Ukuhlaziywa Kwezingxenye Eziyinhloko Ezibalweni
I-Pendahuluan
Ukuhlaziywa Kwezingxenye Eziyinhloko (i-PCA) kuyindlela yezibalo esetshenziselwa ukunciphisa ubukhulu bedatha ngenkathi kugcinwa izici ezibalulekile zesethi yedatha. Isetshenziswa kabanzi emikhakheni efana nokuqashelwa kwamaphethini, ukucubungula izithombe, kanye nokuhlaziywa kwedatha ye-genomic, lapho inani elikhulu ledatha lingenza kube nzima ukuhumusha nokucubungula. I-PCA isiza ukwenza lula idatha ngaphandle kokulahlekelwa ulwazi olubalulekile, okwenza kube ithuluzi eliwusizo kakhulu ekuhlaziyweni kwedatha yesimanje.
Umbono Oyisisekelo we-PCA
Isimiso esiyisisekelo se-PCA ukuguqulwa kwedatha ibe yisethi entsha yama-coordinates, lapho ukuguquguquka okuphezulu kwedatha kubanjwa yisakhi sokuqala, ukuguquguquka kwesibili okuphezulu kakhulu yisakhi sesibili, njalo njalo. Lezi zingxenye zibizwa ngokuthi izingxenye eziyinhloko. Inqubo ihilela izinyathelo eziningana ezibalulekile:
1. Ukulinganiswa Kwedatha: Idatha ehlukene ivame ukuba nezikali ezihlukene, ezingathinta imiphumela ye-PCA. Ngakho-ke, idatha ivame ukulinganiswa ngokukhipha isilinganiso bese ihlukanisa ngokuphambuka okujwayelekile.
2. I-Covariance Matrix: Isinyathelo esilandelayo ukubala i-covariance matrix yedatha ejwayelekile. Le matrix isiza ekuqondeni ukuthi iziguquguquko ezimbili zishintsha kanjani ndawonye.
3. I-Eigenvalue kanye ne-Eigenvector: I-eigenvalue kanye ne-eigenvector ye-covariance matrix ziyabalwa. I-eigenvector inquma isiqondiso sezingxenye eziyinhloko, kuyilapho i-eigenvalue inquma ukubaluleka kwazo.
4. Ukuhlela Izingxenye: Izingxenye eziyinhloko zihlelwa ngokwe-eigenvalues zazo, kusukela kwenkulu kuya kwencane kakhulu. Ukukhethwa kwezingxenye eziyinhloko kuvame ukusekelwe ku-eigenvalues, lapho izingxenye ezine-eigenvalues ezinkulu zikhethwa ukuze zihlaziywe kabanzi.
5. Ukuguqulwa Kwedatha: Idatha yokuqala ibe isiguqulwa ibe yindawo eyinhloko yokuhlaziywa okwengeziwe.
Izinyathelo ku-PCA
1. Ukuqoqa Imininingwane
Isinyathelo sokuqala ku-PCA ukuqoqa idatha efanele. Le datha kumele ibe nkulu ngokwanele ukuze ukuhlaziywa kuveze imiphumela enenjongo. Isibonelo, kuhlelo lokusebenza lwezempilo, umuntu angase aqoqe idatha yesiguli njengokuphakama, isisindo, umfutho wegazi, njalo njalo.
2. Ukulinganisa Idatha
Ngemva kokuba idatha isiqoqiwe, isici ngasinye (ikholomu) ngaphakathi kwaso kumele silinganiswe. Isizathu ngemuva kokuma okujwayelekile ukuqinisekisa ukuthi isici ngasinye sinikela ngokulinganayo ku-PCA, kungakhathaliseki ukuthi singakanani isikali saso sokuqala. Ukuma okujwayelekile kufezwa ngokukhipha isilinganiso esicini ngasinye bese sihlukaniswa ngokuphambuka okujwayelekile.
Ukwakheka:
\[ Z = \frac{X – \mu}{\sigma} \]
Lapho i-\(X\) iyinani lesici sokuqala, i-\(\mu\) iyisilinganiso sesici, kanti i-\(\sigma\) iyi-deviation standard yesici.
3. Ukudala i-Covariance Matrix
Isinyathelo esilandelayo ukudala i-covariance matrix kusuka kudatha ejwayelekile. I-covariance matrix iyi-square matrix emele ukuguquguquka kwezici kanye nobudlelwano phakathi kwazo.
Ukwakheka:
\[ Cov(X, Y) = E[(X – E[X])(Y – E[Y])] \]
Lapho \(E\) kuyilindele noma isilinganiso.
