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Davis Signal Processing Noise Vyacheslav P

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(1)THE ELECTRICAL ENGINEERING AND APPLIED SIGNAL PROCESSING SERIES Edited by Alexander Poularikas The Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems Stergios Stergiopoulos The Transform and Data Compression Handbook K.R. Rao and P.C. Yip Handbook of Multisensor Data Fusion David Hall and James Llinas Handbook of Neural Network Signal Processing Yu Hen Hu and Jenq-Neng Hwang Handbook of Antennas in Wireless Communications Lal Chand Godara Noise Reduction in Speech Applications Gillian M. Davis Signal Processing Noise Vyacheslav P. Tuzlukov Digital Signal Processing with Examples in MATLAB® Samuel Stearns Applications in Time-Frequency Signal Processing Antonia Papandreou-Suppappola The Digital Color Imaging Handbook Gaurav Sharma Pattern Recognition in Speech and Language Processing Wu Chou and Biing Huang Juang. Forthcoming Titles Propagation Data Handbook for Wireless Communication System Design Robert Crane Smart Antennas Lal Chand Godara Nonlinear Signal and Image Processing: Theory, Methods, and Applications Kenneth Barner and Gonzalo R. Arce. ‹E\&5&3UHVV//&.

(2) Forthcoming Titles (continued) Soft Computing with MATLAB® Ali Zilouchian Signal and Image Processing Navigational Systems Vyacheslav P. Tuzlukov Wireless Internet: Technologies and Applications Apostolis K. Salkintzis and Alexander Poularikas. ‹E\&5&3UHVV//&.

(3) PATTERN RECOGNITION in SPEECH and LANGUAGE PROCESSING Edited by. WU CHOU Avaya Labs Research. BIING HWANG JUANG Georgia Institute of Technology. CRC PR E S S Boca Raton London New York Washington, D.C. ‹E\&5&3UHVV//&.

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(7) Preface. #RRTQCEJGU VQ VJG RTQDNGOU QH FGUKIPKPI URGGEJ CPF NCPIWCIG RTQEGUUKPI CNIQTKVJOU HQT JWOCP OCEJKPG EQOOWPKECVKQP WUGF VQ DG VCMGP HTQO VJG RGTURGEVKXGU QH NKP IWKUVKEU CPF URGGEJ UEKGPEG WPVKN VJG NCVG U &WG VQ VJG CFXCPEGU KP EQORWV KPI CPF UVCVKUVKECN OQFGNKPI FCVC FTKXGP RCVVGTP TGEQIPKVKQP OGVJQFU JCXG DGEQOG C HCUV OQXKPI TGUGCTEJ CTGC FWTKPI VJG RCUV VYQ FGECFGU CPF EQPVTKDWVGF OWEJ VQ VJG RTQITGUU KP VJKU ſGNF #U VJG GTC QH KPHQTOCVKQP CIG EQPVKPWGU VQ FGXGNQR YG YKVPGUU CP GXGT KPETGCUKPI PGGF KP KPVGNNKIGPV JWOCPOCEJKPG EQOOWPKECVKQPU CU YGNN CU VJG ETGCVKQP QH OCEJKPG WPFGTUVCPFCDNG OGVCFCVC HQT 9GD EQPVGPV CPF QVJGT KPHQTOCVKQP UQWTEGU 6JKU JCPFDQQM KU VQ ſNN VJG PGGF QH C U[UVGOCVKE CPF WRVQFCVG RTGUGPVCVKQP QH PGY RCVVGTP TGEQIPKVKQP CRRTQCEJGU KP URGGEJ CPF NCPIWCIG RTQEGUUKPI 6JG DQQM UVCTVU YKVJ HWPFCOGPVCNU CPF TGEGPV VJGQTGVKECN CFXCPEGU KP RCVVGTP TGEQI PKVKQP YKVJ CP GORJCUKU QP ENCUUKſGT FGUKIP ETKVGTKC CPF QRVKOK\CVKQP RTQEGFWTGU +V EQXGTU UGXGTCN TGEGPV TGUGCTEJ CFXCPEGU KP VJKU CTGC UWEJ CU VJG OKPKOWO GTTQT TCVG /%' OGVJQF VJG OKPKOWO $C[GU TKUM CRRTQCEJ CFCRVKXG U[UVGO FGUKIP CPF FGEKUKQP TWNGU PGWTCN PGVYQTMU FKUVTKDWVGF TGEQIPK\GTU CPF FGEKUKQP HWUKQP 6JGUG OGVJQFU FGRCTV HTQO VJG EQPXGPVKQPCN RCTCFKIO YJKEJ NKPMU C ENCUUKſGT FGUKIP VQ VJG ENCUUKECN RTQDNGO QH FKUVTKDWVKQP GUVKOCVKQP +PUVGCF OQTG OGCPKPIHWN ETKVGTKC CTG KPVTQFWEGF YJKEJ UKIPKſECPVN[ KORTQXG VJG FKUETKOKPCVKQP RQYGT QH C ENCUUKſGT RCTVKEWNCTN[ YJGP CRRNKGF VQ URGGEJ RTQDNGOU KP YJKEJ VJG PQVKQP QH FCVC FKUVTKDWVKQP KU FKHſEWNV VQ TGCNK\G 6JG UGEQPF RCTV QH VJG DQQM KU VJGTGHQTG URGEKCNN[ HQEWUGF QP VJG CRRTQCEJGU CPF OGVJQFU CRRNKGF VQ URGGEJ RTQEGUUKPI +V EQXGTU VQRKEU UWEJ CU $C[GU OKPKOWO TKUM CRRTQCEJ VQ URGGEJ TGEQIPKVKQP NCTIG XQECDWNCT[ URGGEJ TGEQIPKVKQP DCUGF QP UVCVKU VKECN OGVJQFU TGEQIPKVKQP QH URQPVCPGQWU URGGEJ KP FKCNQIWG KPVGTCEVKQP URGGEJ CPF URGCMGT XGTKſECVKQP CPF CWFKQ KPHQTOCVKQP TGVTKGXCN CPF KPFGZKPI 6JGUG EJCRVGTU RTQXKFG C EQORTGJGPUKXG EQXGTCIG QH TGEGPV CFXCPEGU KP CRRN[KPI RCVVGTP TGEQIPK VKQP VQ TGCN U[UVGOU KP URGGEJ CPF CWFKQ RTQEGUUKPI 6JG VJKTF RCTV QH VJG DQQM KU FGXQVGF VQ VQRKEU QH RCVVGTP TGEQIPKVKQP KP NCPIWCIG RTQEGUUKPI +V EQPVCKPU EJCRVGTU KP NCPIWCIG OQFGNKPI DCUGF QP NCVGPV UGOCPVKE KP FGZKPI UCNKGPV KPHQTOCVKQP TGRTGUGPVCVKQP CPF RTQEGUUKPI KP PCVWTCN NCPIWCIG FKC NQIWG U[UVGO UVCVKUVKECN OCEJKPG VTCPUNCVKQP OGVJQFU KP VQRKE FGVGEVKQP VTCEMKPI CPF PCOG KFGPVKV[ KFGPVKſECVKQP 6JGUG VQRKEU CTG PGY VTGPFU KP NCPIWCIG RTQEGUU KPI CPF UKIPKſECPV RTQITGUU JCU DGGP OCFG KP TGEGPV [GCTU +V JCU C FKTGEV KORCEV VQ VJG RTCEVKEG CPF KORNGOGPVCVKQP QH KPHQTOCVKQP RTQEGUUKPI U[UVGOU HQT 9GD EQPVGPV DTQCFECUV PGYU CPF QVJGT EQPVGPVTKEJ KPHQTOCVKQP TGUQWTEGU 6JKU DQQM KU C EQNNGEVKXG GHHQTV OQVKXCVGF D[ VJG GZEKVGOGPV QH VJG PGY CFXCPEGU KP ‹E\&5&3UHVV//&.

(8) VJKU ſGNF CPF VJG WTIGPV PGGF VQ DTKPI VJGUG CFXCPEGU VQ C IGPGTCN CWFKGPEG 6JG EQP VTKDWVKPI CWVJQTU QH VJKU DQQM CTG NGCFKPI GZRGTVU KP VJG ſGNF QH URGGEJ CPF NCPIWCIG RTQEGUUKPI #VVGORVU CTG OCFG VQ OCMG GCEJ EJCRVGT UGNHEQPVCKPGF CPF EQORTG JGPUKDNG HQT TGCFGTU YKVJ IGPGTCN DCEMITQWPF KP RCVVGTP TGEQIPKVKQP CPF KPHQTOCVKQP RTQEGUUKPI +V KU KPVGPFGF VQ DG C JCPFDQQM QT TGHGTGPEG VGZVDQQM HQT TGUGCTEJGTU ITCFWCVG UVWFGPVU CPF CFXCPEGF WPFGTITCFWCVG UVWFGPVU YJQ YCPV VQ HQNNQY VJG PGY CFXCPEGU KP RCVVGTP TGEQIPKVKQP 5WHſ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asking Ridge, New Jersey September, 2002. ‹E\&5&3UHVV//&.

(9) Contributors. A. Abella 5RGGEJ 4GUGCTEJ #66 .CDQTCVQTKGU (NQTJCO 2CTM 0, James Allan &GRCTVOGPV QH %QORWVGT 5EKGPEG 7PKXGTUKV[ QH /CUUCEJWUGVVU #OJGTUV #OJGTUV /# T. Alonso 5RGGEJ 4GUGCTEJ #66 .CDQTCVQTKGU (NQTJCO 2CTM 0, Jerome R. Bellegarda 5RQMGP .CPIWCIG )TQWR #RRNG %QORWVGT +PE %WRGTVKPQ %# William Byrne %GPVGT HQT .CPIWCIG CPF 5RGGEJ 2TQEGUUKPI ,QJPU *QRMKPU 7PKXGTUKV[ $CNVKOQTG /&. 7PKXGTUKVyG FG 2CTKU 5WF 1TUC[ %GFGZ (TCPEG Vaibhava Goel 6, 9CVUQP 4GUGCTEJ %GPVGT +$/ ;QTMVQYP *GKIJVU 0; Allen L. Gorin 5RGGEJ 4GUGCTEJ #66 .CDQTCVQTKGU (NQTJCO 2CTM 0, Qiang Huo &GRCTVOGPV QH %QORWVGT 5EKGPEG CPF +PHQTOCVKQP 5[UVGOU 6JG 7PKXGTUKV[ QH *QPI -QPI *QPI -QPI %JKPC Biing-Hwang Juang #XC[C .CDU 4GUGCTEJ $CUMKPI 4KFIG 0,. Wu Chou #XC[C .CDU 4GUGCTEJ $CUMKPI 4KFIG 0,. Shigeru Katagiri +PVGNNKIGPV %QOOWPKECVKQP .CDQTCVQT[ CPF 5RGGEJ 1RGP .CDQTCVQT[ 0KRRQP 6GNGITCRJ CPF 6GNGRJQPG %QTRQTCVKQP 6QM[Q ,CRCP. Sadaoki Furui &GRCTVOGPV QH %QORWVGT 5EKGPEG 6QM[Q +PUVKVWVG QH 6GEJPQNQI[ 6QM[Q ,CRCP. Lori Lamel .+/5+%045 7PKXGTUKVyG FG 2CTKU 5WF 1TUC[ %GFGZ (TCPEG. Jean-Luc Gauvain .+/5+%045. Qi (Peter) Li $GNN .CDQTCVQTKGU. ‹E\&5&3UHVV//&.

(10) .WEGPV 6GEJPQNQIKGU /WTTC[ *KNN 0, John Makhoul $$0 6GEJPQNQIKGU %CODTKFIG /# Hermann Ney .GJTUVWJN HWGT +PHQTOCVKM 8+ *WOCP .CPIWCIG 6GEJPQNQI[ CPF 2CVVGTP 4GEQIPKVKQP %QORWVGT 5EKGPEG &GRCTVOGPV 7PKXGTUKV[ QH 6GEJPQNQI[ #CEJGP )GTOCP[ F. J. Och .GJTUVWJN HWGT +PHQTOCVKM 8+ *WOCP .CPIWCIG 6GEJPQNQI[ CPF 2CVVGTP 4GEQIPKVKQP %QORWVGT 5EKGPEG &GRCTVOGPV 7PKXGTUKV[ QH 6GEJPQNQI[ #CEJGP )GTOCP[. ‹E\&5&3UHVV//&. G. Riccardi 5RGGEJ 4GUGCTEJ #66 .CDQTCVQTKGU (NQTJCO 2CTM 0, Richard M. Schwartz $$0 6GEJPQNQIKGU %CODTKFIG /# J. H. Wright 5RGGEJ 4GUGCTEJ #66 .CDQTCVQTKGU (NQTJCO 2CTM 0,.

