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Mixture of linear mixed models Application to repeated data clustering

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(1)Mixture of linear mixed models Application to repeated data clustering Gilles Celeux, Christian Lavergne, Olivier Martin. To cite this version: Gilles Celeux, Christian Lavergne, Olivier Martin. Mixture of linear mixed models Application to repeated data clustering. [Research Report] RR-4566, INRIA. 2002. �inria-00072022�. HAL Id: inria-00072022 https://hal.inria.fr/inria-00072022 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Mixture of linear mixed models Application to repeated data clustering Gilles Celeux, Christian Lavergne, Olivier Martin. N° 4566. ISSN 0249-6399. ISRN INRIA/RR--4566--FR+ENG. THÈME 4. apport de recherche.

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(11) Šmwy xhiq“Ocj}–Z<´ dq¢2k r _ei<uxhY+i<dq¡©xhx²MdDZCs u³fAr ´œdqfhµRd _j— kXZAdqx2¢2i r ZCc6´b¢¶_”vLfpa xpZ·¢2i r ZCc6´:¦,c`a otfpZCx ¨ k dqc`snot_eoC´œ¸¹ZkXZ. Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe, 38330 Montbonnot-St-Martin (France) Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52.

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(278) . X¦,_`cjimaOc`o{imfh†mZ_ex otfho.u_`k i<k8i<fhx dqr _`k ZCx.o&fpimik cjus‰i<k8fpVXfpxhZ'imf{cGª&fpVXiœZV Z_j†<vnVXlOcjZCs xp_`aXYlQZk8xpZCf †m— aXcedgfhZ r †mZk ZCo._`k uc`a r Z r _`k fpVXZ r dgfpZopZfLs Z¦,vncjlGaOZo{fhxhZ_jYxy[Zk8ufimdqk8c-fhudmi<_jk k o©r _jfpfpVX_`imZk †<o Z— kXZAo©ªVXi<opZZvnlXxhZCohop_ji<k r iLZAo©kXiqfopZZCY r _j²MZxhZk8fGZf{ª&ZZk:fhVXZf{ª&i  ¦,cjaOo{fhZxo ¹dmk r |bV d š Zžcedqxh†mZCx,xdqk r imY Z²MZCufJo{fdqk r dmx r r Z š _edgfh_ji<k — U.VX_`oopaX†<†mZCotfhofpVOdgf.’•imx fpfpVXV i8dqfotZfpuV c`Za xhotZŸfpZCdqxhxhožZ fpV r Z:_j²GxZCdqxpkZCk r uimZAYoOZ²MZf{ZCª,ufZCZ_`ko¹YfhVXimZCxhopZ:Z¶opu_`†mc`a kXot_j“OfpZux dmk8Yf — ZYbU.GVXZZxo ¡y— _eotZC&k‚anf xhZotl fhxpdmZAk otZCr k<dmfx dgrfh_jri<Zk¶š ot_edgVXfhig_jªJi<k o ZYxhZCxpi<dmx,opaX_eoxhZopYYZdmk8cjf`ZoRx&xhZfhlXV xhdqi k r xha dmuk _jXr _`i<c _”Y f{s¹ZX²GanZAf©u³foti<— Y7‚Z Zr u_j²Gimk ZCxpuZCcja k r uZAZ–o)fhdqV lXdglGfZC_`dmk‰xRfhGVXZZCf{opª&ZZuZc`kba o{fpfhVXZZ,xo&†m*nZCª&kXZ,Z¹ZV vnd lXš xpZ¹ZA†mopopiL_`iimkr lXr _jxh²GiqZC“ xpc`ZCZCk<o —fJ l U.xpimVX“ ZcjZAuo.cja iqot’

(279) fpZC†mxhZo k r ZC_eo op— lO

(280) ZCxhop_ji<k‰_eokXimf.ZvnlXc`dm_jk Z r 8s š dmxp_edqX_`c _”f{sYZAdmopaXxpZCYZk8fho,XanfJLs iqlO¦,’Mi<cjaOY_jk8o{fJZCfhZdmimx)op’ aX[–šxhV Z_`ZYd<ª o-Z—fhk8VXfZ.o — c`dm¦,xpim†<k ZCotopfZ 8otfhaXdqZCk k8r fpc`dqs)x *qr _jfyZxh_`oxhimr x _ %r Z uš aX_`c”dqffpfp_`imik _`—k<fhU.ZVXxhlX_eoRxhZZf©vLl fpV xpZA_`oyopopuZCcjo

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(285) rop_jµfpfha |qi‰dq¢ fpc`ZC_`imdYk r i o&rfpªi ZceVXY:o,ZCVOxpi<Z¹dmxpZœo&xpZCOxplOZCZCZAcjZ_edgdqk fh Z lXcjr Zbxpi<YulOcjZAaOi8dmo{otfhopZ ZaXr xhxp_jdqZAkXo.k † r dqo{xhZCfhZžotxpfpaOd _`šu³Yfpdqa dg_`c xpfhdmZAZ Xo–r c`Z opª—)_jk _”¥ fhuk VZbd:fp_jf'V uZ¹c`dma cj¡,`otigfp¢ ªJZCx.odmdmfhcjk †<iimdqfxhc`sndq_”fh›motVX_eZbo&Y lXu—imxpim¥k8f“XfhZfžuvLdmimf k ’ * fhGVXZZulGxha igª,u_`ZCdmxtcO’•fhaXi cnµ

(286) r |q_eo{¢$fh_jkXY:†<aXZfp_eotVXV i r fpVXi<cjZi<†motfhsdq_`fpk:_eo{fhfp_`VXuCZdqc˜YaX_jk v8fh_”faXoJxhZ,dmuC’•xudqimYx r ZC_`ª,kX†œi<xpfp› i—Rfp¨ V kZ_`r x *mš _`dmkxpY_edq dqkL_jc`s_”f{s ot_j— fpaOdgfp_`imkOo&*q_jfui<aXc r YaOotZ_`kXfp¥ VX†kœi fpY:r V _eZ’•uimxh.xJi<µdmucjxpJa xdDwotfps ZC rxp&_`dqkXZCfh†otdJfž†mdmµ-ZCk kX_`dqkXZ'c`ZCsnZdmotvnx_eo-lXJ_jxhf©ZCkLohuXotim_e_`a dmimopck r Z rlXVOxhdwyiqš “ xhZ©Z c`ZCrYo._`udqªfpkLimVXsx ZC

(287) dqk *OlXotl fpZCVXcjZ _eZ udqšAfpdq _`xhim *O_ek dquoXdmdq_`kQcjk_ f{rOsZu_eimoaOaXot_jYcZr ’•aXlGGc-imZCxpfhufhiimdmYk<XfaXZ,— _`d–c ¢2r xpZimxh’•ZCxhZdmZxhicjZ_eš otk fpZu_ex Zu * l xpim“ cjZAo&*LlXxhi š _ r _jkX†d:lXxhZCu_`opZžxhZl xpZAotZCk<fdgfh_ji<k‰iq’)ZCd<uV‰†<ZkXZ_jfJ_”fouc`a otfpZx — . . 9:9<; =?>A@%B%B. .

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