Dzimwe nguva, kuti ugadzirise dambudziko, iwe unongoda kutarisa kubva kune imwe kona. Kunyange kana mumakore gumi apfuura matambudziko akafanana akagadziriswa nenzira imwechete nemigumisiro yakasiyana, haisi chokwadi chokuti iyi nzira ndiyo chete.
Pane nyaya yakadai seyemutengi churn. Chinhu chacho hachidzivisiki, nokuti vatengi vekambani chero ipi zvayo vanogona, nokuda kwezvikonzero zvakawanda, kurega kushandisa zvigadzirwa zvayo kana mabasa. Ehe, kune kambani, churn ndeye yakasikwa, asi isiri iyo inonyanya kudiwa chiito, saka munhu wese anoedza kudzikisa iyi churn. Zvichiri nani, fungidzira mukana wechurn kune rimwe boka revashandisi, kana mushandisi chaiwo, uye kurudzira mamwe matanho ekuvachengeta.
Izvo zvinodikanwa kuongorora uye kuedza kuchengetedza mutengi, kana zvichibvira, nekuda kwezvikonzero zvinotevera:
- kukwezva vatengi vatsva kunodhura kupfuura maitiro ekuchengetedza. Kukwezva vatengi vatsva, sekutonga, iwe unofanirwa kushandisa imwe mari (kushambadzira), nepo vatengi varipo vanogona kumisikidzwa nechipo chakakosha nemamiriro akakosha;
- Kunzwisisa zvikonzero nei vatengi vachisiya ndiyo kiyi yekuvandudza zvigadzirwa nemasevhisi.
Kune akajairwa nzira dzekufanotaura churn. Asi pane imwe yemakwikwi eAI, takafunga kuyedza kugovera Weibull kune izvi. Inonyanya kushandiswa kuongororwa kwekupona, kufanotaura kwemamiriro ekunze, kuongororwa kwenjodzi dzinongoitika dzoga, engineering yeindasitiri nezvimwe zvakadaro. Weibull kugovera ibasa rakakosha rekugovera rakamisikidzwa nemaparamita maviri 
ΠΈ .
Wikipedia
Muzhinji, chinhu chinonakidza, asi chekufungidzira kubuda, uye mufintech kazhinji, haina kushandiswa kazhinji. Pazasi pekuchekwa tichakuudza kuti isu (Data Mining Laboratory) takaita sei izvi, panguva imwe chete tichihwina goridhe kuArtificial Intelligence Championship muchikamu che "AI in Banks".
About churn in general
Ngatinzwisise zvishoma nezve izvo mutengi churn uye nei zvakakosha. Nzvimbo yevatengi yakakosha kune bhizinesi. Vatengi vatsva vanouya kune iyi nheyo, semuenzaniso, vadzidza nezvechigadzirwa kana sevhisi kubva kushambadziro, vanorarama kwenguva yakati (kushingairira kushandisa zvigadzirwa) uye mushure menguva yakati rega kuishandisa. Iyi nguva inodaidzwa kuti βMutengi Upenyu Hupenyuβ - izwi rinotsanangura matanho anopinda mutengi paanodzidza nezvechigadzirwa, oita sarudzo yekutenga, kubhadhara, kushandisa uye kuva mutengi akavimbika, uye pakupedzisira anomira kushandisa chigadzirwa. nokuda kwechikonzero chimwe kana chimwe. Saizvozvo, churn ndiyo nhanho yekupedzisira yehupenyu hwemutengi, kana mutengi amira kushandisa masevhisi, uye kune bhizinesi izvi zvinoreva kuti mutengi amira kuunza purofiti kana chero bhenefiti zvachose.
Mutengi wega wega webhangi munhu chaiye anosarudza kadhi rimwe kana rimwe rebhangi zvakananga kune zvaanoda. Kana uchifamba kazhinji, kadhi rine mamaira richauya zvakanaka. Anotenga zvakawanda - mhoro, kadhi rekudzosera mari. Anotenga zvakawanda muzvitoro zvakati - uye kwatove nepurasitiki yakakosha yeiyi. Zvechokwadi, dzimwe nguva kadhi inosarudzwa zvichienderana ne "Cheapest service" chiyero. Kazhinji, pane zvinosiyana zvakakwana pano.
