Hemel, Johannes Bernardus

Voet, Hilko van der

English

Dissertations of the University of Groningen

   University of GroningenMultivariate classification methods and their evaluation in applications.Voet, Hilko van der; Hemel, Johannes BernardusIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1988Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Voet, H. V. D., & Hemel, J. B. (1988). Multivariate classification methods and their evaluation inapplications. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 04-06-2022SUMIVIARYl l h i  s  t h ê s  i  s  i  s  c o n c e r n e d  w i  t h  t h e  a p p l -  i  c a t i  o n  o fm a t h e m a t i c a l  s E a t i s t i c a l  r - o o l s  f o r  p a t t e r n  r e c o g n i t i o n ,e s p e c i a l l y  m u l t i v a r i a t e  c l - a s s i f i c a t i o n  m e t h o d . s  ( M C M s ) ,  t on l : c c i  f i n a 1 - i n n  n r n l r l o m q  i n  ^ n ^ l w t i n a l  c h e m i s t r wy r v s f s r l €C h a p t e r  1 .  I  í s  a  g e n e r a l  i n t r o d u c t i o n  a n d  s e r v e s  t w op u r p o s  e s F i r s t .  i t  d . e s c r i b e s  ( i n  s e c t i o n  1 .  1 .  1  )  t n eb a c k g r o u n d  o f  t h e  r e s e a r c h  i n  t h i s  t h e s i s .  T \ , r ' o  p r a c t i c a lp r o b l  e m s  ,  o n ê  f  r o m  f o o d  c h e m i  s  t r y  a n d  t h e  o t h e r  f r o mc l i n i c a l  c h e m j - s t r y ,  a r e  s h o w n  t o  h a v e  a  s i m i l - a r  s t r u c t u r e ,t . n  l r e  t a c k l  e d  h w  t e c h - i  o r r e s  f o r  m u f t i v a r i a t e  c l a s s i f i c a t i o n .A  s e c o n d  p u r p o s e  o f  t h i s  c h a p t e r  i s  t o  g i v e  t h e  o t h e re h a n t e r s  ^  n r o n p r  e n n t e x t  h r w  r e v i  e w i  n o  s n m e  r e l  a t e d  w o r k  i nu  y r v I J v !t h e  f i t e r a t u r e  i n  c o n n e c t i o n  w i t h  o u r  o w n  r e s u f t s .  I ns e c t i o n  L -  L . 2  m e t h o d s  f o r  m u l - t i v a r i a t e  c l a s s i f i c a t i o n  a r ec o n s i d e r e d ,  i n c l u d i n g  d  p r o p o s a - L  f o r  a  n e w  M C M  ( E L E Q D À ) ,r e l a t e d  t o  m e t h o d . s  a p p l i e d  a m p l y  i n  I a t e r  c h a p t e r s .  I ns e c t i o n  1 . 1 . 3  m e t h o d s  a n d .  c r i t e r i a  f o r  t h e  e v a f u a t i o n  o f  t h es u c c e s s  o f  c l a s s i f i c a t i o n  p r o c e d u r e s  a r e  r e v i e w e d .C h a p t e r  1 . 2  d e s c r i b e s  a  p r e l i m i n a r y  s t u d y  o f  t h ea n n l  i  c a b i  I  j  f v  o f  n = f + ó r n  r o n n a 6 j  f j  6 n  t e e h n i  o r r e s  t O  t h eg P y 4 + v g ! + + 4 9 ] * v v v Y . . + 9 + v 4 ln r n h l  e m  n f  d r  - ^ * r  * r  - - r '  n -  L ^ t w e e n  w i n e s  o f  d i f f e r e n tP ! v ! f  e l r  a u f  r r Yn o n o r a n h i  c  n r i  o i - n A  d a t a  s e t  c o n s i s t i n q  o f  d i v e r s ec h e m l c a l  m e a s u r e m e n t s  o n  s a m p . I e s  o f  r e d  w i n e s  f r o m  t h e  w e l ] -known  Bo rd .eaux  and  Bou rgogne  reg i i ons  i s  desc r i bed  and  used .I  ' ' - - ^  |  n : t J - ê r r r  r a n a n n i  l - i  n n  t - a n h n i  n r r o c  : r r : i  l  a l - r ' l  oL v  e v  P q L L s l r r  ! € u u Y r r fi  n  t h e  q o f t w a r c  n à ^ L - = ^ ó r  À p r H r r D  A L L o c  a n d  s P S S ,  I t  j - sc o n c l - u d . e d  t h a t  a  c h e m i c a l  d i f f e r e n t i a t i o n  b e t w e e n  t h e  t w ow j - n e  t y p e s  i s  f e a s i b l - e .  