor Usg Clusterg Algorthm. Iteratoal Coferece o Computatoal Itellgece ad Multmeda Applcatos. (007), [5]Kamehr, Keva. Effectveess of support vector mache for crme hot-spots predcto. Appled Artfcal Itellgece. (008), [6]Do Km. Cyber Crmal Actvty Aalyss Models usg Markov Cha for Dgtal Forescs. Iteratoal Coferece o Iformato Securty ad Assurace. 4(008), 4-6 [7]Oatley, Gles C. Crmes aalyss software: 'Ps maps', clusterg ad Bayes et predcto. Expert Systems wth Applcatos.5(003), [8]L Jahu. A urba crmal statstc profle vector Algorthm. Iteratoal Coferece o Iformato Maagemet, Iovato Maagemet ad Egeerg. (009),3-8 [9]L Jahu, Huag Tashu. Crme Iformato Aalyss ad Complex Socal System Tedecy Researches. Computer egeerg ad applcato.7( 0),