Uye munhu anosarudzawo bhangi pachayo - pane chinangwa chekusarudza kadhi kubva kubhangi ane matavi ari muMoscow chete uye munharaunda, kana iwe uchibva kuKhabarovsk? Kunyange kana kadhi kubva kubhangi rakadaro inenge 2 nguva yakawanda inobatsira, kuvapo kwematavi ebhangi ari pedyo kuchiri chinhu chinokosha. Hongu, 2019 yatove pano uye dhijitari ndiyo yedu zvese, asi akati wandei mamwe mabhanga anogona kugadziriswa chete mubazi. Uyezve, zvakare, chimwe chikamu chehuwandu chinovimba nebhangi remuviri zvakanyanya kupfuura application pane smartphone, izvi zvinodawo kuverengerwa.
Somugumisiro, munhu angave ane zvikonzero zvakawanda zvekuramba zvigadzirwa zvebhangi (kana bhangi pacharo). Ndakachinja mabasa, uye mutero wekadhi wakachinja kubva muhoro kuenda kune βKuvanhuwo zvavo,β izvo zvisingaite purofiti. Ndakatamira kune rimwe guta uko kusina mapazi ebhanga. Ndakanga ndisingafarire kudyidzana nemushandisi asina kukodzera pabazi. Ndiko kuti, panogona kunge paine zvikonzero zvakatowanda zvekuvhara account pane kushandisa chigadzirwa.
Uye mutengi haagoni kungotaura zvakajeka chinangwa chake - kuuya kubhangi uye kunyora chirevo, asi kungomira kushandisa zvigadzirwa pasina kugumisa chibvumirano. Zvakasarudzwa kushandisa muchina kudzidza uye AI kunzwisisa matambudziko akadai.
Zvakare, mutengi churn anogona kuitika mune chero indasitiri (telecom, Internet vanopa, makambani einishuwarenzi, kazhinji, pese pane vatengi uye periodic transaction).
Taita sei
Chokutanga pane zvose, zvakanga zvakakodzera kutsanangura muganhu wakajeka - kubva panguva ipi yatinotanga kufunga kuti mutengi asiya. Kubva pakuona kwebhangi iro rakatipa data rebasa redu, mamiriro ekuita kwemutengi aive binary - angave anoshanda kana kwete. Panga paine ACTIVE_FLAG mureza mutafura ye "Chiitiko", kukosha kwayo kungava "0" kana "1" ("Isingashande" uye "Active" zvichiteerana). Uye zvese zvingave zvakanaka, asi munhu akadaro zvekuti anogona kushingairira kuishandisa kwenguva yakati, uye obva abuda kunze kwechinyorwa chinyorwa kwemwedzi - akarwara, akaenda kune imwe nyika pazororo, kana kutoenda kunoedza. kadhi kubva kune rimwe bhangi. Kana kuti pamwe mushure menguva refu yekusaita basa, tanga kushandisa masevhisi ebhangi zvakare
Naizvozvo, takasarudza kudaidza nguva yekusaita imwe nguva inoenderera panguva iyo mureza wayo wakaiswa ku "0".
Vatengi vanosimuka kubva pakusashanda kuenda kune vanoshanda mushure menguva yekusaita zvehurefu hwakasiyana. Isu tine mukana wekuverenga iyo dhigirii yeempirical kukosha "kuvimbika kwenguva yekusaita basa" - ndiko kuti, mukana wekuti munhu atange kushandisa zvigadzirwa zvebhangi zvakare mushure mekusaita kwenguva pfupi.
Semuenzaniso, iyi girafu inoratidza kutangwazve kwechiitiko (ACTIVE_FLAG=1) chevatengi mushure memwedzi yakati wandei vasingashande (ACTIVE_FLAG=0).
Pano isu tichajekesa zvishoma data seti yatakatanga kushanda nayo. Saka, bhangi rakapa ruzivo rwakaunganidzwa kwemwedzi gumi nemapfumbamwe mumatafura anotevera:
- "Chiito" - mwedzi nemwedzi mutengi kutengeserana (nemakadhi, muInternet banking uye mobile banking), kusanganisira mubhadharo uye ruzivo rwekuchinja.
- "Makadhi" - data pamusoro pemakadhi ese ane mutengi, ane yakadzama tariff chirongwa.
- "Zvibvumirano" - ruzivo pamusoro pezvibvumirano zvemutengi (zvose zvakavhurika uye zvakavharwa): zvikwereti, madhipoziti, nezvimwewo, zvichiratidza miganhu yeimwe neimwe.