(11) Contents. 1. Minimum Classification Error (MCE) Approach in Pattern Recognition Wu Chou #XC[C .CDU 4GUGCTEJ #XC[C +PE 75#  +PVTQFWEVKQP  1RVKOCN %NCUUKſGT HTQO $C[GU &GEKUKQP 6JGQT[  &KUETKOKPCPV (WPEVKQP #RRTQCEJ VQ %NCUUKſGT &GUKIP  5RGGEJ 4GEQIPKVKQP CPF *KFFGP /CTMQX /QFGNKPI  *KFFGP /CTMQX /QFGNKPI QH 5RGGEJ  /%' %NCUUKſGT &GUKIP 7UKPI &KUETKOKPCPV (WPEVKQPU  /%' %NCUUKſGT &GUKIP 5VTCVGI[  1RVKOK\CVKQP /GVJQFU  1VJGT 1RVKOK\CVKQP /GVJQFU  *// CU C &KUETKOKPCPV (WPEVKQP  4GNCVKQP DGVYGGP /%' CPF //+  &KUEWUUKQPU CPF %QOOGPVU  'ODGFFGF 5VTKPI /QFGN $CUGF /%' 6TCKPKPI  5VTKPI /QFGN $CUGF /%' #RRTQCEJ  %QODKPGF 5VTKPI /QFGN $CUGF /%' #RRTQCEJ  &KUETKOKPCVKXG (GCVWTG 'ZVTCEVKQP  8GTKſECVKQP CPF +FGPVKſECVKQP  5RGCMGT 8GTKſECVKQP CPF +FGPVKſECVKQP  7VVGTCPEG 8GTKſECVKQP  5WOOCT[. 2 Minimum Bayes-Risk Methods in Automatic Speech Recognition Vaibhava Goel £ and William ByrneÝ £ +$/ Ý ,QJPU *QRMKPU 7PKXGTUKV[  /KPKOWO $C[GU4KUM %NCUUKſECVKQP (TCOGYQTM  .KMGNKJQQF 4CVKQ $CUGF *[RQVJGUKU 6GUVKPI  /CZKOWO #2QUVGTKQTK 2TQDCDKNKV[ %NCUUKſECVKQP  2TGXKQWU 5VWFKGU QH #RRNKECVKQP 5GPUKVKXG #54  2TCEVKECN /$4 2TQEGFWTGU HQT #54  5WOOCVKQP QXGT *KFFGP 5VCVG 5GSWGPEGU  /$4 4GEQIPKVKQP YKVJ 0DGUV .KUVU  /$4 4GEQIPKVKQP YKVJ .CVVKEGU  5GIOGPVCN /$4 2TQEGFWTGU  5GIOGPVCN 8QVKPI  418'4 ‹E\&5&3UHVV//&.

(12) .   3.  G418'4 'ZRGTKOGPVCN 4GUWNVU  2CTCOGVGT 6WPKPI YKVJKP VJG /$4 %NCUUKſECVKQP 4WNG  7VVGTCPEG .GXGN /$4 9QTF CPF -G[YQTF 4GEQIPKVKQP  418'4 CPF G418'4 HQT /WNVKNKPIWCN #54 5WOOCT[ #EMPQYNGFIGOGPVU. A Decision Theoretic Formulation for Robust Automatic Speech Recognition Qiang Huo 6JG 7PKXGTUKV[ QH *QPI -QPI *QPI -QPI %JKPC  +PVTQFWEVKQP  1RVKOCN $C[GUŏ &GEKUKQP 4WNG HQT #54  #FCRVKXG &GEKUKQP 4WNGU %QPUVTWEVGF HTQO 6TCKPKPI 5CORNGU  2NWIKP $C[GUŏ &GEKUKQP 4WNGU YKVJ /CZKOWONKMGNKJQQF &GPUKV[ 'UVKOCVG  /CZKOWO&KUETKOKPCPV &GEKUKQP 4WNGU /KPKOK\KPI VJG 'O RKTKECN %NCUUKſECVKQP 'TTQT  &KUEWUUKQP  8KQNCVKQPU QH /QFGNKPI #UUWORVKQPU KP #54  6[RGU QH &KUVQTVKQPU  6QYCTFU #FCRVKXG CPF 4QDWUV #54  +ORTQXKPI #FCRVKXG &GEKUKQP 4WNGU XKC &GEKUKQP 2CTCOGVGT #FCRVC VKQP  &GEKUKQP 2CTCOGVGT #FCRVCVKQP HQT 5VCVKQPCT[ 1RGTCVKPI %QP FKVKQPU  &GEKUKQP 2CTCOGVGT #FCRVCVKQP HQT 5NQYN[ %JCPIKPI 1RGT CVKPI %QPFKVKQPU  &GEKUKQP 2CTCOGVGT #FCRVCVKQP HQT 5YKVEJKPI 1RGTCVKPI %QP FKVKQPU  &KUEWUUKQP  4QDWUV &GEKUKQP 4WNGU  &GEKUKQP 4WNG 4QDWUVPGUU  /KPKOCZ %NCUUKſECVKQP 4WNG  $C[GUKCP 2TGFKEVKXG %NCUUKſECVKQP 4WNG  &KUEWUUKQP  5WOOCT[. 4 Speech Pattern Recognition using Neural Networks Shigeru Katagiri 066 %QOOWPKECVKQP 5EKGPEG .CDQTCVQTKGU  +PVTQFWEVKQP  $C[GU &GEKUKQP 6JGQT[  2TGRCTCVKQPU  &GEKUKQP 4WNG  /KPKOWO 'TTQTTCVG %NCUUKſECVKQP ‹E\&5&3UHVV//&.

(13) .   .  2TQDCDKNKV[ (WPEVKQP 'UVKOCVKQP  &KUETKOKPCVKXG 6TCKPKPI 5RGGEJ 4GEQIPK\GTU $CUGF QP 0GWTCN 0GVYQTMU  2TGRCTCVKQPU  %NCUUKſECVKQP 'TTQT /KPKOK\CVKQP  5SWCTGF 'TTQT /KPKOK\CVKQP  %TQUU 'PVTQR[ /KPKOK\CVKQP (WUKQP QH /WNVKRNG %NCUUKſECVKQP &GEKUKQPU  2TKPEKRNGU  'ZCORNGU QH 'ODQFKOGPV %QPENWFKPI 4GOCTMU #RRGPFKZ /CZKOK\KPI /WVWCN +PHQTOCVKQP. 5. Large Vocabulary Speech Recognition Based on Statistical Methods Jean-Luc Gauvain and Lori Lamel .+/5+ (TCPEG  +PVTQFWEVKQP  1XGTXKGY  .CPIWCIG /QFGNKPI  6GZV 2TGRCTCVKQP  8QECDWNCT[ 5GNGEVKQP  0ITCO 'UVKOCVKQP  ./ #FCRVCVKQP  2TQPWPEKCVKQP /QFGNKPI  #EQWUVKE /QFGNKPI  #EQWUVKE (TQPVGPF  /QFGNKPI #NNQRJQPGU  *// 2CTCOGVGT 'UVKOCVKQP  *// #FCRVCVKQP  &GEQFKPI  5RGGEJ0QPURGGEJ &GVGEVKQP  &GEQFKPI 5VTCVGIKGU  'HſEKGPE[  %QPſFGPEG /GCUWTGU  +PFKECVKXG 2GTHQTOCPEG .GXGNU  &KEVCVKQP  5RGGEJ 4GEQIPKVKQP HQT &KCNQI 5[UVGOU  6TCPUETKRVKQP HQT #WFKQ +PFGZCVKQP  2QTVCDKNKV[ CPF .CPIWCIG &GRGPFGPEKGU. 6. Toward Spontaneous Speech Recognition and Understanding Sadaoki Furui 6QM[Q +PUVKVWVG QH 6GEJPQNQI[  +PVTQFWEVKQP  (QWT %CVGIQTKGU QH 5RGGEJ 4GEQIPKVKQP 6CUMU  5RQPVCPGQWU 5RGGEJ 4GEQIPKVKQP CPF 7PFGTUVCPFKPI  4GXKGY  %CVGIQT[ + JWOCPVQJWOCP FKCNQIWG. ‹E\&5&3UHVV//&.

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peaker Authentication Qi Li£ and Biing-Hwang Juang Ý £ $GNN .CDU Ý #XC[C .CDU 4GUGCTEJ  +PVTQFWEVKQP  5RGCMGT 4GEQIPKVKQP CPF 8GTKſECVKQP  8GTDCN +PHQTOCVKQP 8GTKſECVKQP  2CVVGTP 4GEQIPKVKQP KP 5RGCMGT #WVJGPVKECVKQP  $C[GUKCP &GEKUKQP 6JGQT[  5VQEJCUVKE /QFGNU HQT 5VCVKQPCT[ 2TQEGUU  5VQEJCUVKE /QFGNU HQT 0QP5VCVKQPCT[ 2TQEGUU  5RGGEJ 5GIOGPVCVKQP  5VCVKUVKECN 8GTKſECVKQP  5RGCMGT 8GTKſECVKQP 5[UVGO  8GTDCN +PHQTOCVKQP 8GTKſECVKQP  7VVGTCPEG 5GIOGPVCVKQP  5WDYQTF *[RQVJGUKU 6GUVKPI  %QPſFGPEG /GCUWTG %CNEWNCVKQP  5GSWGPVKCN 7VVGTCPEG 8GTKſECVKQP  8+8 'ZRGTKOGPVCN 4GUWNVU  5RGCMGT #WVJGPVKECVKQP D[ %QODKPKPI 58 CPF 8+8. ‹E\&5&3UHVV//&.

(15) . 5WOOCT[. 8. HMMs for Language Processing Problems Richard M. Schwartz and John Makhoul $$0 6GEJPQNQIKGU 8GTK\QP  +PVTQFWEVKQP  7UG QH 2TQDCDKNKVKGU  *KFFGP /CTMQX /QFGNU  0COG 5RQVVKPI  6QRKE %NCUUKſECVKQP  6JG /QFGN  'UVKOCVKPI *// 2CTCOGVGTU  %NCUUKſECVKQP  'ZRGTKOGPVU  +PHQTOCVKQP 4GVTKGXCN  # $C[GUKCP /QFGN HQT +4  6TCKPKPI VJG +4 *//  2GTHQTOCPEG  'XGPV 6TCEMKPI  7PUWRGTXKUGF 6QRKE &GVGEVKQP  5WOOCT[. 9. Statistical Language Models With Embedded Latent Semantic Knowledge Jerome R. Bellegarda #RRNG %QORWVGT +PE  +PVTQFWEVKQP  5EQRG .QECNKV[  5[PVCEVKECNN[Ō&TKXGP 5RCP 'ZVGPUKQP  5GOCPVKECNN[Ō&TKXGP 5RCP 'ZVGPUKQP  1TICPK\CVKQP  .CVGPV 5GOCPVKE #PCN[UKU  (GCVWTG 'ZVTCEVKQP  5KPIWNCT 8CNWG &GEQORQUKVKQP  )GPGTCN $GJCXKQT  .5# (GCVWTG 5RCEG  9QTF %NWUVGTKPI  9QTF %NWUVGT 'ZCORNG  &QEWOGPV %NWUVGTKPI  &QEWOGPV %NWUVGT 'ZCORNG  5GOCPVKE %NCUUKſECVKQP  (TCOGYQTM 'ZVGPUKQP  5GOCPVKE +PHGTGPEG  %CXGCVU  0ITCO .5# .CPIWCIG /QFGNKPI  .5# %QORQPGPV  +PVGITCVKQP YKVJ 0ITCOU. ‹E\&5&3UHVV//&.

(16) . .  .  %QPVGZV 5EQRG 5GNGEVKQP 5OQQVJKPI  9QTF 5OQQVJKPI  &QEWOGPV 5OQQVJKPI  ,QKPV 5OQQVJKPI 'ZRGTKOGPVU  'ZRGTKOGPVCN %QPFKVKQPU  'ZRGTKOGPVCN 4GUWNVU  %QPVGZV 5EQRG 5GNGEVKQP +PJGTGPV 6TCFG1HHU  %TQUU&QOCKP 6TCKPKPI  &KUEWUUKQP %QPENWUKQP. 10 Semantic Information Processing of Spoken Language – How May I sm Help You? A. L. Gorin, A. Abella, T. Alonso, G. Riccardi, and J. H. Wright, #66 .CDQTCVQ TKGU.     . +PVTQFWEVKQP %CNN%NCUUKſECVKQP .CPIWCIG /QFGNKPI HQT 4GEQIPKVKQP CPF 7PFGTUVCPFKPI &KCNQI %QPENWUKQPU. 11 Machine Translation Using Statistical Modeling Herman Ney, and F. J. Och #CEJGP 7PKXGTUKV[ QH 6GEJPQNQI[ )GTOCP[  +PVTQFWEVKQP  5VCVKUVKECN &GEKUKQP 6JGQT[ CPF .KPIWKUVKEU  6JG 5VCVKUVKECN #RRTQCEJ  $C[GU &GEKUKQP 4WNG HQT 9TKVVGP .CPIWCIG 6TCPUNCVKQP  4GNCVGF #RRTQCEJGU  #NKIPOGPV CPF .GZKEQP /QFGNU  %QPEGRV QH #NKIPOGPV /QFGNNKPI  *KFFGP /CTMQX /QFGNU  /QFGNU +$/ Ō  6TCKPKPI  5GCTEJ  #NIQTKVJOKE &KHHGTGPEGU DGVYGGP 5RGGEJ 4GEQIPKVKQP CPF .CPIWCIG 6TCPUNCVKQP  #NKIPOGPV 6GORNCVGU (TQO 5KPING 9QTFU VQ 9QTF )TQWRU  %QPEGRV  6TCKPKPI  5GCTEJ  'ZRGTKOGPVCN 4GUWNVU  6JG 6CUM CPF VJG %QTRWU ‹E\&5&3UHVV//&.

(17)  1HƀKPG 4GUWNVU  +PVGITCVKQP KPVQ VJG 8 '4$/1$+. 2TQVQV[RG 5[UVGO  (KPCN 'XCNWCVKQP  5RGGEJ 6TCPUNCVKQP 6JG +PVGITCVGF #RRTQCEJ  2TKPEKRNG  2TCEVKECN +ORNGOGPVCVKQP  5WOOCT[  4GHGTGPEGU 12 Modeling Topics for Detection and Tracking James Allan 7PKXGTUKV[ QH /CUUCEJWUGVVU #OJGTUV  6QRKE &GVGEVKQP CPF 6TCEMKPI  6QRKE CPF 'XGPVU  6&6 6CUMU  %QTRQTC  'XCNWCVKQP  $CUKE 6QRKE /QFGNU  8GEVQT 5RCEG  .CPIWCIG /QFGNU  +ORNGOGPVKPI VJG /QFGNU  0COGF 'PVKVKGU  &QEWOGPV 'ZRCPUKQP  %NWUVGTKPI  6KOG &GEC[  %QORCTKPI /QFGNU  0GCTGUV 0GKIJDQTU  &GEKUKQP 6TGGU  /QFGNVQ/QFGN  /KUEGNNCPGQWU +UUWGU  &GHGTTCN  /WNVKOQFCN +UUWGU  /WNVKNKPIWCN +UUWGU  7UKPI 6&6 +PVGTCEVKXGN[  &GOQPUVTCVKQPU  6KOGNKPGU  /QFGNKPI 'XGPVU  %QPENWUKQP. ‹E\&5&3UHVV//&.

