25.04.2014 Views

Modelling Spikes with Mixtures of Factor Analysers Dilan Gioriur ...

Modelling Spikes with Mixtures of Factor Analysers Dilan Gioriur ...

Modelling Spikes with Mixtures of Factor Analysers Dilan Gioriur ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Ö<br />

©£! "¤§#¡$&%')(*+¡,"<br />

¡£¢¥¤§¦¨¦©¥©¤©<br />

'.¦/0¤" -<br />

no¬OwiŽqtsux47s|ik}­qt®Ow§d¨jƒqts|y~i°ḠyqtwiŽqtshd¨g|p*yx0s|ik¬Os|±XsT¬7vYdg²ikwƒvOzty~iOp³xTzty~<br />

£.¤¦¥§¨©Yª¨§~«<br />

zm¬Os|iO}~pŠlXikyµi§d¨pRṕ Ōshl~w+ṕ ÿ ź qts|iO}OŠs|p¦djK®kd¨g|g|wik}¨shiO}*¯7zty~‚kg|w;·<br />

wƒeXq´zmdjwg|g|vkghdz¦ztwjƒÿ<br />

ikṕ sh¬Owƒz²qt®kw+ṕ Ōs|lºw+ṕ yź qtshiO}E¯7zty~‚Oghwƒ»vkṕ s|ik}Ed}~wiOwƒzmdqts|±ºw0)yX¬Owg¼ŠŽ½­¾|¿¨À¼Á7´ÃKÄ<br />

¸¹w+jÿ<br />

a 2TâY2 atãÔ 5X3Y6NL > =K< 6AI€\Y6 < F^6Õ57I+ImáA2T\OLEI J;á a 2 < 6 aKb 5 a<br />

57à<br />

L^Lï aƒ= 5OàL¨3T3 > 3U5 = Imá‹57àLÌ2UIL34L¨à aK= 24à¨5X343 ã)bA< J I ?~äå< > = è a 2Tá;L¨3TL~à aK=ƒ< DGL¨I^ö a L aK=ƒ< DNL¨I÷<br />

aKb<br />

=K< âY2UDGL aKb LÌJ;2T6A2TJ°5X3G6 > JW‹L = 6NL¨àL¨IƒIK5 =Kã­aK< 2UDGL6 a 2 äåã.aƒb L^Imá‹5 a 2U5X3Yá < IK2 a 2 < 6 = àL<br />

á<br />

=¨?A@ 5 = 3CBEDGF*5 = DH57IKJ > IKIKL6 ?NM 6AD = L¨5OIPRQNS < 3T2U57I ?NV 57WN2U5X6¥PY2T6AZ ? 576AD<br />

1§243457698;:<br />

< I^];QN_ 3 a Q€Bï aƒ= 5Xè<br />

> 345 = L34L¨à aƒ=K< DGL~I*2T6 aK=ƒ< D > àL¨D2T6 aK =K< 6 b 5ºâOLÒW²LL¨6<br />

àL343<br />

> à¨àL~IKI ä > 343 ã > IKL¨D äå a*= L~à 3 a 576NL < > IK3 ã;äå=ƒ< JñJ > 3 a 2TáA3TLÔ6NL > =K< 6AI*2T6 D ã°aKb L¨2 = 246 a L = 57à a 2 < 6AÏ QGB34L¨àè<br />

Im24J<br />

DNL¨IáN345OàL~Dò246 aKb L¹Lï aK= 57àL¨3T3 > 3U5 = JÕL~DG2 > Jóà576 = L¨à =ƒ< 6‹I§W > aÒaƒb 24I­34L¨5ODNI > I aƒ L~I a 2 < 6 24I b 246 ` W²L a F*LL¨6 aKb L<br />

< 6 aƒb L = L3U5 a 24â7L°IKáN24\7L£5XJ;áN342 a > DGL~I < 6ôDG2TøRL = L6 a L34L¨à aK=ƒ< DGL¨Ï QCH^L¨à 3 a 2Tè a 2TáùL34L¨à aƒ=K< DGL~I^24JÕá =K< âOL¨I aKb L.24DNL6 a 2Tú‹à5 a 2 < 6 5X306NL > =ƒ< 6‹Ià < JÕá‹5 = L¨D<br />