4. Ukubala ama-Eigenvalues kanye nama-Eigenvector
Uma i-covariance matrix isidaliwe, isinyathelo esilandelayo ukubala ama-eigenvalues kanye nama-eigenvector. Ama-Eigenvector kanye nama-eigenvalues angumgogodla we-PCA ngoba anquma isiqondiso nokubaluleka kwezingxenye eziyinhloko. I-eigenvalue enkulu ikhombisa ukwehluka okwengeziwe esiqondisweni esinikezwe yi-eigenvector ehambisanayo.
5. Ukuhlunga Izingxenye Ngokusekelwe Kumanani E-Eigen
Izingxenye eziyinhloko zihlelwa ngama-eigenvalue azo, kusukela kwenkulu kuya kwencane kakhulu. Ingxenye eyinhloko ene-eigenvalue enkulu kakhulu inikela kakhulu ekuguqukeni kwedatha.
6. Ukukhetha Inani Lezingxenye Okufanele Zigcinwe
Akuzona zonke izingxenye eziyinhloko ezidinga ukugcinwa. Ukukhethwa kwezingxenye kusekelwe kuma-eigenvalues. Indlela eyodwa evamile 'Ukwehluka Okuchazwe Okuhlanganisiwe,' okubonisa ukuthi iyiphi ingxenye yokwehluka okuphelele kwedatha echazwa yizingxenye eziningana eziyinhloko.
7. Ukuguqulwa Kwedatha
Isinyathelo sokugcina ukuguqula idatha yokuqala ibe yizixhumanisi zesikhala sengxenye eyinhloko ekhethiwe. Amanani kulesi sikhala sengxenye eyinhloko aba yizimfanelo ezintsha ezingahlaziywa kabanzi.
Izinhlelo zokusebenza ze-PCA
Ukuhlukaniswa Nokuqashelwa Kwephethini
I-PCA isetshenziswa kabanzi ekuhlukaniseni nasekuboneni amaphethini. Ngokunciphisa ubukhulu bedatha, i-PCA yenza inqubo yokuhlela isebenze kahle futhi inciphise ubunzima bekhompyutha. Isibonelo, ekubonweni kobuso, i-PCA inciphisa ubukhulu bobuso ezithombeni ukuze amakhompyutha akwazi ukububona ngokushesha.
Ukucutshungulwa Kwesithombe
I-PCA inganciphisa usayizi wesithombe ngaphandle kokulahlekelwa imininingwane ebalulekile. Le ndlela isetshenziswa futhi ukukhipha izici ezithombeni ezingasetshenziswa ezinhlelweni ezahlukahlukene njengokuqashelwa kwezinto, ukutholwa komphetho, kanye nokuhlukaniswa kwezithombe.
Ukuhlaziywa Kwedatha Ye-Genome
Ku-biology, idatha ye-genomic ivame ukuba nkulu kakhulu futhi iyinkimbinkimbi. I-PCA isetshenziselwa ukunciphisa ubukhulu bedatha ye-genomic, okwenza kube lula ukuthola nokuhlaziya amaphethini kanye nokuxhumana ngaphakathi kwedatha. Lokhu kusiza kakhulu ocwaningweni lwezakhi zofuzo kanye nokuthuthukiswa kwemithi.
Ezezimali kanye Nezomnotho
I-PCA isetshenziswa ekuhlaziyweni kwengozi yephothifoliyo kanye nokubikezela intengo yesitoko. Ngokunciphisa ubukhulu bedatha yezezimali, ukuhlaziywa kungagxila kakhulu ezintweni ezithinta kakhulu imakethe.
Isiphetho
Ukuhlaziywa Kwezingxenye Eziyinhloko (i-PCA) kuyindlela enamandla kakhulu kwizibalo kanye nokufunda komshini. Ngokunciphisa ubukhulu bedatha ngaphandle kokulahlekelwa ulwazi olubalulekile, i-PCA ivumela ukuhlaziywa okusebenzayo nokuchazayo. Nakuba i-PCA inamandla, kubalulekile ukuqonda ukulinganiselwa kwayo: isebenza kuphela uma idatha ihlelwe ngendlela eqondile. Ukuqonda i-PCA kanye nezinhlelo zayo ezingaba khona kusenza sikwazi ukukhipha ukuqonda okujulile kumasethi edatha amakhulu, ayinkimbinkimbi, okwenza kube ithuluzi elibalulekile ekuhlaziyweni kwedatha yesimanje.
