Assessing a Mixture Model for Clustering with the Integrated Classification Likelihood
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Assessing a Mixture Model for Clustering with the Integrated Classification Likelihood Christophe Biernacki, Gilles Celeux, G´erard Govaert. No 3521 ` THEME 4. ISSN 0249-6399. apport de recherche.
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(121) T³ ´¥~µÄ² sE©{w{|¥uTdh2²¶w{p«1wLgzQwLyfh yYu«|Tw{ropbuTmow{y ¤ c&dfmo|²¶w{pf1rop|uTh |wLrxpfuTmow{y%¦Qg<hCTLmxy1wLg<zGw{yh yYuv~ |! s{y <mxyYuvww{yfh2 rxp|uThCC¦mo|svhCsL|wLys}¨rxh/|wLrxpfuTmow{y5s{|mxu«s}zzQh?s}|¥²¶TwLg mxLpfvh!f¦f dfmtd5zfTw ©nm hC| uv|Tdfw{roh pb~uvmxhCwLyy |Tm¯du-sL|w}²·s}rtuT|dfw<h§¨Gzfh Th w{yW hC|T1h uTromohCw{1yuT|.h ~ w{²Gph?|Ts{moyfd<guTdfm¯h nuT± p¥Th§´ w{ gTmxuTzGhCw{Tyfmow{hCyyLuVw}²VwLy<´6uTh dfroh hpb²¶5wLpfs}\y ~ wYknwLwL ~TwLmxyg<s}hCuTyfh?|Odfw%s bhC| ¤ c&; d¤ mo| . ,ÁA,%¿ B"? & , 1 ½ h<yfw 1wLy|m ~ hC«h nzGh vmog<hCyYu§²¶vw{g#s®gmxnuTpfvh-w{²6s®pyfm¯²¶wLTg#s{y ~ s s}p|v|Tmos{y^1rop|uvh ¤ yfhqw{² uv²¶wLdfrxhrow W 5| |Tmxg-pfrts uTh ~~ s us|Th1u|!mt| ~ mt|zfrtsE{h ~ moy mxLpfTh5s}y ~ uvdfhgm¯nuvpfTh®dQs}s{)uvh vmo|uTmt |/s{Ths{| $. . . . )0&-, . 3 3 ^ ) , ^ ) ,. yw{ybª s}p|v
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(125) #" ( 1 % & G(0? 1 1. ½  G½Y¾ ½ c&dmo|6¢|uh bs{gzfrxhw{yvhCs}r ~ s} uvs<1wLy 1hCTy|6pfyf m ~ mogh y |TmxwLys}r ~ s uvs ¤. h!1wLy|Tm ~ hC¥uTdfh²¶w{p¥gw ~ hCro| sE© s{mxrts}¨froh!moy ~ mxghCy|mow{yWwLyf~Jh K¦ ʦ ʦ m¯uv~d . E®s}y ~ ~ . <uTw w{gzfpbuvhuTdfh®º¥³T´«¦´&k s{y ³T´¥µ1vm¯uvh vmosw{yuTdh hCTpfzfuTmow{y pfs uvmxwLy|/w}²¥uTdfh r s{m¯uvdb²¶pfr L~ h mo|Tbzf|Trth sE# {h ~ moy Cs{crxmos}yf¨mrxh?s}$| y ~¦fº¥2w s} y g~ s} y ¤ ³¸ y®uv df wL ¤|Th± us}pf¨fgrohCh |Cv¦ moC ± s}r © ns{mxyrxpf~ h?mo|Cs w}uv²hC|CuT¦YdmohCy |Th^s{rxr·1v m¯sLuvh |h?vmo|\s¨s}pbvu¥h5wLTyfh?h{|¦YzGuvhCd1s uTu¥mo©{uThCdfrxh s}ro{w{vmxuTdfg ~ m ~ yw}u« w{yn©{hCTLh«²¶wLuTdh-1wLyb¢Lpfvs}uTmow{y5s u§dQs}y ~»¤ fwLuvdfhq|Tw{ropbuTmow{yW|Th rohC)uvh ~ ¨n º¥ w{³Tyn´ ©{hC TgLwh y~ h h/r w}² Ä%¦· ¨fm¯uvpf2d u« mxumt. | ~5;pf )¦bh2³Tuv´¥w®µ uTdmt|&h2yf² w}s{u1u§sE©uvds}mos rou«s{¨fuTrodfh hn¨f pb uuvdfh/w{zGTh h?s{s |TuTw{wLy§²¶rowLhC6s ~uvdf|mt|&uvw mo|&s yf~ w{hCu&{uThCdfyfh/h yfs wLuvy h zQs}TuTmxuTmow{y uvdfThCh1rop|uThCv|qmxy|uTh?s ~ w{²¥²¶wLpfH ¤ º¥³T´$s{y ~ ´&kÄ|Th rohC)uqsJ1w{pzfrxh ) ,¢fuuvmxyfJ 6hCrxr uvdfh-|ThC w{y ~ ~ zGhCs{£5w}²OuTdh ~ hCy|mxu |Th h mo{pf¤ vh2i s. dfhCTh?s{|§³T´¥µÄzfvh1²¶h |§sgm¯nuTpTh2 mxuTdgw{vh |Th zQs}s uTh 1wLg<zGw{yh yYuv| |Th h mo{pfvhqi ¶¨. Ww{~ vh w ©L¤ h ?¦fmxumt|§ ¥w{TuTdWyw}uTmoyfuTds}u³T´¥µ mo|§uTdfh|Tw{roh TmxuThCTmow{ydfwnwL|Tmxy' . ²¶w{|Tw{gh/w}²uvdfh!gw h rt| . . R. . R. R. . R . . R . L-LNMKO PHQHRS. . . .
(126) BIC. ICL. 4. 4. 2. 2. 2. 0. 0. 0. x2. 4. x2. x2. 4 clusters. −2. −2. −2. −4. −4. −4. −2. 0. 2. As 6uTvpfh!zs{uvm¯uvmxwLy ¶¨ &º¥³T´\ª´&k®zs{uvm¯uvmxwLy ¥³T´¥µ mo{pfvh fwLpf1rop|uThCv|& mxuTd ~ m&GhCThCyYuw ©{h vrts}zfzfmoyf ¤ 4 x1. 6. 8. 10. −2. 0. 2. 4 x1. 6. 8. 10. −2. 0. zs}TuTmxuTmow{y 2. 4 x1. i º¥´&³Tk ´ {W $A$ ³T´¥µ = i $A$ cs{¨frohi º¥w ~ w{Ls{y |6|vs}gzfrohC| zQhCv h yYuvs{{hw}²OdfwnwL|Tmxyf m¯uvduTdfh!gw ~ h r . 6. 8. 10. . . R . . ¤. i º¥´&³Tk ´ U i U i ³T´¥µ cs}¨rxh2 V± {w ybª s}pQ|T|Tmos{y rxp|uThC|Ts{gzfrxh?| zGh 1hCyLus}Lhw{²dfwnwY|moyf mxuTduvdfh!gw ~ h r ¤ R. * . . . R R . . R. R . . . ªÊªÊininbb ªÊinb ªÊinb cs{¨frx
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