I t  w a s  u s e f u l -  t o  l - i n i t  t h ed i m e n s r o n a l i t y  o f  t ' h e  m e a s u r e m e n t s  b y  v a r i a b l - e  s e l - e c t i o nn r n n o d r r  r o cI n  t h e  r e m a i n i n g  t h r e e  c h a p t e r s  o f  P a r t  1  t h e  a t t e n t j - o ni s  f o c u s s e d .  o n  a p p l i c a t i o n s  i n  t h e  f i e L d  o f  e f i n i c a lc h e m i s t r y .  l n  C h a p t e r  J .  J  t h e  u s u a l -  p r a c t i c e  o f  d i a g n o s i n gp a t i e n t s  o n  t h e  b a s r s  o f  s e p a r a t e  u n i v a r i a t e  r e f e r e n c ei n t e r v a ] s  f o r  a  r n u l - t i t u d . e  o f  b l - o o d  c o n s t i t u e n t s  i sr e s p e c t e d ,  a n d  a  r e c e n t  m e t h o d  f o r  o b t a i n i n g  s u c h  ' n o r m a l 'i n t e r v a l s  f r o m  a  p o p u l a t i o n  o f  h o s p i t a l i z e d  ( a n d  t h e r e f o r eo f t e n  ' n o n - n o r m a f ' )  p e r s o n s  i s  c r i t i c a ] 1 y  d i s c u s s e d .R e f e r e n c e  l i m i t s  a r e  d e t e r m i n e d  u s i n g  t h e  d a t a b a s e  o f  t h eí l r n n i  n d o n  I l n r  r r o r c  i  1 -  r r  Ë I n c n i  f  a l3 8 5' Sunnaryfn  Chapter  1 .4  the  in rpor tance o f  a  mu l t , i var ia te  approacht o  m e d i c a l  c l i a g n o s i s  i s  s t r e s s e d .  f t  i s  s h o w n  t h a tnu l t i var ia te  tecbn iques  fo r  d isp lay ing  the  da ta  rnay  d iscLosedata  charac ter is t i cs  tha t  remain  unnot iced  in  a  un i .var ia tea n a l  y s  1  s .T h e  s u b j e c t  o f  C h a p t e r  1 . 5  i s  s o m e w h a t  o u t s i d e  t h e  m a j - nl i n e  o f  t h i s  t h e s i s .  T h e  s e t s  o f  t ê s t s  r e q u e s t e d  f r o m  t h ec l in ica l  chemica l  labara tory  by  the  phys ic ians  are  ana lyzedfor  d .epar tment -spec i f i c  pa t te rns .  I t  i s  sho ! . rn  tha t  miss lngva lues  in  a  da ta  mat r ix  w j - th  on ly  the  resu l ts  o f  reques tedtes ts  a re  no t  occur r ing  in  a  random fash ion .In  Chapters  2 .  1  and 2 .2  t \ ^ ro  moi l i f i ca t ions  o f  the  inchemomet r ics  we l l -known c lass i f i ca t ion  method SIMCÀ areproposed.  I t  i s  shown how pos ter io r  p robab i l i t ies  o f  c lassmembersh ip  can be  a t tache i l  to  the  s lass i f i ca t ion  resu l - ts  o fS IMCA.  The o ther  p roposec l  nod. i f i ca t ion  is  more  fundamenta l .S IMCÀ f i t s  p r i -nc ipa l -component  mo i le ls  to  the  i la ta  o f  eacht r a i n i n g  c l a s s ,  a n d  a  d . i f f e r e n t  t y p e  o f  m o d e l l i n g  i s  a p p l i e din  the  subspace spanned by  the  most  inpor tan t  e i -genvec tors( t e r n e d  b y  u s  t h e  i n s i d e - m o d e 1  Ê p a c e )  a n d  t h e  s u b s p a c e  o fthe  remain ing  e igenvec tors  ( the  ou ts ide-moi le l  space ) .  