(18) 1 Minimum Classification Error (MCE) Approach in Pattern Recognition Wu Chou Avaya Labs Research, Avaya Inc., USA. CONTENTS        . +PVTQFWEVKQP 1RVKOCN %NCUUKſGT HTQO $C[GU &GEKUKQP 6JGQT[ &KUETKOKPCPV (WPEVKQP #RRTQCEJ VQ %NCUUKſGT &GUKIP 5RGGEJ 4GEQIPKVKQP CPF *KFFGP /CTMQX /QFGNKPI /%' %NCUUKſGT &GUKIP 7UKPI &KUETKOKPCPV (WPEVKQPU 'ODGFFGF 5VTKPI /QFGN $CUGF /%' 6TCKPKPI 8GTKſECVKQP CPF +FGPVKſECVKQP 5WOOCT[ #EMPQYNGFIGOGPV 4GHGTGPEGU. 1.1 Introduction 2CVVGTP TGEQIPKVKQP KU C HCUV OQXKPI TGUGCTEJ CTGC 6JG CFXGPV QH RQYGTHWN EQORWV KPI FGXKEGU CPF VJG UWEEGUU QH UVCVKUVKECN CRRTQCEJGU UWEJ CU JKFFGP /CTMQX OQFGN HQT URGGEJ CPF NCPIWCIG RTQEGUUKPI VTKIIGTGF C TGPGYGF RWTUWKV HQT OQTG RQYGTHWN UVCVKUVKECN OGVJQFU VQ HWTVJGT TGFWEG VJG RCVVGTP TGEQIPKVKQP GTTQT TCVG CPF KORTQXG VJG TQDWUVPGUU QH VJG RCVVGTP ENCUUKſGT CETQUU XCTKQWU CFXGTUG EQPFKVKQPU #OQPI VJKU PGY RWTUWKV VJG WUG QH FKUETKOKPCPV HWPEVKQP OGVJQFU KP RCVVGTP TGEQIPKVKQP JCU GOGTIGF CU C RTQOKUKPI CRRTQCEJ CPF KV KU CRRNKGF UWEEGUUHWNN[ VQ URGGEJ CPF NCPIWCIG RTQEGUUKPI 6JKU EJCRVGT KU KPVGPFGF VQ RTQXKFG C TGXKUKV VQ VJG UVCVKUVKECN HQTOWNCVKQP QH VJG OKPKOWO ENCUUKſECVKQP GTTQT /%' DCUGF FKUETKOKPCVKXG OGVJ QFU KP URGGEJ CPF NCPIWCIG RTQEGUUKPI VCMG C ETKVKECN XKGY QH VJG CRRTQCEJ RTQXKFG C EQORTGJGPUKXG QXGTXKGY QH VJG ſGNF CPF JQRGHWNN[ KPURKTG QVJGT KPPQXCVKQPU VJCV YQWNF RQVGPVKCNN[ NGCF VQ PGY FKUETKOKPCVKXG OGVJQFU KP RCVVGTP TGEQIPKVKQP #NVJQWIJ VJG UVCVKUVKECN HQTOWNCVKQP QH /%' DCUGF FKUETKOKPCVKXG OGVJQFU JCU KVU TQQV KP VJG ENCUUKECN $C[GU FGEKUKQP VJGQT[ KV FGRCTVU HTQO VJG EQPXGPVKQPCN RCTCFKIO. ­. 6JKU EJCRVGT KU FGXGNQRGF DCUGF QP Œ&KUETKOKPCPVHWPEVKQPDCUGF OKPKOWO TGEQIPKVKQP GTTQT TCVG RCVVGTPTGEQIPKVKQP CRRTQCEJ VQ URGGEJ TGEQIPKVKQPŒ D[ 9W %JQW CRRGCTGF KP Proceedings of The IEEE 8QN  0Q  E  +'''. ‹E\&5&3UHVV//&.

(19) YJKEJ NKPMU C TGEQIPKVKQP VCUM VQ VJG RTQDNGO QH FKUVTKDWVKQP GUVKOCVKQP +PUVGCF KV VCMGU C FKUETKOKPCPV HWPEVKQP DCUGF UVCVKUVKECN RCVVGTP ENCUUKſECVKQP CRRTQCEJ CPF HQT C IKXGP HCOKN[ QH FKUETKOKPCPV HWPEVKQP QRVKOCN ENCUUKſGTTGEQIPK\GT FGUKIP KPXQNXGU ſPFKPI C UGV QH RCTCOGVGTU YJKEJ OKPKOK\G VJG GORKTKECN RCVVGTP TGEQIPKVKQP GTTQT TCVG 6JG WUG QH FKUETKOKPCPV HWPEVKQP KP RCVVGTP TGEQIPKVKQP YCU UVCTVGF OCP[ [GCTU CIQ 1PG ENCUUKECN GZCORNG QH WUKPI FKUETKOKPCPV HWPEVKQP HQT ENCUUKſGT FGUKIP KP UVCVKUVKECN NKVGTCVWTG KU VJG VYQ ENCUU ENCUUKſECVKQP RTQDNGO WUKPI NKPGCT FKUETKOKPCPV HWPEVKQPU = ? +P RCTVKEWNCT C YKPFQY DCUGF OGVJQF YCU FGUETKDGF KP =? HQT VJG VYQ ENCUU ENCUUKſECVKQP RTQDNGO WUKPI NKPGCT FKUETKOKPCPV HWPEVKQPU VJCV OKPKOK\G VJG RTQDCDKNKV[ QH ENCUUKſECVKQP GTTQT TCVG 6JG HQEWU QH VJKU EJCRVGT KU QP VJG TGEGPV FGXGNQROGPV QH VJG IGPGTCN /%' DCUGF FKUETKOKPCVKXG OGVJQFU 6JG FKUETKOKPCPV HWPEVKQPU VJCV YG GPEQWPVGT CTG WUWCNN[ PQPNKPGCT CPF QHVGP TGNCVGF VQ VJG UVTWEVWTG QH VJG UVCVKUVKECN HTCOGYQTM WUGF KP URGGEJ CPF NCPIWCIG RTQEGUUKPI UWEJ CU JKFFGP /CTMQX OQFGNU 6JG TGCUQP QH VCMKPI C FKUETKOKPCPV HWPEVKQP DCUGF CRRTQCEJ VQ ENCUUKſGT FGUKIP CU YKNN DG HWTVJGT GNCDQTCVGF KU FWG OCKPN[ VQ VJG HCEV VJCV YG NCEM EQORNGVG MPQYNGFIG QH VJG HQTO QH VJG FCVC FKUVTKDWVKQP CPF VTCKPKPI FCVC CTG KPCFGSWCVG RCTVKEWNCTN[ KP FGCNKPI YKVJ URGGEJ CPF NCPIWCIG RTQDNGOU 6JG RGTHQTOCPEG QH C TGEQIPK\GT KU PQTOCNN[ FGſ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ſGT ECP DG FKTGEVN[ GXCNWCVGF CPF QRVKOK\GF %NCUUKſGT FGUKIP YKVJQWV CUUWOKPI VJG MPQYNGFIG QH ENCUU RQUVGTKQT RTQDCDKNKVKGU YJKEJ CTG VJG DCUKU QH VJG FKUVTKDWVKQP GUVKOCVKQP DCUGF ENCUUKGT FGUKIP JCU DGGP UVWFKGF KP OCP[ CTGCU +P RCTVKEWNCT 6U[RMKP =? CPF #OCTK = ? RKQPGGTGF VJKU CRRTQCEJ HQT UGNHNGCTPKPI CPF UGNHQTICPK\KPI PGVU 6JG[ HQTOWNCVGF VJG RTQDNGO QH UGNHNGCTPKPI KPVQ C ENCUUKſECVKQP RTQDNGO YJKEJ EQPUKUVU QH QRVKOCN RCTVKVKQPKPI QH VJG QDUGTXCVKQP URCEG KPVQ TGIKQPU   HQT YJKEJ VJG GZRGEVGF TKUM  KU OKPKOK\GF +P CFFKVKQP C OCVJGOCVKECN OKPKOK\CVKQP RTQEGFWTG IGPGTCNK\GF RTQDCDKNKUVKE FG UEGPV )2& CNIQTKVJO QT UVQEJCUVKE CRRTQZKOCVKQP YCU RTQRQUGF CU C OGCPU HQT ENCUUKſGT FGUKIP WPFGT VJKU HTCOGYQTM 5KPEG VJGP XCTKQWU NQUU HWPEVKQPU JCXG DGGP WUGF KP FGUKIPKPI ENCUUKſGTU KPENWFKPI VJQUG RQRWNCT OGCPUSWCTG GTTQT DCUGF NQUU HWPEVKQPU *QYGXGT OCP[ VTCEVCDNG NQUU HWPEVKQPU FQ PQV JCXG C FKTGEV TGNCVKQP VQ VJG TGEQIPKVKQP GTTQT TCVG OKPKOK\CVKQP CPF VJGTGHQTG CNDGKV DCUGF QP FKUETKOKPCPV HWPEVKQPU VJG[ CTG PQV FKTGEVN[ TGNCVGF VQ TGEQIPKVKQP GTTQT TCVG YJKEJ UJQWNF DG VJG OQUV UGPUKDNG EJQKEG HQT ENCUUKſGT FGUKIP 1XGT VJG RCUV FGECFG VJG /%' DCUGF CRRTQCEJ JCU DGGP FGXGNQRGF VQ QXGTEQOG VJG HWPFCOGPVCN NKOKVCVKQPU QH VJG VTCFKVKQPCN CRRTQCEJ CPF VQ FKTGEVN[ NKPM VJG ENCUUKſGT FGUKIP RTQDNGO VQ ENCUUKſECVKQP GTTQT TCVG OKPKOK\CVKQP +P QTFGT VQ CNNGXKCVG VJG FGRGPFGPE[ QP VJG ENCUU RQUVGTKQT FKUVTKDWVKQPU C FKUETKOKPCPV HWPEVKQP DCUGF /%' CRRTQCEJ YCU RTQRQUGF D[ ,WCPI GV CN =? CU CP CNVGTPCVKXG VQ QRVKOCN ENCUUKſGT FG. . ‹E\&5&3UHVV//&. .

