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鍓嶉缍�(w菐ng)绲�(lu貌)鍜屽弽楗嬬恫(w菐ng)绲�(lu貌)鏄叐绋吀鍨嬬殑缍�(w菐ng)绲�(lu貌)锛屽叾涓墠楗嬬恫(w菐ng)绲�(lu貌)涓昏鐢ㄤ簬瀵�(sh铆)鐝�(xi脿n)杓稿叆鑸囪几鍑虹殑鏄犲皠鍜屽嚱鏁�(sh霉)閫艰繎;鍙嶉缍�(w菐ng)绲�(lu貌)涓昏鐢ㄤ簬鐛插緱鑱�(li谩n)鎯冲瓨鍎�(ch菙)鍜屽劒(y艒u)鍖栬▓(j矛)绠�銆傝€宐p缍�(w菐ng)绲�(lu貌)鑸噐bf缍�(w菐ng)绲�(lu貌)鏄叐绋吀鍨嬬殑鍓嶉缍�(w菐ng)绲�(lu貌)锛屼絾bp缍�(w菐ng)绲�(lu貌)瀛樺湪钁楁敹鏂傞€熷害鎱�銆佹槗闄峰叆灞€閮ㄦサ灏忕瓑缂洪粸(di菐n)锛岀洝绠p缍�(w菐ng)绲�(lu貌)涓紩鍏ヤ簡閬哄偝绠楁硶銆佹ā鎿€€鐏畻娉�銆佽(di脿o)鏁村嫊(d貌ng)閲忓洜瀛愮瓑绠楁硶锛屼絾鏄痓p缍�(w菐ng)绲�(lu貌)鐢ㄤ簬鍦ㄧ窔妾㈡脯閭勬槸瀛樺湪钁楀紛绔痆3]銆傚洜姝�锛屾湰鏂囨噳(y墨ng)鐢ㄤ簡鐒¤珫寰為€艰繎鑳藉姏閭勬槸瀛�(xu茅)缈�(x铆)閫熷害鏂归潰鍧囧劒(y艒u)浜巄p缍�(w菐ng)绲�(lu貌)鐨勫緫鍚戝熀鍑芥暩(sh霉)缍�(w菐ng)绲�(lu貌)rbf锛坮adial basis function锛�锛屽苟涓斿埄鐢ㄧ恫(w菐ng)绲�(lu貌)瀹屾垚浜嗛浕纾佺劇鎼嶅湪绶氬(sh铆)鏅�(sh铆)妾㈡脯涓殑瀹氶噺璀�(sh铆)鍒�;鐐轰簡鍔犲揩鍦ㄧ窔妾㈡脯鐨勯€熷害锛屾湰鏂囧埄鐢ㄤ簡鏀归€�(j矛n)鐨刧ram-schmidt姝ｄ氦鍖栨柟娉曞劒(y艒u)鍖栫恫(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)銆� 缍�(w菐ng)绲�(lu貌)鐨勫(xu茅)缈�(x铆)绠楁硶[4] rbf缍�(w菐ng)绲�(lu貌)鏄竴绋柈闅卞堡鍓嶉缍�(w菐ng)绲�(lu貌)锛屽寘鎷毐灞ょ殑鑷(di脿o)鏁磋檿鐞嗗柈鍏冨拰杓稿嚭灞ょ殑绶氭€ц几鍑哄柈鍏�銆傚嵆闅卞惈灞ら噰鐢ㄩ潪绶氭€ц畩鎻涳紝寰為毐鍚堡鍒拌几鍑哄堡閲囩敤绶氭€ц畩鎻�銆傚叾涓毐灞や腑鐨勫熀鍑芥暩(sh霉)閲囩敤寰戝悜?q奴)唯Q鍑芥暩(sh霉)锛屽皪杓稿叆婵€鍕�(l矛)鐢�(ch菐n)鐢熶竴鍊�(g猫)灞€閮ㄥ寲鐨勯熆鎳�(y墨ng)锛屽嵆鍍呯暥(d膩ng)杓稿叆钀藉湪杓稿叆绌洪枔涓竴鍊�(g猫)寰堝皬鐨勬寚瀹氬崁(q奴)鍩熸檪(sh铆)锛岄毐鍠厓鎵嶅仛鍑烘湁鎰忕京鐨勯潪闆堕熆鎳�(y墨ng)銆� rbf缍�(w菐ng)绲�(lu貌) 浠ュ杓稿叆鍠几鍑虹偤渚�锛岄毐灞ょ缍�(j墨ng)鍏僫鐨勬椿鍖栧嚱鏁�(sh霉)ai鍙婅几鍑簎i鍒嗗垾鐐�: 缍�(w菐ng)绲�(lu貌)瑷�(x霉n)绶存柟寮� rbf缍�(w菐ng)绲�(lu貌)鐨勮〒(x霉n)绶撮亷绋嬪垎鐐哄叐鍊�(g猫)闅庢:绗竴闅庢鐐哄緫鍚戝熀鍑芥暩(sh霉)涓績鐨勯伕鍙�;绗簩闅庢鐐烘瑠(qu谩n)鍊紈鐨勬眰鍙�銆� 寰戝悜鍩哄嚱鏁�(sh霉)涓績鐨勯伕鍙� 寰戝悜鍩哄嚱鏁�(sh霉)涓績鍊肩殑閬稿彇閫氬父閲囩敤k鍧囧€艰仛椤炵畻娉�銆傚畠鏄竴绋劇鐩�(ji膩n)鐫ｅ(xu茅)缈�(x铆)绠楁硶锛屽叿楂旈亷绋嬪彲鎻忚堪濡備笅:棣栧厛灏囬毐鍚堡鍠厓婵€鍕�(l矛)鍑芥暩(sh霉)涓績cj锛坖=1,2, 