À  ne \ ,vn u l t i v a r i a t e  c l - a s s i f i c a t i o n  n e t h o c l  i s  p r o p o s e d ,  t h a t  t r e a t sthe  ou ts ide-mode l  spacê as  in  S IMCA,  bu t  tha t  uses  kerne ldens i t ies  (we l1-known f rom the  ÀLLOC nethod. )  fo r  node l l ingin  the  ins ide-no i le l  space.  The resu l t ing  metho i l  i s  te rmedCLÀSSY and has  been imp lemented in  the  CLÀS program (seeC h a p t e r  3 . 1 ) .  ï n  C h a p t e x  2 . 2  i t  i s  c o m p a r e d  t o  o t h e r  m e t h o d su s i n g  s o m e  p r a c t i c a l  d a t a  s e t s .Chapter  2 .3  i -n t roduces  s tepwise  de le t ion ,  a  nes t  p roposa lf o r  t h e  p r e p r o c e s s i n g  o f  d a t a  m a t r i c e s  c o n t a i n i n g  r a n d o m l yoccur r ing  n iss ing  vaLues.  The method a i rns  a t  max i rn iz i -ng  thet o t a l  n u m b e r  o f  d . a t a  v a l u e s  i n  t h e  f i n a l ,  m i s s i n g - v a l u e - f r e edata  na t r i x  by  i - te ra t i ve ly  de le t ing  e i ther  rows or  coLumnsin  the  or ig ina l  mat r i x .  I t  i s  shown to  re ta in  o f ten  rnore  o fthe  or i -g ina l  i la ta  than the  de fe t ion  o f  on fy  rows (cases)  o ro n l y  c o l u m n s  ( v a r i a b l e s ) .Chapter  3 .  1  descr ibes  the  CLÀS computer  p rogram fo rc l a s s i f i c a t i o n  a n d  e v a l u a t i o n .  I n  t h i s  p r o g r a m  s e v e r a ln u l t i v a r i a t e  c l a s s i f i c a t i o n  r n e t h o d s  a n d  p r e p r o c e s s i n gmetho i l s  a re  imp lemented,  inc lud ing  t ,he  proposa ls  f rom Par t  2o f  t h i s  t h e s i s .  T h e  c e n t r a l  a i m  o f  t h e  p r o g r a m  i sc o m p a r a t i v e  e v a l u a t i o n  o f  t h e  c f a s s i f i c a t i o n  n e t h o d . s  u s i n gp r a c t i  c a Iva I  i  da t i  oni mpI ementes  h o r t c u t s .the  eva fuaprobabi- I  i  sprogram isIrL Chatr.the CLÀSgood a l te rn n l -  n n  l  r rprobab i  1  i  si  n f  l -  uenceand thec l a s s i f i c af ree  mul t it h e  a s s i gprobab i  I  i  sChaptetb y  c o n s i dS I M C A ,  Cuncor re l  a tcovar i  anc€s  i  mu l  a t i  o rper fo rmi  nci  nves  t i  ga td a t a  n o  c cthe  da ta  sÀ  s i m u L a tcomponenESIMCÀ ands i m p l e  a v eI n Ché.mul- t i  vari- eI  abora tor ls u p p o r t  s lP r a c t i  c a Ic n l  r r o À  Icommon oc(p i l o t  s t rper fo rmed^ L  ^  - 4 ^ ,v t t a P c c Jp r a c t l  c a lf h ê  n a r f rapproachrn  tha td . i s c L o s er ivar i  a tethe mai- nlrom theanal yz ed.:  m i s s i n g:eques ted.> f  t h e  i n.MCÀ areo f  c l a s sru l -  t s  o flamenta l - .r  o f  e a c hr  a p p l i e dr n v e c t o r sr s p a c e  o f. À nevlt  l . r ê à f crs  kerne lrodel 1i- ngs  te rmed.: a m  ( s e e' m e t h o d spropos aJ-rand.omlyz i n g  t h e. L u e -  f  r e e' col-umnsr  mOrê Ofa s e s  )  o r' ram f  o rs  e v e r a lo c e s s i n gm  P a r t  2g r a m  i ss  usr -n9SummarYp r a c t i c a l  d a t a .  T o  t h i s  e n d  t h e  l e a v e - o n e - o u t  ( c r o s s -va l - ida t ion)  methoc l  o f  eva lua t ion  is  made ava i lab le  fo r  a I Ii m p l e m e n t e d  m e t h o d s ,  í f  p o s s i b l e  b y  u s i n g  c o m p u t a t i o n a fs h o r t c u t s .  