(20) UKIP #NVJQWIJ VJKU CRRTQCEJ CRRNKGU VQ VJG RCVVGTP TGEQIPKVKQP RTQDNGO KP IGPGTCN KV ſPFU XCTKQWU CRRNKECVKQPU KP URGGEJ CPF NCPIWCIG RTQEGUUKPI +V YCU ſTUV CRRNKGF VQ F[PCOKE VKOG YCTRKPI DCUGF RCVVGTP TGEQIPKVKQP U[UVGOU = ? #RRNKECVKQP VQ JKFFGP /CTMQX OQFGN DCUGF EQPVKPWQWU URGGEJ TGEQIPKVKQP U[UVGOU YCU HQTOWNCVGF CU C UGIOGPVCN CPF UVTKPI OQFGN DCUGF /%' CRRTQCEJ = ? CPF UWEEGUUHWN CR RNKECVKQPU QH VJKU CRRTQCEJ YGTG TGRQTVGF KP =     ? 6JKU CRRTQCEJ YCU HWTVJGT GZVGPFGF VQ HQTO C EQODKPGF UVTKPI OQFGN KP YJKEJ VTCKPKPI QH QVJGT OQFGN EQORQPGPVU KP URGGEJ CPF NCPIWCIG RTQEGUUKPI ECP DG CEJKGXGF WPFGT C WPK ſGF /%' HTCOGYQTM = ? +V YCU CRRNKGF VQ FKUETKOKPCVKXG OQFGN EQODKPCVKQP = ? CPF VQ CRRNKECVKQPU KP URGCMGT KFGPVKſECVKQP CPF XGTKſECVKQP =  ? 6JG DCUKE KFGC QH VJG /%' CRRTQCEJ YCU HWTVJGT FGXGNQRGF HQT CRRNKECVKQPU KP WVVGT CPEG XGTKſECVKQP RTQDNGOU =  ? # IGPGTCN HTCOGYQTM QH EQODKPKPI FG VGEVKQP CPF XGTKſECVKQP KP URGGEJ TGEQIPKVKQP CPF WPFGTUVCPFKPI YCU CNUQ RTQRQUGF KP YJKEJ VJG FKUETKOKPCPV HWPEVKQP DCUGF RCVVGTP TGEQIPKVKQP CRRTQCEJ YCU CRRNKGF KP DQVJ FGVGEVKQP CPF XGTKſECVKQP RTQEGUUGU = ? 9G DGIKP KP VJG PGZV UGEVKQP YKVJ C DTKGH TGXKGY QH VJG $C[GU FGEKUKQP VJGQT[ CPF KVU CRRNKECVKQP VQ VJG HQTOWNCVKQP QH UVCVKUVKECN RCVVGTP TGEQIPKVKQP RTQDNGO 9G KP VTQFWEG VJG FKUETKOKPCPV HWPEVKQP DCUGF UVCVKUVKECN RCVVGTP TGEQIPKVKQP CRRTQCEJ KP 5GEVKQP  +P 5GEVKQP  YG RTQXKFG C DTKGH KPVTQFWEVKQP VQ URGGEJ TGEQIPKVKQP CPF JKFFGP /CTMQX OQFGNKPI 6JG FKUETKOKPCPV HWPEVKQP DCUGF /%' RCVVGTP TGEQIPKVKQP CRRTQCEJ CPF KVU CRRNKECVKQP VQ *// DCUGF URGGEJ TGEQIPKVKQP U[UVGOU CTG KPVTQ FWEGF KP 5GEVKQP  %QORCTKUQPU CTG OCFG VQ QVJGT ETKVGTKC KP URGGEJ TGEQIPKVKQP CPF KP RCTVKEWNCT YG UVWF[ VJG TGNCVKQP DGVYGGP /%' CPF //+ OCZKOWO OWVWCN KPHQTOCVKQP ETKVGTKC KP ENCUUKſGT FGUKIP KP VJG UGEQPF JCNH QH 5GEVKQP  +P 5GEVKQP  YG UVWF[ VJG GODGFFGF UVTKPI OQFGN DCUGF /%' CRRTQCEJ CPF KVU GZVGPUKQP VQ VJG JKIJGT NGXGN EQODKPGF UVTKPI OQFGN 9G FKUEWUU KUUWGU CPF CRRNKECVKQPU KP FKUETKO KPCVKXG OQFGN EQODKPCVKQP FKUETKOKPCVKXG NCPIWCIG OQFGN GUVKOCVKQP CPF FKUETKO KPCVKXG HGCVWTG GZVTCEVKQP WPFGT VJG IGPGTCN VJGQTGVKECN HTCOGYQTM QH VJG EQODKPGF UVTKPI OQFGN 5GEVKQP  KU FGXQVGF VQ CRRNKECVKQPU QH FKUETKOKPCPV HWPEVKQP DCUGF RCVVGTP TGEQIPKVKQP CRRTQCEJ KP XGTKſECVKQP CPF KFGPVKſECVKQP 6JG FKUETKOKPCPV HWPEVKQP CRRTQCEJ KU UVWFKGF HQT XCTKQWU CRRNKECVKQPU KP URGGEJ CPF NCPIWCIG RTQ EGUUKPI UWEJ CU URGCMGT KFGPVKſECVKQP CPF XGTKſECVKQP WVVGTCPEG XGTKſECVKQP TGEQI PKVKQP DCUGF QP IGPGTCNK\GF EQPſFGPEG OGCUWTGU FGVGEVKQP CPF XGTKſECVKQP DCUGF CRRTQCEJ KP URGGEJ TGEQIPKVKQP CPF WPFGTUVCPFKPI 6JG EJCRVGT KU UWOOCTK\GF YKVJ FKUEWUUKQPU KP 5GEVKQP . 1.2 Optimal Classifier from Bayes Decision Theory. . (QT CP ENCUU ENCUUKſECVKQP RTQDNGO C ENCUUKſGT KU VQ ENCUUKH[ GCEJ TCPFQO UCORNG  6JG Z KPVQ QPG QH VJG / ENCUUGU 9G FGPQVG VJGUG ENCUUGU D[      ENCUUKſGT   FGſPGU C OCRRKPI HTQO VJG UCORNG URCEG ¾ VQ VJG FKUETGVG. . ‹E\&5&3UHVV//&.      .

(21) ECVGIQTKECN UGV  ¾   .GV     DG VJG LQKPV RTQDCDKNKV[ FKUVTKDWVKQP QH  CPF   C SWCPVKV[ YJKEJ KU CUUWOGF VQ DG MPQYP VQ VJG FGUKIPGT QH VJG ENCUUKſGT +P QVJGT YQTFU VJG FGUKIPGT JCU HWNN MPQYNGFIG QH VJG TCPFQO PCVWTG QH VJG UQWTEG (TQO VJG UGV QH LQKPV RTQDCDKNKV[ FKUVTKDWVKQPU VJG OCTIKPCN CPF VJG EQPFKVKQPCN RTQDCDKNKV[ FKUVTKDWVKQPU ECP DG GCUKN[ ECNEWNCVGF +P QTFGT VQ EJCTCEVGTK\G VJG RGTHQTOCPEG QH VJG ENCUUKſGT GXGT[ ENCUU RCKT   ECP DG CUUQEKCVGF YKVJ C EQUV QT NQUU HWPEVKQP   YJKEJ UKIPKſGU VJG EQUV QH ENCUUKH[KPI QT TGEQIPK\KPI C ENCUU  QDUGTXCVKQP KPVQ C ENCUU  GXGPV 6JG NQUU HWPEVKQP KU IGPGTCNN[ PQPPGICVKXG YKVJ     TGRTGUGPVKPI EQTTGEV ENCUUKſECVKQP 6JG NQUU HWPEVKQP KU C HWPEVKQP HTQO    YJGTG KU VJG UGV QH TGCN PWODGTU +P ENCUUKſECVKQP YG OCMG C FGEKUKQP   HQT QDUGTXKPI C TCPFQO UCORNG  5KPEG      KU VJG ENCUU RQUVGTKQT RTQDCDKNKV[ VJCV VJG TCPFQO KPRWV  KU HTQO    VJG CXGTCIG NQUU CUUQEKCVGF YKVJ OCMKPI C FGEKUKQP      ECP DG FGſPGF CU =?.    .      . . . .  . . . . 6JKU NGCFU VQ C TGCUQPCDNG RGTHQTOCPEG OGCUWTG HQT VJG ENCUUKſGT KG VJG GZRGEVGF NQUU FGſPGF CU.      

(22)  . . YJGTG   TGRTGUGPVU VJG ENCUUKſGTŏU FGEKUKQP CUUWOKPI QPG QH VJG őXCNWGUŒ         DCUGF QP C TCPFQO QDUGTXCVKQP  FTCYP HTQO C RTQDCDKNKV[ FKUVTKDWVKQP   6JG FGEKUKQP HWPEVKQP   FGRGPFU QP VJG ENCUUKſGT FGUKIP 1DXKQWUN[ KH VJG ENCUUKſGT KU UQ FGUKIPGF VJCV HQT GXGT[ .      .    .   VJG GZRGEVGF NQUU KP GSWCVKQP  YKNN DG OKPKOK\GF (QT OCP[ CRRNKECVKQPU KPENWFKPI URGGEJ TGEQIPKVKQP VJG NQUU HWPEVKQP   KU WUWCNN[ EJQUGP VQ DG VJG \GTQQPG NQUU HWPEVKQP FGſPGF D[.  .  .            . . . YJKEJ CUUKIPU PQ NQUU VQ EQTTGEV ENCUUKſECVKQP CPF C WPKV NQUU VQ CP[ GTTQT TGICTFNGUU QH VJG ENCUU 9KVJ VJKU V[RG QH NQUU HWPEVKQP VJG GZRGEVGF NQUU  KU VJWU VJG GTTQT RTQDCDKNKV[ QH ENCUUKſECVKQP QT TGEQIPKVKQP 6JG EQPFKVKQPCN NQUU DGEQOGU.    .     .  . .     . .   . 6JG QRVKOCN ENCUUKſGT VJCV CEJKGXGU OKPKOWO  KU VJWU VJG QPG VJCV KORNGOGPVU VJG HQNNQYKPI     KH          .  . ‹E\&5&3UHVV//&.

(23) (QT OKPKOWO GTTQT TCVG ENCUUKſECVKQP VJG ENCUUKſGT GORNQ[U VJG FGEKUKQP TWNG QH  YJKEJ KU ECNNGF VJG őOCZKOWO C RQUVGTKQTŒ /#2 FGEKUKQP 6JG OKPKOWO GTTQT TCVG CEJKGXGF D[ /#2 FGEKUKQP KU ECNNGF ő$C[GU TKUMŒ 9JGP CNN RQUVGTKQT RTQDCDKNKVKGU CTG MPQYP VJG ENCUUKſGT DCUGF QP /#2 TWNG KU CP QRVKOCN ENCUUKſGT DCUGF QP VJG $C[GU FGEKUKQP VJGQT[ *QYGXGT KH VJGUG RTQDCDKNKVKGU CTG PQV MPQYP QT VJG FGEKUKQP TWNG KU PQV DCUGF QP VJG ENCUU RQUVGTKQT RTQDCDKNKV[ VJGP YG ECPPQV WUG VJKU TGUWNV FKTGEVN[ +P RTCEVKEG VJGUG RTQDCDKNKVKGU JCXG VQ DG GUVKOCVGF HTQO C VTCKPKPI FCVC UGV YKVJ MPQYP ENCUU NCDGNU 6JG ENCUUKECN $C[GU FGEKUKQP VJGQT[ VJWU GHHGEVKXGN[ VTCPUHQTOU VJG ENCUUKſGT FGUKIP RTQDNGO KPVQ C FKUVTKDWVKQP GUVKOCVKQP RTQDNGO 6JKU KU VJG DCUKU QH VJG $C[GUKCP UVCVKUVKECN CRRTQCEJ VQ RCVVGTP TGEQIPKVKQP YJKEJ ECP DG UVCVGF CU IKXGP QT EQNNGEV C UGV QH VTCKPKPI FCVC QDUGTXCVKQPU  ½  ¾        YKVJ MPQYP ENCUU NCDGNU GUVKOCVG VJG C RQUVGTKQT RTQDCDKNKVKGU               HQT CP[  VQ KORNGOGPV VJG OCZKOWO C RQUVGTKQT FGEKUKQP HQT OKPKOWO $C[GU TKUM 6JG C RQUVGTKQT RTQDCDKNKV[      ECP DG TGYTKVVGP CU.              . . 5KPEG   KU PQV C HWPEVKQP QH VJG ENCUU KPFGZ CPF VJWU JCU PQ GHHGEV KP VJG /#2 FGEKUKQP VJG PGGFGF RTQDCDKNKUVKE MPQYNGFIG ECP DG TGRTGUGPVGF D[ VJG ENCUU RTKQT    CPF VJG EQPFKVKQPCN RTQDCDKNKV[       6JGTG CTG UGXGTCN KUUWGU CUUQEKCVGF YKVJ VJKU ENCUUKECN CRRTQCEJ (KTUV VJG FKUVTKDW VKQPU WUWCNN[ JCXG VQ DG RCTCOGVGTK\GF KP QTFGT HQT VJGO VQ DG RTCEVKECNN[ WUGHWN HQT VJG KORNGOGPVCVKQP QH VJG /#2 TWNG QH   6JG ENCUUKſGT FGUKIPGT VJGTGHQTG JCU VQ FGVGTOKPG VJG TKIJV RCTCOGVTKE HQTO QH VJG FKUVTKDWVKQPU (QT OQUV QH VJG TGCN YQTNF RTQDNGOU VJKU KU C FKHſEWNV VCUM 1WT EJQKEG QH VJG FKUVTKDWVKQP HQTO KU QHVGP NKO KVGF D[ VJG OCVJGOCVKECN VTCEVCDKNKV[ QH VJG RCTVKEWNCT FKUVTKDWVKQP HWPEVKQPU CPF KU XGT[ NKMGN[ VQ DG KPEQPUKUVGPV YKVJ VJG CEVWCN FKUVTKDWVKQP 6JKU OGCPU VJCV VJG VTWG /#2 FGEKUKQP ECP TCTGN[ DG KORNGOGPVGF CPF VJG OKPKOWO $C[GU TKUM IGPGTCNN[ TGOCKPU CP WPCEJKGXCDNG NQYGT DQWPF 5GEQPF IKXGP C RCTCOGVGTK\GF FKUVTKDWVKQP HQTO VJG WPMPQYP RCTCOGVGTU FGſPKPI VJG FKUVTKDWVKQP JCXG VQ DG GUVKOCVGF HTQO C ſPKVG COQWPV QH NCDGNGF VTCKPKPI FCVC TGSWKTKPI VJCV VJG GUVKOCVKQP OGVJQF JCU VQ DG CDNG VQ RTQFWEG EQPUKUVGPV RCTCOGVGT XCNWGU YJGP VJG UK\G QH VJG VTCKPKPI UCORNGU XCTKGU 6JKTF KV TGSWKTGU C VTCKPKPI FCVC UGV QH UWHſEKGPV UK\G KP QTFGT VQ JCXG TGNK CDNG RCTCOGVGT GUVKOCVGU $WV KP RTCEVKEG CPF HQT URGGEJ CPF NCPIWCIG RTQEGUUKPI KP RCTVKEWNCT VTCKPKPI FCVC CTG CNYC[U URCTUG EQORCTGF VQ CNN RQUUKDNG TGCNK\CVKQPU CPF XCTKCVKQPU KP JWOCP URGGEJ CPF NCPIWCIG 6JGUG VJTGG DCUKE KUUWGU RQKPV QWV C HWPFCOGPVCN HCEV VJCV KU FGURKVG VJG EQPEGRVWCN QRVKOCNKV[ QH VJG $C[GU FGEKUKQP VJGQT[ CPF KVU CRRNKECVKQPU VQ RCVVGTP TGEQIPKVKQP KV ECPPQV CNYC[U DG CEEQORNKUJGF KP RTCEVKEG DGECWUG OQUV RTCEVKECN ő/#2Œ FGEKUKQPU KP URGGEJ CPF NCPIWCIG RTQ EGUUKPI CTG PQV VTWG /#2 FGEKUKQPU 6JKU WPFGTUVCPFKPI KU ETKVKECN HQT VJG FKUEWUUKQP VJCV HQNNQYU. ‹E\&5&3UHVV//&.