- "Vatengi" - seti yedemographic data (vakadzi nezera) uye kuwanikwa kweruzivo rwekusangana.
Kubasa taida matafura ese kunze kwe "Mepu".
Pakanga pane imwe dambudziko pano - mune iyi data bhangi harina kuratidza rudzi rwekuita kwakaitika pamakadhi. Kureva kuti, taigona kunzwisisa kuti pane matransaction here kana kuti kwete, asi takanga tisisakwanise kuona mhando yavo. Naizvozvo, hazvina kujeka kana mutengi aibvisa mari, achitambira muhoro, kana kushandisa mari yacho kutenga. Isu takanga tisinawo data pamabalance eakaundi, izvo zvaizobatsira.
Sample pachayo yakanga isina rusaruro - mune iyi sampuli, pamusoro pemwedzi ye19, bhangi harina kuita chero kuyedza kuchengetedza vatengi uye kuderedza kubuda.
Saka, nezvenguva dzekusaita basa.
Kugadzira tsananguro yechurn, nguva yekusaita basa inofanirwa kusarudzwa. Kugadzira fungidziro yechurn pane imwe nguva munguva , iwe unofanirwa kuve nenhoroondo yevatengi ingangoita mwedzi mitatu panguva . Nhoroondo yedu yakanga yakaganhurirwa kumwedzi 19, saka takasarudza kutora nguva yokusashanda kwemwedzi mitanhatu, kana iripo. Uye kwenguva shoma yekufembera kwemhando yepamusoro, takatora mwedzi mitatu. Takatora nhamba dze6 uye 3 mwedzi empirically zvichibva pakuongororwa kwemaitiro evatengi data.
Isu takagadzira tsananguro yechurn seinotevera: mwedzi wevatengi churn uno ndiwo mwedzi wekutanga uine ACTIVE_FLAG=0, apo kubva mwedzi uno kune anokwana mazero matanhatu akatevedzana mundima yeACTIVE_FLAG, nemamwe mazwi, mwedzi uyo mutengi anga asingashande kwemwedzi mitanhatu.
Nhamba yevatengi vakaenda
Nhamba yevatengi vasara
Ko churn inoverengwa sei?
Mumakwikwi akadaro, uye mukuita kazhinji, kubuda kunowanzofanotaurwa nenzira iyi. Mutengi anoshandisa zvigadzirwa nemasevhisi panguva dzakasiyana dzenguva, data pakudyidzana naye inomiririrwa sevector yezvimiro zvehurefu hwakatarwa n. Kazhinji ruzivo urwu runosanganisira:
- Dhata inoratidzira mushandisi (demographic data, chikamu chekushambadzira).
- Nhoroondo yekushandiswa kwezvigadzirwa zvebhangi nemasevhisi (izvi zviito zvevatengi zvinogara zvakasungirirwa kune yakatarwa nguva kana nguva yenguva yatinoda).
- Data yekunze, kana zvaikwanisika kuiwana - semuenzaniso, wongororo kubva pasocial network.
Uye mushure meizvozvo, ivo vanowana tsananguro yechurn, yakasiyana kune rimwe nerimwe basa. Ipapo ivo vanoshandisa muchina kudzidza algorithm, iyo inofanotaura mukana wekuti mutengi aende zvichibva pane vector yezvinhu . Kudzidzisa iyo algorithm, imwe yeanozivikanwa masisitimu ekuvaka ensembles yemiti sarudzo inoshandiswa, , , kana kuvandudzwa kwayo.
Iyo algorithm pachayo haina kushata, asi ine zvakati wandei zvakakomba kana zvasvika pakufanotaura churn.
- Haana inonzi "memory". Iko kupinza kweiyo modhi nhamba yakatarwa yezvimiro zvinoenderana nenzvimbo iripo panguva. Kuti uchengetedze ruzivo nezve nhoroondo yekuchinja kweparameters, zvinodikanwa kuverenga akakosha maficha anoratidza shanduko mumaparamita nekufamba kwenguva, semuenzaniso, nhamba kana huwandu hwekutengeserana kwebhangi pamusoro pekupedzisira 1,2,3, XNUMX, XNUMX mwedzi. Iyi nzira inogona kuratidza zvishoma chimiro chekuchinja kwechinguvana.