J<br />

I a 5X6‹DN5 = DÐIK2T6 ` 34Lè a 24áL¨3TL~à aK=ƒ< DGL¨I)öKû üXý¼÷Q<br />

aK<<br />

PYáN24\7L,I I > 573T3 ã D < 6NL.246 aƒbN= L¨L,I a Lá‹I ? 6A5XJ;L3 ã ImáA2T\OL,DGL a L¨à a 2 < 6 ?Aä L¨5 a > = L<br />

aK= 57à a 2 < 6ò5X6‹Dôà3 > I a L = 2T6 ` Q01ÒL a L = J;2T6A5 a 2 < 6 =ƒ= L¨6AàL 5X343 ã 5Oà b 24Lâ7L~D£W ã£b 2 `7b èoáA5OIKI*ú‹3 a L = 2T6 `Õäå< 3T3 < FEL~D£W ã°aƒbN= L~I bA< 3UDG2T6 ` 2UIÌ\Y6 < F^657I aKb L<br />

><br />

ImáN24\7L£DNL a L~à a 2 < 6òI a LáCQ0þ´6 aKb L ä L¨5 a > = L°Lï aK= 57à a 2 < 6ôI a 5 ` L ? 5 ä L~5 a > = L£âOL¨à aK I a L = 2T6 ` 2UI^D < 6NL < 6 aƒb 24I3 < FêDN2TJ;L6‹Im2 < 6A573 ä L¨5 a > = L)ImáA5OàLOQ


«Y« ÿ dqmdztwjƒÿ zm¬Os|iO}Ìd¨ik¬ztwƒŌztwṕ wiŽqmdqtshÿ i ¦e7q´zmdjwg|g|vkghdz¦µ!d±ºwƒxUyzt)pCdztw+ztwƒjÿ zm¬7w¬µsuqt®­d<br />

<br />

C±ºwƒź Òqts|)wqt®Owṕ sh}¨iYdgGwƒe7jww¬7w¬­qt®kwqt®Oztwƒṕ ®ky~gh¬)s|i)y~iOwEyxAqt®OwjK®kd¨ikiOwg|pŠXd̵s|iY¬Oyµ<br />

qtwKq´ztyX¬Ow~·<br />

= L ? FELá = L¨IKL6 a 576 5 > aƒ< J°5 a L¨DîFÌ5 ãç = L­Lï aK= 57à a 2 < 6CQYþ a J < DGL¨34I<br />

JÕL<br />

LÌImáA2T\OLF*5ºâOL äå Im3 ãÐ< àà > =ƒ= 246 ` IKáN2T\OL¨I§F b 24à b 2UI§5 b 5 = D a 57IK\ äå


57à aK L¨D9DN5 a 5°âOL¨à aK IK2T6 ` 5R]kè´DG24JÕL¨6AIK2 < 6A5X3CâOL¨à aK


° ÿ ·YŒ ‰<br />

F b L = L ª<br />

Ÿ<br />

Ÿ<br />

c<br />

Ÿ<br />

Ÿ<br />

†<br />

·ñDG2UI aƒ= 24W > a 2 < 6924I a áA5OIKIK2T6 `)aKbN=ƒ< > `7b<br />

aKb<br />

ˆ ®ks|ps|pEwÍŽvOsh±¨d¨g|wiŽq!qty­)shiOs|)shṕ s|iO}Òqt®kwÆ4NÎ ¬Os|±ºwƒzt}¨wikjw*‚Gwƒqoµ+wwi\ß_àWájâ!diY¬8ãÌàWáTä1åwæ çÑâK·<br />

Þ<br />

Ÿ<br />

Ÿ<br />

Ÿ<br />

z ‰ vOzŠNE· ·¢¡Ed¨ṕ Òvkṕ ṕ wiAŠ¤£· ¥N· ˆ y~g|shd¨pŠYÓ+·¦¥Xshï §~Š¨©Ò· Ô·¢Ay~}¨ÿ qt®kwKqtshp<br />

ÿ<br />

; 246ADG2Uà5 a L¨I aƒb 5 a^aƒb L)LïN57JÕáA3TLÔFÌ57I ` L¨6NL = 5 a L¨DW ã°aKb Lh«²±Z³ÕJ;2Tï a > = L7QAS b L<br />

aKb 5 a W‹L~I a J < DGL¨3 aƒb L.à < âŽ5 = 2U5X6AàLÔI aK= > à a > = L<br />

5X6AD´‰<br />

> 6N\Y6 < F^6áA5 = 5XJ;L a L = I e<br />

† k<br />

5X3 `7< è<br />

6AD£W ã J°5ŽïG2TJ > Jñ342T\OL342 bN IK2T6 `.aKb L­B9<br />

= 2 aKb J ? DNL¨Iƒà = 2TW²L¨DW‹L¨3 < F)Q<br />

þ´6 aKb L äå< 343 < F^246 `‹? £ 24I aKb L < WAIKL = âŽ5 a 2 < 6 J°5 aK= 2hï&5X6‹D%µ 5 = L aKb L > 6 < W‹ImL = âOL¨D<br />