鈥�,p锛宲鐐洪毐鍚堡绡€(ji茅)榛�(di菐n)鏁�(sh霉)锛夌殑鍒濆€肩疆鐐烘渶鍒濈殑p鍊�(g猫)瑷�(x霉n)绶存ǎ鏈�锛岀劧鍚庡皣鎵€鏈夌殑瑷�(x霉n)绶存ǎ鏈寜鏈€杩戠殑鑱氶涓績鍒嗙祫锛屽鏋渪i鑸嘽j婊胯冻minj||xi-cj||锛屽墖xi灞簬cj鐨勯泦鍚埼竕锛堝嵆mj=mj+1, mj琛ㄧず灞簬胃j鐨勫厓绱犵殑鍊�(g猫)鏁�(sh霉)锛�锛屾渶鍚庤▓(j矛)绠楄仛椤炰腑蹇僣j锛堬級銆� 娆�(qu谩n)鍊紈鐨勬眰鍙� 姹傝В娆�(qu谩n)鍊紈鐝�(xi脿n)鍦ㄨ純甯哥敤鐨勭偤姝ｄ氦鏈€灏忎簩涔樻硶ols锛坥rthogonal least squares锛�銆� 灏嶄簬瀛樺湪nr鍊�(g猫)妯ｆ湰鐨勬儏娉佷笅锛屽紡锛�2锛夊彲浠ュ鎴愮煩闄ｅ舰寮�:d=uw+e 锛�3锛� 寮忎腑 e鈥斺€旇宸煩闄� e=[蔚锛�1锛� ,蔚锛�2锛�,鈥�,蔚锛坣r锛塢t u鈥斺€旈毐灞ょ缍�(j墨ng)鍏冪殑杓稿嚭鐭╅櫍 u=[u1,u2,鈥�,up] ui鈥斺€旈毐灞ょ缍�(j墨ng)鍏冪殑杓稿嚭鍚戦噺 ui=[ui锛�1锛�,ui锛�2锛�,鈥�,ui锛坣r锛塢t 1鈮鈮 w鈥斺€旇几鍑烘瑠(qu谩n)閲嶅悜閲� w=[w1,w2,鈥�,wp]t d鈥斺€攏鍊�(g猫)妯ｆ湰鐨勬湡鏈涜几鍑虹煝閲� d=[d锛�1锛�,d锛�2锛�,鈥�,d锛坣r锛塢t 灏噖閫�(j矛n)琛屾浜や笁瑙掑垎瑙ｏ紙鍒╃敤gram-schmidt姝ｄ氦鍖栫畻娉曪級銆� u=qr 锛�4锛� 鍓囧皣寮忥紙4锛変唬鍏ワ紙3锛夊彲寰�: d=qrw+e 锛�5锛� 浠w=g锛屽墖锛�5锛夊紡鍙互瀵垚: d=qg+e 锛�6锛� 鏍规摎(j霉)宸茬煡鐨剄鍜宒鐭╅櫍锛屽彲姹傚緱锛�6锛夊紡涓殑鏈煡鐭╅櫍g鈥�銆傚叾涓璯(sh霉)鈥�= qtd 鍒╃敤涓€鑸殑姹傝В绶氭€ф柟绋嬬祫鐨勬柟娉�锛屽嵆鍙眰鍑烘瑠(qu谩n)鍊肩煩闄銆� mgs鏂规硶鍎�(y艒u)鍖栫恫(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)[4] 绁炵稉(j墨ng)缍�(w菐ng)绲�(lu貌)鐨勭祼(ji茅)妲�(g貌u)鍎�(y艒u)鍖栵紙鍗抽毐绡€(ji茅)榛�(di菐n)鍊�(g猫)鏁�(sh霉)鐨勯伕鍙栵級涓€鐩存槸涓€鍊�(g猫)闆ｉ粸(di菐n)銆傛櫘閬嶉噰鐢ㄧ殑缍�(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)涓毐鍚瘈(ji茅)榛�(di菐n)鏁�(sh霉)閮藉緢澶э紝鏄撲娇缍�(w菐ng)绲�(lu貌)鐢�(ch菐n)鐢熼亷瀛�(xu茅)缈�(x铆)銆傞噰鐢ㄤ簡鏂囩嵒(xi脿n)[4]鎻愬嚭鐨勭敤mgs鏂规硶鍎�(y艒u)鍖栫恫(w菐ng)绲�(lu貌)绲�(ji茅)妲�(g貌u)鐨勬柟娉�: 棣栧厛浠ら毐鍚瘈(ji茅)榛�(di菐n)鏁�(sh霉)p绛変簬妯ｆ湰鏁�(sh霉)nr锛屽墖鐣�(d膩ng)t=1鏅�(sh铆)锛岃▓(j矛)绠楄宸绺瘮 [err]k锛坱锛�=g2k/锛坉td锛� 锛坘=1,2,鈥�, nr锛� 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