- Fixed forecasting horizon. Iyo modhi inokwanisa chete kufanotaura mutengi churn kwenguva yakafanotaurwa yenguva, semuenzaniso, kufanotaura mwedzi mumwe pamberi. Kana kufanotaura kuchidikanwa kune imwe nguva yenguva, semuenzaniso, mwedzi mitatu, saka iwe unofanirwa kuvaka patsva seti yekudzidziswa uye kudzidzisazve muenzaniso mutsva.
Maitiro edu
Takabva tangosarudza kuti hatizoshandisa nzira dzakajairika. Pamusoro pedu, vamwe vanhu 497 vakanyoresa mumakwikwi, mumwe nemumwe wavo aive neruzivo rwakakura kumashure kwavo. Saka kuedza kuita chimwe chinhu maererano nechirongwa chemazuva ose mumamiriro ezvinhu akadaro haisi pfungwa yakanaka.
Uye isu takatanga kugadzirisa matambudziko akatarisana neiyo binary classification modhi nekufanotaura mukana wekugovera kwevatengi churn nguva. Nzira yakafanana inogona kuonekwa , inokutendera iwe kufanotaura churn zvakanyanya kuchinjika uye kuyedza zvakanyanya kuomarara hypotheses kupfuura mune yekirasi nzira. Semhuri yekugovera kuenzanisa nguva yekubuda, takasarudza kugovera nokuda kwekushandiswa kwayo kwakapararira mukuongorora kupona. Maitiro emutengi anogona kuonekwa semhando yekupona.
Heino mienzaniso yeWeibull probability density distributions zvichienderana nemaparameter ΠΈ :
Iri ndiro mukana wekuti density basa revatengi vatatu vakasiyana churn nekufamba kwenguva. Nguva inoratidzwa mumwedzi. Nemamwe manzwi, girafu rino rinoratidza nguva apo mutengi angangotanga kunetsa mumwedzi miviri iri kutevera.Sezvauri kuona, mutengi ane anogovera ane mukana mukuru wekusimuka kupfuura vatengi vane Weibull(2, 0.5) uye Weibull. (3,1) kugoverwa.
Mhedzisiro iyi modhi iyo, kune wese mutengi, kune yega
mwedzi inofanotaura zvimiro zvekugovera kweWeibull, izvo zvinonyatso ratidza kuitika kwemukana wekubuda nekufamba kwenguva. In more details:
- Izvo zvinonangwa zvimiro pane yekudzidziswa seti inguva yasara kusvika churn mumwedzi chaiwo kune chaiyo mutengi.
- Kana pasina churn rate yemutengi, tinofungidzira kuti nguva yechurn yakakura kupfuura nhamba yemwedzi kubva pamwedzi wazvino kusvika pakupera kwenhoroondo yatinayo.
- Model inoshandiswa: inodzokororwa neural network ine LSTM layer.
- Sebasa rekurasikirwa, isu tinoshandisa iyo isina kunaka log-inogona basa rekugovera Weibull.
Hezvino zvakanakira nzira iyi:
- Kugovera mukana, kuwedzera kune mukana wakajeka wekugadzirisa mabhinari, unobvumira kufanotaura kunoshanduka kwezviitiko zvakasiyana-siyana, somuenzaniso, kana mutengi acharega kushandisa mabasa ebhangi mukati memwedzi ye3. Zvakare, kana zvichidikanwa, akasiyana metrics anogona kuverengerwa pamusoro pekugovera uku.
- Iyo LSTM inodzokororwa neural network ine ndangariro uye zvino shandisa iyo yese iripo nhoroondo. Sezvo nyaya yacho ichiwedzerwa kana kunatswa, kururama kunowedzera.
- Iyo nzira inogona kuyerwa nyore nyore kana uchipatsanura nguva kuita diki (semuenzaniso, kana uchipatsanura mwedzi kuita mavhiki).
Asi hazvina kukwana kugadzira modhi yakanaka; iwe unofanirwawo kunyatso ongorora kunaka kwayo.
Hunhu hwakaongororwa sei?
Isu takasarudza Lift Curve seye metric. Inoshandiswa mubhizinesi kune zviitiko zvakadaro nekuda kwekududzirwa kwayo kwakajeka, inotsanangurwa zvakanaka ΠΈ . Kana iwe ukatsanangura zvinorehwa nemetric iyi mumutsara mumwe, ingave "Kangani iyo algorithm inoita fungidziro yakanakisa mukutanga. % pane zvisina kurongeka."