(24) 1.3 Discriminant Function Approach to Classifier Design &KUETKOKPCPV HWPEVKQPU QP VJG QVJGT JCPF CTG VJQUG HWPEVKQPU YJKEJ EJCTCEVGTK\G VJG FGEKUKQP TWNG QH VJG ENCUUKſ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½  ¾  ENCUUKſECVKQP RTQDNGO 6JG ENCUUKſGT WUGU C FKUETKOKPCPV HWPEVKQP   UWEJ VJCV. . KH KH.    VJGP Z KU ENCUUKſGF VQ ½    VJGP Z KU ENCUUKſGF VQ ¾. . .KPGCT FKUETKOKPCPV HWPEVKQPU CTG VJQUG HWPEVKQPU QH VJG HQTO.      ¼ YJGTG  . .   ¾        CPF ¼ C TGCN PWODGT 1T OQTG IGPGTCNN[.  ½.   ¼  ½ ½ .      

(25) . . YJGTG. 

(26) .   ½ .     ¼       ½ .      .  ¼. . YJGTG KU VJG VTCPURQUKVKQP PQVCVKQP CPF VJG  CTG MPQYP NKPGCTN[ KPFGRGPFGPV HWPEVKQPU QH  (QT / ENCUU ENCUUKſECVKQP RTQDNGO WUKPI FKUETKOKPCPV HWPEVKQPU C UGV QH FKUETKOKPCPV HWPEVKQPU      .    CTG WUGF CPF VJG ENCUUKſGT   KU FGſPGF UWEJ VJCV     KHH  

(27)   .  . 9JGP VJG NQUU HWPEVKQP     KU URGEKſGF VJG RTQDNGO QH QRVKOCN ENCUUKſGT FGUKIP WUKPI FKUETKOKPCPV HWPEVKQPU DGEQOGU C OKPKOK\CVKQP RTQDNGO QH ſPFKPI C DGUV UGV QH FKUETKOKPCPV HWPEVKQPU       .    HTQO C ENCUU QH FKUETKOK PCPV HWPEVKQPU YJKEJ OKPKOK\GU VJG GZRGEVGF NQUU  CU FGſPGF KP 'S   +P QVJGT YQTFU VJG ENCUUKſGT FGUKIP RTQDNGO KU VQ ſPF.         .    . . ‹E\&5&3UHVV//&. .

(28)   ´µ ´  µ.     . .

(29)  . YJGTG     KU VJG IKXGP HCOKN[ QH FKUETKOKPCPV HWPEVKQPU +H VJG NQUU HWPEVKQP KU IKXGP CU KP 'S  CPF VJG RCTVKEWNCT UGV QH FKUETKOKPCPV HWPEVKQPU WUGF KP VJG ENCUUKſGT CTG VJG őVTWGŒ ENCUU RQUVGTKQT RTQDCDKNKV[     VJGP 'S  KORNG OGPVU VJG UCOG /#2 FGEKUKQP TWNG CU FGſPGF KP 'S   *QYGXGT KV KU KORQTVCPV VQ RQKPV QWV VJCV VJG FKUETKOKPCPV HWPEVKQP CRRTQCEJ VQ VJG QRVKOCN ENCUUKſGT FGUKIP CU URGEKſGF KP 'S  QHVGP JCU CP KPſPKVG PWODGT QH UQNWVKQPU GXGP HQT VJG UCOG  KU CP QRVKOCN UQNWVKQP VQ 'S ENCUUKſGT +V KU GCU[ VQ UGG VJCV KH       .   VJGP HQT CP[                KU CPQVJGT QRVKOCN UQNWVKQP CPF FGſPGU VJG UCOG ENCUUKſGT #ICKP VJKU KU SWKVG FKHHGTGPV HTQO VJG FKUVTKDWVKQP GUVKOCVKQP DCUGF CRRTQCEJ KP RCVVGTP ENCUUKſECVKQP +H VJG FKUETKOK PCPV HWPEVKQPU CTG NKOKVGF VQ VJG ENCUU RQUVGTKQT RTQDCDKNKVKGU CP[ FGXKCVKQP HTQO VJG őVTWGŒ ENCUU RQUVGTKQT RTQDCDKNKV[     YKNN TGUWNV KP C FKHHGTGPV ENCUUKſGT CPF YKNN DG KPHGTKQT VQ VJG QRVKOCN /#2 ENCUUKſGT VJCV CEJKGXGU VJG OKPKOWO $C[GU TKUM.  .     . 

(30) 

(31)   

(32) .  .  . 6JG WUG QH FKUETKOKPCPV HWPEVKQPU KP UVCVKUVKECN RCVVGTP TGEQIPKVKQP KU VQ UQNXG VJG ENCUUKſGT FGUKIP RTQDNGO YJGP VJG GZCEV HQTO CPF XCNWG QH VJG ENCUU RQUVGTKQT RTQDC DKNKVKGU     CTG PQV MPQYP GXGP YKVJ VJG JGNR QH VTCKPKPI FCVC QT VJG ENCUUKſGT JCU VQ DG DCUGF QP C RCTVKEWNCT ENCUU QH FKUETKOKPCPV HWPEVKQPU 6JGUG FKUETKOKPCPV HWPEVKQPU KP VJG ENCUUKſ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peech Recognition and Hidden Markov Modeling 5RGGEJ TGEQIPKVKQP KU C RTQDNGO QH TGEQIPK\KPI C YQTF UGSWGPEG HTQO JWOCP URGGEJ +V ECP DG XKGYGF CU C EQOOWPKECVKQP RTQDNGO 6JG JWOCP DTCKP UGTXGU CU VJG VGZV IGPGTCVQT YJKEJ IGPGTCVGU VJG YQTF UVTKPI   6JG YQTF UVTKPI IQGU VQ VJG CEQWUVKE EJCPPGN YJKEJ EQPUKUVU QH C URGCMGTŏU CTVKEWNCVQT[ CRRCTCVWU CPF QVJGT CEQWUVKE RTQ EGUUGU VJCV EQPXGTV VJG VGZV UVTKPI KPVQ CP CWFKDNG CEQWUVKE YCXGHQTO 6JG CEQWUVKE EJCPPGN KP XGTDCN EQOOWPKECVKQP CEVU CU C FCVC VTCPUFWEGT CPF EQORQUGT 6JG URGGEJ TGEQIPK\GT KU C FGEQFGT YJKEJ RGTHQTOU CP KPXGTUG QRGTCVKQP VQ FGEQFG VJG OGUUCIG HTQO VJG URGGEJ YCXGHQTO 6JGTGHQTG C FGEQFGT RGTHQTOU C OCZKOWO C RQUVGTKQT  UWEJ VJCV FGEKUKQP VJCV FGVGTOKPGU VJG YQTF UGSWGPEG .  

(33)      

(34)        Ï Ï ‹E\&5&3UHVV//&. .

(35) YJGTG      KU VJG UEQTG HTQO CEQWUVKE OQFGNKPI CPF    KU VJG UEQTG HTQO VJG NCPIWCIG OQFGN # V[RKECN URGGEJ TGEQIPKVKQP U[UVGO EQPUKUVU QH VJG HQNNQYKPI DCUKE EQORQPGPVU . . . . #EQWUVKE HGCVWTG GZVTCEVKQP #EQWUVKE HGCVWTG GZVTCEVKQP KU VQ GZVTCEV VJG HGC VWTGU HQT URGGEJ TGEQIPKVKQP HTQO VJG URGGEJ YCXGHQTO +V V[RKECNN[ KPENWFGU C UJQTVVKOG EGRUVTCN CPCN[UKU YJKEJ IGPGTCVGU C HGCVWTG XGEVQT QH NQY HTG SWGPE[  EGRUVTCN EQGHſEKGPVU HQT GXGT[  8CTKQWU UKIPCN RTQEGUU KPI RTQEGFWTGU CTG RGTHQTOGF VQ UGRCTCVG VJG UCNKGPV CEQWUVKE KPHQTOCVKQP HQT URGGEJ TGEQIPKVKQP RWTRQUGU (TQO PQY QP YG YKNN WUG VJG PQVCVKQP   ½      Ì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Ò  ½      Ò ½  YJKEJ KU VJG RTQDCDKNKV[ QH QDUGTXKPI YQTF Ò IKXGP VJG YQTF JKUVQT[ ½      Ò ½  &GEQFKPI GPIKPG 6JG FGEQFKPI GPIKPG UGCTEJGU HQT VJG DGUV YQTF UGSWGPEG IKXGP VJG HGCVWTG CPF VJG OQFGN (QT URGGEJ TGEQIPKVKQP DCUGF QP *// OQF GNKPI VJKU KU CEJKGXGF VJTQWIJ 8KVGTDK FGEQFKPI (QT C FKUETGVG QDUGTXCVKQP RTQDCDKNKV[ DCUGF U[UVGO YQTF UVTKPI  KU IKXGP D[  .   . Ï.  

(36) Ï   . YJGTG

(37) Å KU VJG DGUV UVCVG UGSWGPEG IKXGP EQPVKPWQWU FGPUKV[ *//U  . CPF VJG OQFGN. 

(38) Ï   .     . Ï.  . 

(39) . (QT. . YJKEJ KU DCUGF QP VJG NQINKMGNKJQQF UEQTG CNQPI VJG DGUV UVCVG UGSWGPEG  É . 1.4.1 Hidden Markov Modeling of Speech 5RGGEJ KU IGPGTCVGF HTQO JWOCP CTVKEWNCVQT CPF KV KU WPKSWG KP OCP[ YC[U 9JGP YG URGCM QWT CTVKEWNCVQT[ CRRCTCVWU VJG NKRU LCY VQPIWG CPF XGNWO OQFWNCVGU VJG CKT RTGUUWTG CPF ƀQY VQ RTQFWEG CP CWFKDNG UGSWGPEG QH UQWPFU &WG VQ VJG RJ[UKECN EQPUVTCKPVU VJG CTVKEWNCVQT EQPſIWTCVKQP ECPPQV WPFGTIQ XGT[ FTCUVKE EJCPIGU CPF FWTKPI VJG UJQTV KPVGTXCN YJGTG VJG CTVKEWNCVQT[ EQPſIWTCVKQP UVC[U TGNCVKXGN[ EQP UVCPV C TGIKQP QH őSWCUKUVCVKQPCTKV[Œ KP VJG RTQFWEGF URGGEJ ECP QHVGP DG QDUGTXGF. ‹E\&5&3UHVV//&.

(40) *KFFGP /CTMQX OQFGNKPI KU C RQYGTHWN UVCVKUVKECN HTCOGYQTM HQT VKOG XCT[KPI SWCUK UVCVKQPCT[ RTQEGUU CPF C RQRWNCT EJQKEG HQT UVCVKUVKECN OQFGNKPI QH URGGEJ UKIPCN )KXGP C URGGEJ WVVGTCPEG NGV  Ü ½ Ü Ü  DG C HGCVWTG XGEVQT UGSWGPEG GZVTCEVGF HTQO VJG URGGEJ YCXGHQTO YJGTG Ü  FGPQVGU C UJQTVVKOG XGEVQT OGCUWTG OGPV CPF KV KU EQPXGPVKQPCNN[ C EGRUVTCN XGEVQT (WTVJGT EQPUKFGT C ſTUVQTFGT UVCVG /CTMQX EJCKP IQXGTPGF D[ C UVCVG VTCPUKVKQP RTQDCDKNKV[ OCVTKZ      YJGTG  KU VJG RTQDCDKNKV[ QH OCMKPI C VTCPUKVKQP HTQO UVCVG VQ UVCVG  #UUWOG VJCV CV   VJG UVCVG QH VJG U[UVGO  KU URGEKſGF D[ CP KPKVKCN UVCVG RTQDCDKNKV[       6JGP HQT CP[ UVCVG UGSWGPEG Õ      VJG RTQDCDKNKV[ QH Õ DGKPI IGPGTCVGF D[ VJG /CTMQX EJCKP KU. .   . . . .     .   . . Õ     ¼ ¼ ½ ½¾    Ì ½Ì .  5WRRQUG VJG U[UVGO YJGP CV UVCVG   RWVU QWV CP QDUGTXCVKQP Ü  CEEQTFKPI VQ C FKUVTKDWVKQP

(41) Ø Ü   Ü             6JG JKFFGP /CTMQX OQFGN WUGF CU C FKUVTKDWVKQP HQT VJG URGGEJ WVVGTCPEG  KU VJGP FGſPGF CU     

(42)           Õ       Õ  Õ     ¼  Ø ½ Ø

(43) Ø Ü   YJGTG     

(44)      KU VJG RCTCOGVGT UGV HQT VJG OQFGN #U ECP DG UGGP KP   

(45) Ø  FGſPGU VJG FKUVTKDWVKQP HQT UJQTVVKOG QDUGTXCVKQPU CPF  EJCTCEVGTK\GU VJG DGJCXKQT CPF KPVGTTGNCVKQPUJKR DGVYGGP FKHHGTGPV UVCVGU QH VJG. URGGEJ IGPGTCVKQP RTQEGUU +P QVJGT YQTFU VJG UVTWEVWTG QH C JKFFGP /CTMQX OQFGN RTQXKFGU C TGCUQPCDNG OGCPU HQT EJCTCEVGTK\KPI VJG FKUVTKDWVKQP QH C URGGEJ UKIPCN 0QTOCNN[  VJG VQVCN PWODGT QH UVCVGU KU OWEJ UOCNNGT VJCP  VJG VKOG FWTCVKQP QH VJG URGGEJ WVVGTCPEG 6JG UVCVG UGSWGPEG Õ FKURNC[U C EGTVCKP FGITGG QH UVCDKNKV[ COQPI CFLCEGPV ¼ U FWG VQ VJG CDQXG OGPVKQPGF őSWCUKUVCVKQPCTKV[Œ 6JG WUG QH *//U CU URGGEJ FKUVTKDWVKQPU KU UJQYP VQ DG RTCEVKECNN[ GHHGEVKXG +V UJQWNF DG PQVGF VJCV VJG EJQKEG QH UVCVG QDUGTXCVKQP FKUVTKDWVKQPU Ø Ü  KU PQV URGEKſ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ſPF C DGUV UVCVG UGSWGPEG Õ YJKEJ KU QRVKOCN KP C EGTVCKP UGPUG IKXGP VJG URGGEJ HGCVWTG UGSWGPEG  5KPEG UVCVGU KP *// CTG TGNCVGF VQ YQTFU CPF YQTF ENCUUGU VJG YQTF UGSWGPEG KP URGGEJ WVVGTCPEG ECP DG KFGPVKſGF D[ VTCEKPI VJTQWIJ VJG YQTF NCDGNU KP UVCVG UGSWGPEG Õ 6JG GUVKOCVKQP RTQDNGO KU VQ GUVKOCVG. .