T h e  p r o g r a m  i s  a l s o  a b l e  t o  c o m p u t e  c r i t e r i a  f o rt h e  e v a f u a t i o n  o f  t h e  p o s t e r i o r  p r o b a b i f i t i e s  g i v e n  b yp r o b a b i l i s t i c  c l a s s i f i c a t i o n  m e t h o d s .  A  P C  v e r s i o n  o f  t h ep r o g r a m  i s  d e s c r j - b e d ,  t o o .L n  C h a p t e r  3 . 2  i t  i s  s h o w n  b y  s i r n u l a t i o n  s t u i l i e s  u s i n gthe  CLÀS progran,  tha t  leave-one-out  eva lua t ion  is  o f ten  agooa l  a f te rna t ive  fo r  eva lua t ion  us ing  independent  tes t  da ta ,n o t  o n l y  f o r  e r r o r - r a t e  e s t i m a t i o n ,  b u t  a l s o  i fp r o b a b i l i s t i c  e v a l u a t i o n  c r i t e r i a  a r e  c o n s i d e r e d .  T h ei n f l u e n c e  o f  t h e  n u m b e r  o f  o b j e c t s ,  t h e  n u n b e r  o f  v a r i a b l e s ,a n d  t h e  i n t e r - c l a s s  d i s t a n c e  o n  t h e  r e s u l t s  o f  A L L O Cc l a s s i f i c a t i o n  a r e  i n v e s t i g a t e d  i n  t h e  c a s e  o f  c o r r e l a t l o n -f ree  mul t i -var ia te  normal  d is t r ibu t ions .  Overconf idence int h e  a s s j - g n e d  p r o b a b Í l i t i e s  i s  s h o w n  t o  b e  a  p r o b l e m  i np r o b a b i l i s t i c  c l a s s i  f i c a t i o n .Chapter  3 .  3  ex tends  the  resu l ts  o f  the  prev ious  chapterby  cons ider ing  nore  c lass i f i ca t ion  metho i l s  (LDA,  ALLOC,SIMCA,  CLÀSSY)  and more  i la ta  types  (s imu la t ions  w i thuncor re la ted  var iab les ,  cor re la ted  var iab les ,  unequa lc o v a r j - a n c e  m a t r i c e s ,  f u r t h e r  a l s o  p r a c t i c a l  d a t a ) .  I n  t h es i -mu la t ions  CLASSY is  shown to  be  a  robus t  method. ,  a lwaysper fo rming  about  equa l ly  we l l  as  the  bes t  o f  the  o ther  th reei n v e s t i g a t e d  m e t h o d s .  F r o m  t h e  e v a l u a t i o n s  w i t h  p r a c t i c a ld a t a  n o  c o n s l s t e n t  p a t t e r n  e m e r g e d . ,  s u g g e s t i n g  t h a t  m u c h  o fthe  da ta  s t ruc tu re  remains  h id .den fo r  the  human eva lua tor .À  s imu la t ion  method fo r  choos ing  the  number  o f  p r inc ipa l -component  axes  to  be  inc lu i led  in  the  ins ide-mode l  space o fS ï M C À  a n d  C L A S S Y  c l a s s  m o d e l s  i s  s h o w n  t o  b e  s u p e r i o r  t o  t h es i m p l e  a v e r a g e - e i g e n v a l u e  c r i t e r i o n .I n  C h a p t e r  3 . 4  t h e  a t t e n t i o n  i s  o n  a p p l i c a t i o n s  o fm u l t i v a r i a t e  c l a s s i f i c a t i o n  i n  t h e  c l i n i c a l  c h e n i c a Ll a b o r a È o r y .  T h e  p o s s i b i l i t y  o f  c o n s t r u c t i n g  a  d . i a g n o s t i csuppor t  sys ten  us ing  a l read.y  ava i lab le  da ta  i s  exp lo red . ,P r a c t i c a l  p r o b l e m s  i n  t h e  p r o c e s s  a r e  i - d e n t i f i e d  ( a n d  p a r t l yso f  vec l ) ,  as  ! ' /e I l -  as  more  fund.anenta l  po in ts ,  such as  thec o m m o n  o c c u r r e n c e  o f  m u l t i p l e  d i a g n o s e s  f o r  o n e  p a t i e n t .  