Mienzaniso yekudzidzisa
Mamiriro emakwikwi haana kumisa chaiyo yemhando metric iyo mhando dzakasiyana uye nzira dzinogona kuenzaniswa. Uyezve, tsananguro yechurn inogona kuve yakasiyana uye inogona kutsamira pane dambudziko chirevo, icho, ichowo, chinotemerwa nezvinangwa zvebhizinesi. Naizvozvo, kuti tinzwisise kuti ndeipi nzira iri nani, takadzidzisa mhando mbiri:
- Iyo inowanzo shandiswa bhinari yekuisa nzira uchishandisa ensemble sarudzo muti muchina kudzidza algorithm ();
- Weibull-LSTM modhi
Muedzo wakaiswa waive ne500 vatengi vakambosarudzwa vaive vasiri muchirongwa chekudzidziswa. Hyper-parameters yakasarudzwa yemuenzaniso uchishandisa muchinjika-kusimbisa, wakaputswa nemutengi. Maseti akafanana ezvimiro akashandiswa kudzidzisa modhi imwe neimwe.
Nekuda kwekuti iyo modhi haina chiyeuchidzo, akakosha maficha akatorwa kwairi, achiratidza chiyero chekuchinja kwemaparamita kwemwedzi mumwe kusvika kuavhareji kukosha kwema parameter mumwedzi mitatu yapfuura. Chii chakaratidza chiyero chekuchinja kwemitengo mukati menguva yekupedzisira yemwedzi mitatu. Pasina izvi, iyo Random Sango-yakavakirwa modhi yaizove isina mukana wehukama neWeibull-LSTM.
Nei LSTM ine Weibull kugovera iri nani pane ensemble sarudzo yemuti maitiro
Zvose zvakajeka pano mumifananidzo miviri chete.
Kuenzanisa kweLift Curve yeiyo classical algorithm uye Weibull-LSTM
Kuenzanisa kweLift Curve metric pamwedzi yeiyo classical algorithm uye Weibull-LSTM
Kazhinji, LSTM yakakwirira kune yekirasi algorithm mune angangoita ese kesi.
Churn kufanotaura
Modhi yakavakirwa pane inodzokororwa neural network ine LSTM maseru ane Weibull kugovera inogona kufanotaura churn pachine nguva, semuenzaniso, kufanotaura mutengi churn mukati memwedzi inotevera n. Funga nezvenyaya ye n = 3. Muchiitiko ichi, pamwedzi wega wega, neural network inofanira kunyatsoona kuti mutengi achabva here, kutanga kubva pamwedzi unotevera uye kusvika pamwedzi wenth. Mune mamwe mazwi, inofanira kunyatsoona kana mutengi acharamba mushure memwedzi n. Izvi zvinogona kutorwa sekufanotaura kumberi: kufanotaura nguva iyo mutengi achangotanga kufunga nezvekuenda.
Ngatienzanise Lift Curve yeWeibull-LSTM 1, 2 uye 3 mwedzi isati yabuda:
Isu takatonyora pamusoro apa kuti kufanotaura kwakagadzirirwa vatengi vasingachashandi kwenguva yakati kwakakoshawo. Naizvozvo, pano isu tichawedzera kumuenzaniso nyaya dzakadai kana mutengi aenda anga atove nemwedzi mumwe kana miviri asingashande, uye tarisa kuti Weibull-LSTM inorongedza nenzira kwayo nyaya dzakadai sechurn. Sezvo nyaya dzakadai dzaivepo mumuenzaniso, tinotarisira kuti network ivabate nemazvo:
Mutengi kuchengetedza
Chaizvoizvo, ichi ndicho chinhu chikuru chinogona kuitwa, kuve neruzivo rwekuti vatengi vakadaro uye vakadaro vari kugadzirira kurega kushandisa chigadzirwa. Kutaura nezvekuvaka muenzaniso unogona kupa chimwe chinhu chinobatsira kune vatengi kuitira kuti vazvichengetedze, izvi hazvigone kuitwa kana iwe usina nhoroondo yekuedza kwakafanana kunoguma zvakanaka.
Isu takanga tisina nyaya yakadaro, saka takasarudza nenzira iyi.
- Isu tiri kuvaka modhi inozivisa zvigadzirwa zvinonakidza kune yega yega mutengi.