(46). . . ‹E\&5&3UHVV//&. .

(47) *// RCTCOGVGTU  HTQO C IKXGP UGV QH VTCKPKPI UCORNGU CEEQTFKPI VQ UQOG OGCP KPIHWN ETKVGTKQP 6JG EQPXGPVKQPCN CRRTQCEJ KU DCUGF QP VJG OCZKOWO NKMGNKJQQF. /. RTKPEKRNG CPF VJG OQFGN RCTCOGVGT UGV  KU GUVKOCVGF UQ VJCV VJG NKMGNKJQQF QP VJG VTCKPKPI FCVC KU OCZKOK\GF 8CTKQWU JKIJN[ GHſEKGPV /. DCUGF CNIQTKVJOU CTG FGXGNQRGF KP URGGEJ TGEQIPKVKQP HQT *//U UWEJ CU $CWO9GNEJ CNIQTKVJO =? CPF UGIOGPVCN MOGCPU CNIQTKVJO =? /QTG FKUEWUUKQPU QH RCTCOGVGT GUVKOCVKQP RTQD NGO HQT *//U ECP DG HQWPF KP =? +V UJQWNF DG PQVGF VJCV VJG EQPXGPVKQPCN /. OGVJQF KP URGGEJ TGEQIPKVKQP FQGU PQV PGEGUUCTKN[ NGCF VQ C OKPKOWO GTTQT TCVG RGT HQTOCPEG HQT VJG TGEQIPK\GT 6JKU KU FWG OCKPN[ VQ  VJG NKMGN[ OKUOCVEJ DGVYGGP VJG EJQUGP FKUVTKDWVKQP HQTO CPF VJG CEVWCN URGGEJ FCVC FKUVTKDWVKQP CPF  VJG ſPKVG VTCKPKPI MPQYP FCVC UGV YJKEJ KU QHVGP KPCFGSWCVG. 1.5 MCE Classifier Design Using Discriminant Functions #U KV KU PQVGF YKVJQWV VJG MPQYNGFIG QH VJG HQTO QH VJG ENCUU RQUVGTKQT RTQDCDKNK VKGU TGSWKTGF KP VJG ENCUUKECN $C[GU FGEKUKQP VJGQT[ ENCUUKſGT FGUKIP D[ FKUVTKDWVKQP GUVKOCVKQP QHVGP FQGU PQV NGCF VQ CP QRVKOCN RGTHQTOCPEG 6JKU OQVKXCVGU VJG GHHQTV QH UGCTEJKPI HQT QVJGT CNVGTPCVKXG ETKVGTKC KP ENCUUKſGT FGUKIP +P RCTVKEWNCT ETKVGTKC QH //+ OCZKOWO OWVWCN KPHQTOCVKQP CPF /&+ OKPKOWO FKUETKOKPCVKXG KPHQT OCVKQP CTG WUGF KP OCP[ CRRNKECVKQPU = ? #NVJQWIJ VJGUG OGVJQFU FGOQPUVTCVG UKIPKſECPV RGTHQTOCPEG CFXCPVCIGU QXGT VJG VTCFKVKQPCN /. CRRTQCEJ VJG[ CTG PQV DCUGF QP C FKTGEV OKPKOK\CVKQP QH C NQUU HWPEVKQP YJKEJ NKPMU VQ VJG ENCUUKſECVKQP GTTQT TCVG &Q6W GV CN =? UVWFKGF /%' UQNWVKQP HQT VJG VYQ ENCUU PQPRCTCOGVTKE ENCUUK ſECVKQP RTQDNGO WUKPI NKPGCT FKUETKOKPCPV HWPEVKQPU 6JG[ GORNQ[GF C YKPFQYGF UEJGOG VQ QXGTEQOG VJG RTQDNGO QH UKPIWNCT ITCFKGPV HWPEVKQPU CUUQEKCVGF YKVJ VJG GTTQT EQWPV KPFKECVQT HWPEVKQP QH VJG ENCUUKſGT # IGPGTCN CRRTQCEJ HQT OWNVKENCUU CPF PQPNKPGCT FKUETKOKPCPV HWPEVKQPU CTG RTQRQUGF D[ ,WCPI GV CN =? 6JKU IGP GTCN CRRTQCEJ KU ECNNGF őOKPKOWO ENCUUKſECVKQP GTTQT /%' OGVJQFŒ KP YJKEJ VJG ENCUUKſGT FGUKIP CPF RCTCOGVGT GUVKOCVKQP CTG VQ EQTTGEVN[ FKUETKOKPCVG VJG QDUGTXC VKQPU HQT DGUV TGEQIPKVKQPENCUUKſECVKQP TGUWNVU TCVJGT VJCP VQ ſV VJG FKUVTKDWVKQPU VQ VJG FCVC. 1.5.1 MCE Classifier Design Strategy .GV WU EQPUKFGT C UGV QH ENCUU FKUETKOKPCPV HWPEVKQPU              FG ſPGF D[ VJG RCTCOGVGT UGV  6JG ENCUUKſGT   KU VJG QPG VJCV HQT CP QDLGEV   . . KHH. .   

(48)   . . . 6JG IGPGTCN /%' ENCUUKſGT FGUKIP UVTCVGI[ KU DCUGF QP C URGEKCN V[RG QH NQUU HWPEVKQP 2CTCOGVGTU QH VJG ENCUUKſGT CTG GUVKOCVGF KP UWEJ C YC[ VJCV OKPKOK\KPI VJG GZRGEVGF. ‹E\&5&3UHVV//&.

(49) NQUU TGNCVGU VQ C OKPKOK\CVKQP QH VJG TGEQIPKVKQP GTTQT TCVG QH VJG ENCUUKſGT 6JKU KU CEJKGXGF VJTQWIJ C VJTGG UVGR RTQEGUU  6JG OKUENCUUKſECVKQP OGCUWTG KP VJG /%' DCUGF CRRTQCEJ KU FGſPGF CU.            . . .  . 

(50)     . . . YJGTG  KU C RQUKVKXG PWODGT =? 6JKU OKUENCUUKſECVKQP OGCUWTG KU C EQPVKPWQWU HWPEVKQP QH VJG ENCUUKſGT RCTCOGVGTU  CPF CVVGORVU VQ GOWNCVG VJG FGEKUKQP TWNG IKXGP VJG FKUETKOKPCPV HWPEVKQP    (QT CP  ENCUU WVVGTCPEG        KORNKGU OKUENCUUKſECVKQP CPF      OGCPU C EQTTGEV FGEKUKQP 9JGP  CR RTQCEJGU  VJG VGTO KP VJG DTCEMGV KU VJG  PQTO QP VJG FKUETGVG KPVGIGT UGV     

(51)

(52)

(53)   YJKEJ EQPXGTIGU VQ VJG    PQTO CPF DGEQOGU 

(54)       $[ XCT[KPI VJG XCNWG QH  CPF   QPG ECP VCMG CNN VJG EQORGVKPI ENCUUGU KPVQ EQPUKFGTCVKQP CEEQTFKPI VQ VJG KPFKXKFWCN UKIPKſECPEG YJGP UGCTEJKPI HQT VJG ENCUUKſGT RCTCOGVGT   6JG NQUU HWPEVKQP KU WUGF HQT TGEQIPKVKQP GTTQT TCVG OKPKOK\CVKQP 6JG OKUENCUUKſ ECVKQP OGCUWTG QH  KU GODGFFGF KP C UOQQVJ \GTQQPG HWPEVKQP HQT YJKEJ CP[ OGODGT QH VJG UKIOQKF HWPEVKQP HCOKN[ KU CP QDXKQWU ECPFKFCVG # IGPGTCN HQTO QH VJG loss function ECP VJGP DG FGſPGF CU.        . . YJGTG KU C UKIOQKF HWPEVKQP QPG GZCORNG QH YJKEJ KU.  . 

(55) .   . . YKVJ  PQTOCNN[ UGV VQ  CPF  UGV VQ ITGCVGT QT GSWCN VQ QPG %NGCTN[ YJGP     KU OWEJ UOCNNGT VJCP \GTQ YJKEJ KORNKGU EQTTGEV ENCUUKſECVKQP XKTVWCNN[ PQ NQUU KU KPEWTTGF 9JGP     KU RQUKVKXG KV NGCFU VQ C RGPCNV[ YJKEJ DGEQOGU GUUGPVKCNN[ C ENCUUKſECVKQPTGEQIPKVKQP GTTQT EQWPV  6JG ENCUUKſGT RCTCOGVGT GUVKOCVKQP KU DCUGF QP VJG OKPKOK\CVKQP QH VJG GZRGEVGF NQUU (QT CP[ WPMPQYP QDLGEV   VJG ENCUUKſGT RGTHQTOCPEG KU OGCUWTGF D[.    .   . .     .  . . YJGTG   KU VJG KPFKECVQT HWPEVKQP 6JG GZRGEVGF NQUU YJKEJ KU TGNCVGF VQ TGEQIPK VKQP GTTQT TCVG KU IKXGP D[.      

(56). . 6JKU VJTGGUVGR FGſPKVKQP GOWNCVGU VJG ENCUUKſECVKQP QRGTCVKQP CU YGNN CU VJG TGEQI PKVKQP GTTQT TCVG DCUGF RGTHQTOCPEG GXCNWCVKQP KP C UOQQVJ HWPEVKQPCN HQTO UWKVCDNG. ‹E\&5&3UHVV//&.

(57) HQT ENCUUKſGT RCTCOGVGT QRVKOK\CVKQP +V UJQWNF DG RQKPVGF QWV VJCV KH VJG EQTTGEV HQTO QH VJG RQUVGTKQT RTQDCDKNKV[      KU WUGF VJG $C[GU OKPKOWO TKUM KU VJGP GZRTGUUGF CU.  .                     CPF  TGRTGUGPVU VJG GPVKTG.  . . .     YJGTG      UKIPCN URCEG 6JKU ECP DG CRRTQZKOCVGF D[ VJG NQUU HWPEVKQP KP /%' CRRTQCEJ CU HQNNQYU.   .         . .  .                  .           . . #P KORQTVCPV RQKPV JGTG KU VJCV CRRTQZKOCVKQP CEEWTCE[ QH 'S  ECP DG EQP VTQNNGF D[ XCT[KPI VJG EQPUVCPVU KP VJG UOQQVJ /%' NQUU HWPEVKQP $CUGF QP VJG ETKVGTKQP QH   YG ECP EJQQUG VQ OKPKOK\G QPG QH VYQ SWCPVKVKGU HQT VJG ENCUUKſGT RCTCOGVGT UGCTEJ QPG KU VJG GZRGEVGF NQUU CPF VJG QVJGT VJG GORKTKECN NQUU. 1.5.2 Optimization Methods 6JG RWTRQUG QH VJG VTCKPKPI RTQEGUU KP VJG /%' CRRTQCEJ KU VQ ſPF C UGV QH RCTCOGVGTU  UQ VJCV C RTGUETKDGF NQUU KU OKPKOK\GF #U OGPVKQPGF RTGXKQWUN[ VJG VYQ MKPFU QH NQUU YG HQEWU QP CTG VJG GZRGEVGF NQUU CPF VJG GORKTKECN NQUU 1.5.2.1 Expected Loss (QT C ENCUUKſECVKQP RTQDNGO KPXQNXKPI FKHHGTGPV ENCUUGU VJG GZRGEVGF NQUU KU FG ſPGF CU.    

(58)  .  .   ¾.  

(59)  

(60) . . 8CTKQWU OKPKOK\CVKQP CNIQTKVJOU ECP DG WUGF VQ OKPKOK\G VJG GZRGEVGF NQUU 6JG IGPGTCNK\GF RTQDCDKNKUVKE FGUEGPV )2& CNIQTKVJO KU C RQYGTHWN CNIQTKVJO VJCV ECP DG WUGF VQ CEEQORNKUJ VJKU VCUM =? +P )2& DCUGF OKPKOK\CVKQP CNIQTKVJO VJG VCTIGV HWPEVKQP  KU OKPKOK\GF CEEQTFKPI VQ CP KVGTCVKXG RTQEGFWTG.       

(61)     YJGTG  KU C RQUKVKXG FGſPKVG OCVTKZ =?  KU C UGSWGPEG QH RQUKVKXG PWODGTU CPF 

(62)     KU VJG ITCFKGPV HWPEVKQP QH VJG NQUU HWPEVKQP CV      CPF

(63)  KU . . . . . . VJG VJ VTCKPKPI UCORNG WUGF KP VJG UGSWGPVKCN VTCKPKPI RTQEGUU 6JG EQPXGTIGPEG RTQRGTVKGU QH )2& CNIQTKVJO YCU UVWFKGF KP VJG NKVGTCVWTG GI =   ? CPF UQOGVKOGU WPFGT VJG PCOG QH UVQEJCUVKE CRRTQZKOCVKQP 7PFGT XGT[ IGPGTCN EQPFKVKQPU VJG HQNNQYKPI EQPXGTIGPEG RTQRGTVKGU ECP DG GUVCDNKUJGF =?. ‹E\&5&3UHVV//&.