Àp i lo t  s tuc ly  on  hear t ,  I i ve r ,  and.  k id .ney  pa t ien ts  i sper fo r rned.  us ing  the  CLÀS progran.C h a p t e r  3 . 5  c o n s i d . e r s  t h e  q u e s t i o n  h o w  m u c h  o f  ap r a c t i c a l  d a t a  s e t  c a n  b e  d e l e t e d  w i t h o u t  d e t e r i o r a t i o n  o ft h e  p e r f o r m a n c e  o f  t h e  c l a s s i f j - c a t l o n  s y s t e n .  À  l a r g e- 3 4 7 -Summaryc l i n i c a l  c h e m i c a l  i l a t a  6 e t  i s  u s e  f o r  t h e  d i s c r i m i n a t i o nbetween hear t ,  l i ve r ,  and k ic lney  pa t ien ts .  I t  tu rns  ou ttha t ,  in  th is  case var iab l "e  se lec t ion  is  very  f ru i t fu l  event h o u g h  t h e  c l a s s i f i c a t i o n  t e c h n i q u e  u s e d  ( C L À S S Y )  a p p l i e spr inc ipa l -component  mo i le ls ,  The number  o f  t ra in ing  pa t ien tscou ld  be  reduced.  w i thout  much loss  in  c lass i f i ca to ryper fo rmance.  Overconf idence in  the  ass j -gned pos ter io rprobab i l i t ies  was a lways  a  p rob lem,  however ,The Las t  two chapters  o f  th is  thes is ,  Chapters  3 .6  and3.7 ,  a re  p rS.mar i l y  concerned w i th  an  eva lua t ion  o f  thePOSCON nethod,  wh ich  is  another  recent ly  deve loped proceduref o r  r n u L t i v a r i a t e  p r o b a b i l i s t i c  c l a s s i f i c a t i o n .  I n  C h a p t e r3 . 6  t h i s  m e t h o i l  i s  a p p l i e d  t o  w i n e  d a t a ,  w h e r e a s  i n  C h a p t e r3 . 7  i t s  p e r f o r m a n c e  i s  e v a l u a t e d  i n  a  c l i n i c a l  s h e m i c a lcontex t .  ïn  bo th  s tud . ies  POSCON is  compared to  ALLOC,  SIMCÀand CLASSY.  I t  i s  shown tha t  the  conf ic lence in te rva ls  fo rthe  pos ter io r  p robab i l i t ies ,  wh ich  are  an  un ique fea ture  o fthe  POSCON program,  a rê  o f  l i t t le  va lue  in  p rac t ica ls i tua t ions  where  the  number  o f  ob jec ts  i s  no t  la rge  comparedto  the  number  o f  measured var lab les .  No la rge  d . j . f fe rences  inc lass i f i ca to ry  ab i l i t y  $ /e re  fount l  be t$ teen var ious  POSCONmodels  and the  o ther  i .nves t iga tec t  techn iques .  However ,  j -none casê a  POSCON rnode l  very  much re la tec l  to  c lass ica l  LDÀpro i luced re l iab le  ( ins tead o f  overconf i i len t )  pos ter io rp r o b a b i l i t i e s .- 3 8 8 -I n  d i tf l e s s e n  w i ;in  d i t  v l(  k- l  assen) .pa t iên teng e b a s e e r d . ,var iabeLenKaraktes teeds  memeet resu l  t(  nul t i  variaanpak vta( uni vari  atg e i 1 1  u s  t r ev e r s  c h i l L edan wanneeI n  d e ebes chrevenons een( " normaalw(  Hoofds  tukv a n  o u d s h ev a n  z Í e k e nDe multvan har t -h o o f d s t u kbeves  t i  gd ,a r t s e n  t o ts  p e c i  a I i  s  nI n  h o cverge l i j  k ic l a s s i f i c eherkomst  iw i j  z i jd.Le probal^ L {  ^ ^ +  - iv v )  E U  L  r r rgekozen ,g roo t  de

Multivariate classification methods and their evaluation in applications.

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Multivariate classification methods and their evaluation in applications.

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