- Mwedzi wega wega isu tinomhanyisa classifier uye tinoona vangangosiya vatengi.
- Isu tinopa vamwe vatengi chigadzirwa, zvinoenderana nemuenzaniso kubva pane 1, uye rangarira zviito zvedu.
- Mushure memwedzi mishoma, tinotarisa kuti ndeupi weava angangosiya vatengi asara uye asara. Nokudaro, tinoumba muenzaniso wekudzidzira.
- Isu tinodzidzisa modhi tichishandisa nhoroondo inowanikwa mudanho rechina.
- Sarudzo, tinodzokorora maitiro, tichitsiva modhi kubva padanho rekutanga nemuenzaniso wakawanikwa mudanho rechishanu.
Muedzo wemhando yekuchengetedza kwakadaro unogona kuitwa nekuyedzwa kweA/B nguva dzose - tinogovanisa vatengi vanogona kubuda mumapoka maviri. Isu tinopa zvigadzirwa kune imwe zvichibva pane yedu yekuchengetedza modhi, uye kune imwe isu hatipe chero chinhu. Isu takasarudza kudzidzisa modhi inogona kubatsira nechekare pane 1 yemuenzaniso wedu.
Taida kuita kuti chikamu chacho chidudzire sezvinobvira. Kuti tiite izvi, takasarudza akati wandei anogona kududzirwa zviri nyore: huwandu hwese hwekutengeserana, mubairo, huwandu hweakaundi yekuchinja, zera, murume kana mukadzi. Zvimiro kubva patafura ye "Mepu" hazvina kutorwa sezvisina ruzivo, uye zvikamu kubva patafura 3 "Zvibvumirano" hazvina kuverengerwa nekuda kwekuoma kwekugadzirisa kuitira kudzivirira kudonha kwedata pakati peseti yekusimbisa uye seti yekudzidziswa.
Kubatanidza kwakaitwa uchishandisa Gaussian musanganiswa modhi. Iyo Akaike ruzivo criterion yakatibvumira kuona 2 optima. Yekutanga optimum inoenderana ne1 cluster. Yechipiri optimum, isinganyanyi kutaurwa, inoenderana ne80 masumbu. Zvichienderana nemhedzisiro iyi, tinogona kutora mhedziso inotevera: zvakanyanya kuoma kupatsanura data kuita masumbu pasina ruzivo rwakapihwa. Kuti uunganidze zvirinani, unoda data rinotsanangura mutengi wega wega.
Naizvozvo, dambudziko rekudzidza kwakatariswa rakatariswa kuitira kupa mutengi wega wega chigadzirwa chakasiyana. Zvigadzirwa zvinotevera zvakatariswa: "Term deposit", "Credit card", "Overdraft", "Consumer loan", "Car loan", "Mortgage".
Iyo data yaisanganisira imwe mhando yechigadzirwa: "Yazvino account". Asi isu hatina kuzvifunga nekuda kwekuderera kwayo ruzivo. Kune vashandisi vari vatengi vebhangi, i.e. haina kurega kushandisa zvigadzirwa zvayo, modhi yakavakwa kuti ifanotaura kuti ndechipi chigadzirwa chingave chinofarira kwavari. Logistic regression yakasarudzwa semuenzaniso, uye iyo Lift kukosha kwekutanga gumi percentiles yakashandiswa seyemhando yekuongorora metric.
Unhu hwemuenzaniso hunogona kuongororwa mumufananidzo.
Product kurudziro modhi mhinduro kune vatengi
Mugumisiro
Maitiro aya akatiunzira nzvimbo yekutanga muchikamu che "AI in Banks" kuRAIF-Challenge 2017 AI Championship.
Sezviri pachena, chinhu chikuru chaiva kusvika kune dambudziko kubva kune imwe nzira isina kujairika uye kushandisa nzira inowanzoshandiswa kune mamwe mamiriro ezvinhu.
Kunyangwe kubuda kukuru kwevashandisi kunogona kunge kuri njodzi yemasevhisi.
Iyi nzira inogona kuverengerwa kune chero imwe nzvimbo iyo yakakosha kufungisisa kubuda kunze, kwete mabhangi chete. Semuenzaniso, takashandisa iyo kuverenga kubuda kwedu pachedu - mumatavi eSiberia neSt. Petersburg eRostelecom.
"Data Mining Laboratory" kambani "Search portal "Sputnik"
Source: www.habr.com