(64) ½ .                   such that for all t, the inner product                     where is the Hessian matrix of second order partial derivatives;   £ 

(65)  

(66)    is the unique such that       

(67)      . Property 1 Suppose the following conditions are satisfied:. . . . ½. . . . . . . . . . .  . . . . . Then,  given by.   . . .      . . . . will converge to £ almost surely (i.e. with probability one). %QPFKVKQP  ECP DG EQPUKFGTCDN[ YGCMGPGF 'XGP YKVJQWV EQPFKVKQP NQYKPI KU UVKNN VTWG

(68)      . .  VJG HQN. . YJGTG  KU C UWDUGSWGPEG QH   +P VJKU ECUG  YKNN EQPXGTIG VQ C NQECN OKPKOWO RQKPV £ YJGTG      #FCRVKPI VJG OQFGN RCTCOGVGTU WUKPI C UCORNG D[ UCORNG WRFCVKPI HQTOWNC CU KP 'S  KU OQUV GHſEKGPV KP VGTOU QH VJG WUG QH CXCKNCDNG VTCKPKPI UCORNGU $WV VJG UKPING UCORNG DCUGF ITCFKGPV GUVKOCVKQP ECP DG PQKU[ NGCFKPI VQ ƀWEVWCVKQPU FWT KPI VJG RCTCOGVGT GUVKOCVKQP RTQEGUU $CVEJ OQFG CFCRVCVKQP UEJGOGU DCUGF QP C ITCFKGPV GUVKOCVG YJKEJ KU CP CXGTCIG QH GXGT[  UCORNGU ECP CNUQ DG WUGF 1VJGT XCTKCVKQPU VQ VJG QTKIKPCN )2& CNIQTKVJOU CTG CNUQ RQUUKDNG EJQKEGU VQ URGGF WR VJG EQPXGTIGPEG CPF TGFWEG VJG ƀWEVWCVKQP FWTKPI VJG ENCUUKſGT VTCKPKPI RTQEGUU 6JG EQPXGTIGPEG RTQRGTVKGU QH VJGUG TGNCVGF CFCRVCVKQP CNIQTKVJOU CTG DCUGF QP XCTKQWU UVCVKUVKECN EQPXGTIGPEG VJGQTKGU UWEJ CU OCTVKPICNG VJGQT[ RQVGPVKCN HWPEVKQPU GVE CPF KV KU UVKNN C XGT[ CEVKXG CTGC QH TGUGCTEJ *QYGXGT HTQO CP CRRNKECVKQP RQKPV QH XKGY KP QTFGT VQ CRRN[ VJKU CNIQTKVJO VQ URGGEJ TGEQIPKVKQP UWEJ CU C URGGEJ TGEQIPKVKQP U[UVGO WUKPI *//U VJG )2& CNIQTKVJO JCU VQ CEEQOOQFCVG XCTKQWU EQPUVTCKPVU KORQUGF QP VJG *// UVTWEVWTGU +P RCTVKEWNCT VJG )2& CNIQTKVJO KU CP WPEQPUVTCKPGF OKPKOK\CVKQP UEJGOG VJCV PGGFU OQFKſECVKQP HQT UQNXKPI OKPKOK\C VKQP RTQDNGOU YKVJ EQPUVTCKPVU #U YKNN DG UJQYP UJQTVN[ QPG ECP WVKNK\G RCTCOGVGT URCEG VTCPUHQTOCVKQPU VQ TGUQNXG VJKU KUUWG +P VJKU OGVJQF VJG QTKIKPCN RCTCOGVGTU CTG WRFCVGF VJTQWIJ VJG KPXGTUG VTCPUHQTO HTQO VJG VTCPUHQTOGF RCTCOGVGT URCEG VQ VJG QTKIKPCN RCTCOGVGT URCEG 6JKU KU FQPG KP UWEJ C YC[ VJCV EQPUVTCKPVU QP VJG QTKI KPCN RCTCOGVGTU CTG CNYC[U OCKPVCKPGF /QTG FGVCKNGF KNNWUVTCVKQPU QH VJKU CRRTQCEJ CTG IKXGP KP NCVGT UGEVKQPU. . . 1.5.2.2 Empirical Loss.  . . (QT C IKXGP VTCKPKPI FCVC UGV EQPUKUVKPI QH  UCORNGU      VJG GORKTKECN RTQDCDKNKV[ OGCUWTG   FGſPGF QP VJG VTCKPKPI FCVC UGV KU C FKUETGVG RTQDCDKNKV[ OGC. ‹E\&5&3UHVV//&.

(69) UWTG YJKEJ CUUKIPU GSWCN OCUU CV GCEJ UCORNG 6JG GORKTKECN NQUU QP VJG QVJGT JCPF KU VJWU GZRTGUUGF CU.    .   . . .   .  ¾   .   . .   . . YJGTG  FGPQVGU VJG KPFGZ QH VJG VTCKPKPI WVVGTCPEG   KP VJG VTCKPKPI UGV QH UK\G   CPF  KU VJG GORKTKECN OGCUWTG FGſPGF QP VJG VTCKPKPI UGV +H VJG VTCKPKPI UCORNGU CTG QDVCKPGF D[ CP KPFGRGPFGPV UCORNKPI HTQO C URCEG YKVJ C ſZGF RTQDCDKNKV[ FKUVTK DWVKQP   VJG GORKTKECN RTQDCDKNKV[ FKUVTKDWVKQP   YKNN EQPXGTIG VQ  KP FKUVTKDWVKQP  +P QVJGT YQTFU HQT CP[ OGCUWTCDNG HWPEVKQP  CU . . .  . . . . 6JG GORKTKECN NQUU FGſPGF QP VJG  KPFGRGPFGPV VTCKPKPI UCORNGU YKNN EQPXGTIG VQ VJG GZRGEVGF NQUU CU VJG UCORNG UK\G  KPETGCUGU 9KVJ UWHſEKGPV VTCKPKPI UCORNGU VJG GORKTKECN NQUU KU CP GUVKOCVG QH VJG GZRGEVGF NQUU 6JG IQQFPGUU QH VJKU GUVKOCVG KU FGVGTOKPGF D[ VJG VTCKPKPI UCORNG UK\G   CPF VJG EQPXGTIGPEG TCVG QH VJG GORKTKECN RTQDCDKNKV[ OGCUWTG   VQ VJG NKOKV FKUVTKDWVKQP   8CTKQWU WRRGT DQWPFU QP VJG EQPXGTIGPEG TCVG QH VJG GORKTKECN RTQDCDKNKV[ OGCUWTG ECP DG HQWPF KP =?. 1.5.3 Other Optimization Methods +V UJQWNF DG RQKPVGF QWV VJCV CNVJQWIJ VJG )2& V[RG QH CFCRVCVKQP CNIQTKVJO KU GH HGEVKXG CPF OQUV RQRWNCT QVJGT QRVKOK\CVKQP OGVJQFU ECP CNUQ DG WUGF HQT GTTQT TCVG OKPKOK\CVKQP /%' DCUGF ENCUUKſGT FGUKIP KU XGT[ URGEKſE QP VJG HQTO CPF UVTWEVWTG QH VJG FKUETKOKPCPV HWPEVKQP CPF NQUU HWPEVKQP TGICTFKPI VJG ENCUUKſGT CPF TGNCVKXGN[ WPTGUVTKEVGF VQ YJCV RCTVKEWNCT QRVKOK\CVKQP OGVJQFU YJKEJ CTG WUGF VQ OKPKOK\G VJG NQUU /CP[ KPPQXCVKQPU CTG RQUUKDNG HQT DGVVGT QRVKOK\CVKQP TGUWNVU +P RCTVKE WNCT OGVJQFU QH NKPGCT RTQITCOOKPI =? ITCFKGPV RTQLGEVKQP =? CPF ITQYVJ VTCPUHQTOCVKQP =  ? CTG CNUQ WUGF HQT OKPKOK\CVKQP QH VJG GZRGEVGF NQUU KP /%' ENCUUKſGT FGUKIP +P VJG ITQYVJ VTCPUHQTOCVKQP DCUGF CRRTQCEJ VJG IQCN KU VQ UGGM CVTCPUHQTOCVKQP 

(70)  UWEJ VJCV 

(71)  

(72)  YJGTG

(73) KU C RTQDCDKNKV[ XGEVQT . KG 

(74)    CPF

(75)    6JKU CRRTQCEJ UQOGVKOGU TGHGTTGF VQ CU GZVGPFGF $CWO9GNEJ $9 CNIQTKVJO KP UQOG NKVGTCVWTG YCU QTKIKPCVGF HTQO $CWO'CIQPŏU KPGSWCNKV[ HQT 

(76)  DGKPI C RQN[PQOKCN YKVJ PQPPGICVKXG EQGHſ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‹E\&5&3UHVV//&. .

(77) GUVKOCVKQP NKMG HQTOWNC  . .  .       ¼   ¼    ¼  . . YJGTG  KU C EQPUVCPV VQ DG FGVGTOKPGF CPF VJG UWO KP VJG FGPQOKPCVQT KU VCMGP QXGT CNN RCTCOGVGTU DGNQPIKPI VQ VJG UCOG FKUVTKDWVKQP  +V KU UJQYP KP =? VJCV VJGTG KU C XCNWG  UWEJ VJCV KH    'S  KU C ITQYVJVTCPUHQTOCVKQP     *QYGXGT 'S  ECPPQV DG FKTGEVN[ CRRNKGF VQ CPF       RCTCOGVGT GUVKOCVKQP QH EQPVKPWQWU RTQDCDKNKV[ FGPUKVKGU CPF PGY HQTOWNCVKQPU HQT EQPVKPWQWU FGPUKV[ *//U CTG PGGFGF 7UKPI C FKUETGVG CRRTQZKOCVKQP CTIWOGPV VJG ITQYVJVTCPUHQTOCVKQP OGVJQF KU GZVGPFGF VQ //+DCUGF RCTCOGVGT GUVKOCVKQP YKVJ EQPVKPWQWU FGPUKV[ *//U CPF PGY HQTOWNCVKQPU QH VJG ITQYVJVTCPUHQTOCVKQP HQT EQPVKPWQWU FGPUKV[ *//U KP //+ VTCKPKPI CTG FGTKXGF =? /QTG TGEGPVN[ CP GNGICPV RTQQH QH VJG VJGQTGVKECN RTQRGTVKGU QH VJG ITQYVJVTCPUHQTOCVKQP OGVJQF HQT //+ VTCKPKPI KU IKXGP KP =? YJKEJ GUVCDNKUJGU VJG ITQYVJVTCPUHQTOCVKQP OGVJQF KP C OQTG IGPGTCN UGVVKPI $WV OQTG YQTM TGOCKPU VQ DG FQPG KP QTFGT VQ CRRN[ VJG UKOKNCT OGVJQF HQT IGPGTCN /%' DCUGF RCTCOGVGT GUVKOCVKQP YKVJ EQPVKPWQWU RTQDCDKNKV[ FGPUKVKGU +V KU KPVGTGUVKPI VQ PQVG VJCV KH  KU NCTIG VJGP VJG EQPXGTIGPEG QH VJKU CNIQTKVJO KU UNQY CPF KH  KU VQQ NCTIG VJG CNIQTKVJO KU RTCEVKECNN[ PQV WUGHWN +P QTFGT VQ IGV HCUV EQPXGTIGPEG  PGGFU VQ DG CU UOCNN CU RQUUKDNG /QFKſECVKQPU QH VJG QTKIKPCN CNIQTKVJO CPF WUKPI UGCTEJ JGWTKUVKEU CTG CVVGORVGF VQ URGGF WR VJG EQPXGTIGPEG CPF RGTHQTOCPEG KORTQXGOGPVU QXGT VJG QTKIKPCN CRRTQCEJ CTG CNUQ TGRQTVGF KP = ?. 1.5.4 HMM as a Discriminant Function (QNNQYKPI   YG JCXG UGXGTCN YC[U QH WUKPI CP *// CU VJG FKUETKOKPCPV HWPE VKQP # DCUKE EQORQPGPV KP  KU VJG LQKPV QDUGTXCVKQPUVCVG RTQDCDKNKV[            ¼. . . . .   ½   

(78)  . . YJKEJ KU PQY FGſPGF CU C EQORQPGPV HWPEVKQP      HQT ENCUU CU YGNN 6JG FKUETKOKPCPV HWPEVKQP HQT ENCUU ECP VCMG UGXGTCN RQUUKDNG HQTOU DCUGF QP     . . .     .        . .     . . .      

(79)       . . . .    . . YJGTG  KU VJG VQVCN PWODGT QH RQUUKDNG UVCVG UGSWGPEGU CPF  KU C RQUKVKXG PWODGT CPF.  (WPEVKQPU QH VJG CDQXG. ‹E\&5&3UHVV//&.

(80) 0QVG VJCV  KU GSWKXCNGPV VQ VJG NKMGNKJQQF HWPEVKQP  KU GSWKXCNGPV VQ VJG OCZKOWO LQKPV QDUGTXCVKQPUVCVG UGSWGPEG RTQDCDKNKV[ CPF  KU C IGPGTCNK\GF OKZVWTG OQFGN YJKEJ CRRTQCEJGU  YJGP   9G WUG VJG NQICTKVJO QH.  CU CP GZCORNG KP QWT FGTKXCVKQP DGECWUG KV KU VJG OQUV RQRWNCT EJQKEG HQT *// DCUGF TGEQIPKVKQP U[UVGOU CUUQEKCVGF YKVJ 8KVGTDK FGEQFKPI 6JG CNIQTKVJO DCUGF QP  KU QHVGP ECNNGF segmental GPD =? 9G FGſPG HQT   ܽ  Ü      Ü  CPF Ü           ¼ YKVJ  DGKPI VJG FKOGPUKQP QH Ü  . . .       

(81)   Õ      Õ                Ü   .  . . . . . YJGTG Õ             KU VJG QRVKOCN UVCVG UGSWGPEG VJCV CEJKGXGU

(82)   Õ   9G CNUQ CUUWOG VJCV.  Ü   YJGTG.  .   . . 

