Statistical performances of learning algorithm : Kernel Projection Machine and Kernel Principal Component Analysis
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(26) VYLMÌSLMLMVYQTN µµ[µµµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ }µA GIGRKN]IV ÊE \ p V Ê K$] OîHM\^OMK$ZjAQ^ê K$ZTSXW\PHV¾\^OMVYQTN µÉµ[µµµ[µµµµµ[µµµµµµ[µ }µA GIGRKN]IV Ê6¶ }¶ \^Ì7ò{ZTHQSIN] Q^ê  SINÌ$OMVYQTNI\^X NI\ÞXEjLMVYL µµ[µµµ[µµµµµ[µµµµµµ[µ }µAIµ h N{OMK$ZTHÍ\^OMVYQTN§Q^ê ¶ \PNI\ÞÌ ¹E GI\^Ì$K¼\^XWSK$]  SINÌ$OMVYQTNL µ[µ[µµµµµ[µµµµµµ[µ } µAI µA t LMKQ^êO ¹ K K$LMQPXYäPKN{O µ±µµµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ } µAI µA ¶ \^LMVYÌ K$LSXYOML µ µµ[µµ[µµµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ ÃOÄת"×}áPÓº×}Ö«á{ÔÅ^×}ÑÜPânÔlÓÆ²ÇÉÑĺânÓº×. . ©©. ¦. Iµ IµA. IµA Iµ½. , R ËGR/ I. I* £
(27) Ì *^¹e , RLII · h N{OHQ]}SÌ$OMVYQTN µEµ[µµµµµµ[µµ[µµµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ p Q{OMVYä\^OMVYQTNL¡ê QTH¡O ¹ K k KHMNK$X f HQ{åæK$Ì$OMVYQTN p \^Ì ¹ VWNK µ µµ[µµµ[µµµµµ[µµµµµµ[µ IµAIµ m¹ K È \PSLMLMVW\PN h NPOSVYOMVYQTN \ O\ÞOMVYLMOMVYÌ$VW\PN L f KHLGIK$Ì$OÍV»ä{K µµµµ[µµµµµµ[µ IµAIµA Ê OMKNLMVYQTN§OÍQ\ È KNKHÍ\^X g XW\^LMLMV ë}Ì\^OMVYQTN  HM\PËvKnFQTHMò µ±µµµµ[µµµµµµ[µ IµAIµA j VWNIO ò nVYO ¹ k KHMNK$X f HìVÏNÌ$VWGI\^X g QTËAGIQTNKN{O NI\^X jTLMVYL µµµµµµ[µµµµµµ[µ m¹ K k KHMNK$X f HQ{åæK$Ì$OMVYQTN p \^Ì ¹ VWNK XYZPQTHVYO ¹ Ë µµµµµ[µµµ[µµµµµ[µµµµµµ[µ Ê GIKHVWËvKN{OML µEµ[µµµµµµ[µµ[µµµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ I½µ }µ  VWHLMO s SI\^XYVYO\^OMVYäPK rÊ \PËAGX»K$L µµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ I½µ }Aµ s SI\PN{OMVYO\^OMVYäPK rÊ GRKHVWËvKN{OML µ«µµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µ. µ·¶ ¼ / / ¼ ~ ÈÉʵ ~RÍ*Î .
(28) ©E[ _© ¢. Iµm Iµm. g QTNÌ$XWSLMVYQTN6\PN]
(29) VYLMÌSLMLÍV»QN µµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ GIGRKN]IV Ê¿vF LÍLSIËGOMVYQTNL6\PN]  VWHLMO m¹ K$QHK$OMVYÌ\^X K$LSXYOMLEê QTH§O ¹ K f KNI\ÞX»V¾$K$] g HVYOMKHVYQTN µ_µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Iµ LMLSIËGOÍV»QNL µFµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ K$LîSX»OÍL µ[µµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ rÊ GRKHVWËvKNPOÍL µvµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ Iµm GIGRKN]IV ʶ } KË©V ¸nLîSIGIKHäVYLMK$] j K\PHMNVWNZ µµµµµµ[µµµµµµ[µµµ[µµµµµµ[µ Iµm GIGRKN]IV Êg4éf HQQ^ê L µµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Iµ f HQTQÞêxQ^ê m¹ K$QTHKË RAµ Iµ µvµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ f HQTQÞê LFQ^ê m¹ K$QTHKË©L IAµ Iµ \PN] IAµ IAµ ºµ®µµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ g QNÌ$KNPOHÍ\^OMVYQTN h NK$èISI\^XYVYO j µvµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Iµ g QËËvSINV»Ì\ÞOMVYQTN UIK$O nFK$KN O ¹ K¼\{HVW\PNÌ$K\PN] O ¹ K VYLò µ µµµ[µµµµµµ[µ IAµ Imµ j QÌ\^XYV¾$K$] \^]IKË\^Ì ¹ KH äPKHÍ\^ZPK µ µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ f K$K$XYVWNZ
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(32) VÏË©KNLMVYQTNI\^X GIGIHQ\^Ì ¹Éµ µµµµ[µµµµµµ[µµµ[µµµµµµ[µ Imµ p \^VWN K$LSXYO µ«µ[µµµµµ[µµµµµµ[µµµ[µµµµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Iµ g QËGI\PHVYLMQTO N nV»O ¹ O ¹ K VYLò ¶ QTSIN] QÞê ¼ pµcµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ j VWNIòOnVYO ¹ k fgF SLMVWNZDk KHMNK$X p Q]IK$XYL µIµµ[µµµµµµ[µµµ[µµµµµµ[µ IAµ Imµ ]Iä\PN{O\^Z{K$LQ^ê m¹ K  VWNV»OÍK
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