(83)   Ü    . . .  FGPQVGU C PQTOCN FKUVTKDWVKQP

(84)  CTG VJG OKZVWTG YGKIJVU  .     VJG OGCP XGEVQT CPF   VJG EQXCTKCPEG OCVTKZ YJKEJ HQT UKORNKEKV[ KU       CUUWOGF VQ DG FKCIQPCN KG      +V OC[ DG FGUKTCDNG VQ OCKPVCKP VJG QTKIKPCN EQPUVTCKPVU KP VJG *// CU RTQDCDKNKV[ OGCUWTG UWEJ CU  VJG HWPEVKQP DGKPI PQPPGICVKXG      HQT CNN  CPF    HQT CNN  CPF GVE #NUQ YG CUUWOG     6JG HQNNQYKPI RCTCOGVGT  

(85)    . VTCPUHQTOCVKQPU CNNQY WU VQ OCKPVCKP VJGUG EQPUVTCKPVU FWTKPI RCTCOGVGT CFCRVCVKQP.     

(86)   

(87) .      .

(88)      YJGTG

(89)   

(90)       YJGTG .      .  . .    CPF    . . .   KP VJG VTCKPKPI UGV FKUETKOKPCVKXG CFLWUVOGPV QH VJG .                     . ‹E\&5&3UHVV//&. . .       . +V ECP DG UJQYP VJCV HQT   OGCP XGEVQT HQNNQYU. . . .

(91) YJGTG.      .      . . .       . . . . .  . .  .       .  . Æ     .    Ü . CPF.  .  .  . Ü.    . . .   . .  

(92) . . . . 

(93) .  .  . .  .   . .   . .    Ü .     . .

(94). . .  . .  . . .  . . YJGTG  KU VJG EGPVGT UNQRG QH VJG GZRQPGPVKCN UKIOQKF HWPEVKQP HQT   CU FGſPGF KP.   CPF Æ  FGPQVGU VJG -TQPGEMGT FGNVC HWPEVKQP (KPCNN[                . . . 5KOKNCTN[ HQT VJG XCTKCPEG                .     .    . . YJGTG.    .    Ü  .  . .        .  . Æ     .    Ü . .     .  .  .           

(95)   

(96) . 

(97)                 .  Ü  .      . (KPCNN[. .       

(98)      . . 5KOKNCT FGTKXCVKQPU HQT VJG VTCPUKVKQP RTQDCDKNKVKGU CPF VJG OKZVWTG YGKIJVU ECP DG GCUKN[ CEEQORNKUJGF = ?. ‹E\&5&3UHVV//&.

(99) #U OGPVKQPGF GCTNKGT VJG )2& CNIQTKVJO KU C ITCFKGPV DCUGF CPF WPEQPUVTCKPGF OKP KOK\CVKQP OGVJQF +P QTFGT VQ WUG HQT FKUETKOKPCPV HWPEVKQPU HTQO EGTVCKP HCOKNKGU UWEJ CU RTQDCDKNKV[ FGPUKV[ HWPEVKQPU HTQO *//U ECTG OWUV DG VCMGP UWEJ VJCV VJQUG RTQDCDKNKUVKE EQPUVTCKPVU CTG OCKPVCKPGF 6TCPUHQTOCVKQPU KP 'SU    CTG WUGF HQT VJKU RWTRQUG #PQVJGT KORQTVCPV CPF RGTJCRU VJG OQUV FKHſEWNV KUUWG KP )2& DCUGF NQUU HWPEVKQP OKPKOK\CVKQP CRRTQCEJ KU JQY VQ FGUKIP VJG UVGR UK\G 1PG CRRCTGPV TGCUQP KU VJCV YG PGGF C IQQF UVGR UK\G VQ UVCTV YKVJ UKPEG VJG OQFGN CFCRVCVKQP YKNN DG RGTHQTOGF QPN[ C ſPKVG PWODGT QH VKOGU +H VJG UVGR UK\G KU VQQ NCTIG VJG ENCUUKſ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ſGT JCXG FKHHGTGPV UGPUKVKXKVKGU VQ VJG UVGR UK\G KP RCTCOGVGT CFCRVCVKQP 1PG UVGR UK\G ECP DG VQQ UOCNN HQT UQOG RCTCOGVGTU CPF VQQ NCTIG HQT QVJGTU +P RCTVKEWNCT VJG OCIPKVWFG QH XCTKCPEGU KP VJG OKZVWTG )CWUUKCP QDUGTXCVKQP FGPUKVKGU ECP XCT[ KP VJG TCPIG DGVYGGP ½¼¼ VQ ½¼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ſGT VQYCTFU UQOG URGEKſE RQRWNCVKQPU 9KVJ VJG CFXCPEG QH OKETQRTQEGUUQTU UWEJ OGVJQFU JCXG DGEQOG EQORWVCVKQPCNN[ HGCUKDNG 6JG CDQXGOGPVKQPGF UGIOGPVCN )2& CNIQTKVJO ſPFU OCP[ CRRNKECVKQPU KP URGGEJ TGEQIPKVKQP 6JG TGEQIPKVKQP RGTHQTOCPEG CFXCP VCIG QXGT VJG VTCFKVKQPCN FKUVTKDWVKQP DCUGF /. CRRTQCEJ KU TGRQTVGF HTQO XCTKQWU UKVGU CPF KP FKHHGTGPV CRRNKECVKQPU =    ? 6JG UWEEGUU QH VJKU CNIQTKVJO KP URGGEJ TGEQIPKVKQP RTQXKFGU GZRGTKOGPVCN GXKFGPEG VJCV ENCUUKſGT FGUKIP DCUGF QP GTTQT TCVG OKPKOK\CVKQP KU HGCUKDNG GXGP HQT F[PCOKE RCVVGTPU CU FKHſEWNV CU URGGEJ +ORTQXGF TGEQIPKVKQP RGTHQTOCPEG QXGT VTCFKVKQPCN FKUVTKDWVKQP DCUGF /. CRRTQCEJ CTG CNUQ TGRQTVGF KP CTGCU QWVUKFG QH URGGEJ UWEJ CU 1%4 KOCIG TGEQIPKVKQP CPF JCPFYTKVKPI TGEQIPKVKQP =?. 1.5.5 Relation between MCE and MMI +P CFFKVKQP VQ VJG /%' ETKVGTKQP QVJGT ETKVGTKC CTG CNUQ WUGF KP UQECNNGF FKUETKOKPC VKXG ENCUUKſGT FGUKIP (QT *// DCUGF U[UVGOU VJG ETKVGTKC QH OCZKOWO OWVWCN KPHQTOCVKQP //+ =? EQPFKVKQPCN OCZKOWO NKMGNKJQQF GUVKOCVG %/.' =?. ‹E\&5&3UHVV//&.

(100) OKPKOWO FKUETKOKPCVKQP KPHQTOCVKQP /&+ =? CPF *ETKVGTKC =? CTG QVJGT CN VGTPCVKXGU YJKEJ JCXG HQWPF VJGKT WUG KP URGGEJ TGEQIPKVKQP #OQPI VJGO //+ KU OQUV RQRWNCT CPF CRRNKGF KP OCP[ CRRNKECVKQPU YKVJ UWEEGUU 6JG //+ CRRTQCEJ KU DCUGF QP VJG OWVWCN KPHQTOCVKQP       DGVYGGP VJG CEQWUVKE QDUGTXCVKQP : CPF KVU EQTTGEV NGZKECN U[ODQN    (QT VJG  ENCUU ENCUUKſECVKQP RTQDNGO VJG NQICTKVJO QH VJG OWVWCN KPHQTOCVKQP JCU VJG HQNNQYKPI HQTO       .       .  .  .      . . . . .  . .  .           . . . YJGTG  TWPU QXGT CNN RQUUKDNG  ENCUU U[ODQNU           CPF          CTG VJG NQINKMGNKJQQF UEQTGU QH  QP VJG EQTTGEV NGZKECN U[ODQN CPF VJG VJ NGZKECN U[ODQN TGURGEVKXGN[ (TQO 'S    . .    .    .  .           . . YJKEJ TGNCVGU      VQ VJG RQUVGTKQT RTQDCDKNKV[      +P //+ VTCKPKPI VJG ETKVGTKQP QH VJG ENCUUKſGT FGUKIP CPF RCTCOGVGT GUVKOCVKQP KU VQ OCZKOK\G VJG CXGTCIG OWVWCN KPHQTOCVKQP       QP VJG VTCKPKPI UGV 'ZRGTKOGPVCN URGGEJ TGEQIPKVKQP TGUWNVU KPFKECVG VJCV ENCUUKſGT FGUKIP DCUGF QP VJG //+ ETKVGTKQP ECP NGCF VQ DGV VGT TGEQIPKVKQP RGTHQTOCPEG VJCP VJG EQPXGPVKQPCN CRRTQCEJ WUKPI VJG /. ETKVGTKQP = ? #NVJQWIJ VJKU ETKVGTKQP KU YGNN HQWPFGF KP KPHQTOCVKQP VJGQT[ RQUUGUUKPI IQQF VJGQTGVKECN RTQRGTVKGU CPF WPKSWG KP OCP[ YC[U KV KU PQV DCUGF QP C FKTGEV OKP KOK\CVKQP QH VJG ENCUUKſECVKQP GTTQT TCVG CPF KU SWKVG FKHHGTGPV HTQO VJG /%' DCUGF CRRTQCEJ 6JG TGNCVKQP DGVYGGP //+ CPF /%' KU C XGT[ KPVGTGUVKPI VQRKE CPF UVWF KGF KP = ? +V KU HQWPF VJCV WPFGT EGTVCKP EQPFKVKQPU FKTGEV EQORCTKUQPU ECP DG OCFG DGVYGGP VJGUG VYQ CRRTQCEJGU 6JG FKUEWUUKQP DGNQY KU DCUGF QP =? 9G FGTKXG VJG GZRNKEKV TGNCVKQPU DGVYGGP /%' CPF //+ CPF HTQO VJGTG RTQRGTVKGU QH DQVJ CRRTQCEJGU ECP DG KNNWUVTCVGF .GV WU CUUWOG         

(101)

(102)

(103)    C ECUG QH WUKPI C WPKHQTON[ FKUVTKDWVGF NCPIWCIG OQFGN 6JG OWVWCN KPHQTOCVKQP HTQO 'S  KU IKXGP D[.  .           . . .      .  . CPF VJG //+ OQFGN RCTCOGVGT GUVKOCVKQP ETKVGTKQP KU.  . 

(104)        

(105)       .    . . . . . .       

(106).  .  6JG EQTTGURQPFKPI /%' CRRTQCEJ WUKPI VJG UCOG     CPF    CU KP 'S.   JCU VJG HQNNQYKPI HQTO. ‹E\&5&3UHVV//&.

(107) . ¯ 6JG OKUENCUUKſECVKQP OGCUWTG.          . .   .     . .   . ¯ 6JG /%' OQFGN RCTCOGVGT GUVKOCVKQP KU 

(108)      .  . . . YJGTG.     %QPUKFGT VJG URGEKCN ECUG QH .  .        . YKVJ . . . . VJG HQNNQYKPI CNIGDTCKE TGNCVKQPU ECP DG FGTKXGF.                   . .  . .   . . . .      .   .    

(109) CPF. . .      .   .     

(110).    . . . . (TQO 'S   VJG NQICTKVJO QH VJG OWVWCN KPHQTOCVKQP ECP DG GZRTGUUGF DCUGF QP VJG OKUENCUUKſECVKQP OGCUWTG     QH 'S  KP VJG /%' HQTOWNCVKQP.  

(111)           . .     . .    . .      . .       . .       . (TQO 'S   KV ECP DG UGGP VJCV VJG NQUU HWPEVKQP KP //+ KU XGT[ FKHHGTGPV HTQO VJG QPG WUGF KP /%' CRRTQCEJ +P CFFKVKQP VQ C EQPUVCPV UJKHV    KV KU VJG NQIC TKVJO QH VJG UKIOQKF HWPEVKQP  QP VJG OKUENCUUKſECVKQP OGCUWTG     PQV QP VJG UKIOQKF HWPEVKQP KVUGNH CU KP /%' CRRTQCEJ 6JG F[PCOKE TCPIG QH VJKU NQUU HWPEVKQP KU HTQO   VQ  ½ +V KU CRRCTGPV VJCV VJG //+ QDLGEVKXG HWPEVKQP KU PQV VT[KPI VQ CRRTQZKOCVG VJG TGEQIPKVKQP GTTQT TCVG HWPEVKQP CPF KVŏU QRVKOCNKV[ VQ ENCUUKſGT FGUKIP ECPPQV DG FKTGEVN[ GUVCDNKUJGF HTQO VJG GTTQT TCVG OKPKOK\CVKQP EQPUKFGTCVKQP (TQO VJG FKUETKOKPCPV HWPEVKQP RQKPV QH XKGY //+ KU VQ OKPKOK\G VJG CXGTCIG OKU ENCUUKſECVKQP OGCUWTG    KH       KP 'S  KU CRRTQZKOCVGF D[    6JKU KPVGTRTGVCVKQP KU SWKVG FKHHGTGPV HTQO VJG RQUVGTKQT RTQDCDKNKV[ DCUGF KPVGTRTGVCVKQP FGUETKDGF KP 'S  YJKEJ KU DCUGF QP FKUVTKDWVKQPCN CUUWORVKQPU +V GZRNCKPU VJG GZRGTKOGPVCN TGEQIPKVKQP RGTHQTOCPEG KORTQXGOGPVU QDVCKPGF HTQO VJG //+ CRRTQCEJ GXGP KP VJG ECUG YJGTG VJG FKUVTKDWVKQPCN CUUWORVKQP KU MPQYP PQV XCNKF. ‹E\&5&3UHVV//&.

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