öåJ;24IƒIK2T6 ` ÷é > 576 a 2 a 2TL~I ? 2T6 < > = à¨57IKL aKb L§3U5 a L¨6 a âŽ5 = 2457WN3TL~I


LïN5XJ;áN34L¨I^5 = L `7 =ƒ= L¨6 a áA5 = 57J;L a L = I ½ a<br />


aƒb 3 < F*L = 6 > J,W²L =+


` 6NL~D aƒ< I < J;L I a L = I^ImL¨LJ;L¨D aK< W²L ` L6AL = 5 a L~D äå=ƒ< J DN2høRL = L6 a 6NL > =K< 6AI ?<br />

57IƒIm2<br />

> ImL aKb L¨2 = FÌ5ºâ7L äå L6‹àL I a L = IÔFEL = L£à < J;á < IKL¨D 3 a 24áN34LÐDG2UIW < 2T6 a.= L ` 2 < 6‹IÒ246 aKb L aKb LÐ57J;áN3T2 a > DGL°áN3 I!F*L*à < 6Aà3 > DNL¨D aKb 5 a<br />

5X6AD<br />

LÐà3 > I a L = 2T6 ` FÌ57I)6 ààL¨IƒI ä > 3³2T6 a L = J;I 3Eà3 > I a L = IQ0S b 24I<br />

aKb<br />

atã.aƒ< 24I < 3U5 a L aƒb LIKáN2T\OL¨I!F^2 aKb DG2TøRL = L6 a à b 5 = 57à a L = 2UI a 24à¨I+24Iá =K< WA5XWN3 ã D > L aK a<br />

LïN5XJ;áN34L¨IÒ24I­à3<br />

F b 2Uà b à3 > I a L = 2 a I bN< > 3UD¹5OIKIK2 ` 6576LïN5XJ;áN34L7Q<br />

aK<<br />

b 5ºâ7L¹5X3UI = LIKáA5OàL > ImL~Dò246<br />

,çL<br />

&çÛEاޒ(mÝÃBYßtÛ³Ø<br />

(<br />

b 5ºâOL­DNLJ < 6AI aK= 5 a L¨D¹5;I > à¨àL~IKI ä > 3C5XáAá =K< 57à b°aƒ< ImáN24\7L)I ImL~D¹2T6 aƒb 24I§I a > D ã7?NaKb Lh VGM J < DGL¨3 äå< > 6AD¥5X343Cà3 > I a L = I aƒb 5 a F*L = L<br />

äå 6AD;246°J°5X6 > 573Nà3 > I a L = 2T6 ` F^2 aƒb Im24J;2T3U5 = W < > 6ADN5 = 24L¨I ? LïNàL¨á aäå I a L = F b 2Uà b<br />

a à3 > I a L = L¨D.5OI€5^á‹5 =Ka€


ÿ ·YŒ ‰ ÿ z ‰ vOzŠNE· ·¢¡Ed¨ṕ Òvkṕ ṕ wiAŠ¤£· ¥N· ˆ y~g|shd¨pŠYÓ+·¦¥Xshï §~Š¨©Ò· Ô·¢Ay~}¨ÿ qt®kwKqtshp<br />

)<br />

«*A« ¡Ewjƒÿ zm¬Ow¬­ptd¨)Ōghwƒp0dṕ ṕ s|}~ikw¬)qty̬Os,+NwƒztwiŽq€jg|vkprqtwƒztp€‚Žqt®kw)yX¬Owƒgà¼g|wƒxTqˆâ€diY¬­ptd)¯kg|wp<br />

<br />

ikpŠ’à¼}Î ¯â<br />

}¨wikwKzmdqtw¬£‚ŽÕqt®kw)yX¬7wgöàUzts|}~®ŽqˆâK·Y¸d±~wƒxUyzt)p*ŌztyX¬7vkjw¬;‚XÉàådÎåx*ⳬOs,+NwƒztwiŽqÌiOwvOztÿ<br />

s|­vkguqmdikwÿ vkṕ gu.Ïkzts|ik}ÔiOwvOztÿ ikpŠà¼l¨â0ikÿ shṕ w<br />

iOwdztguṕ<br />

7O· 980dztshdqtshÿ iYdgEs|iOx4wƒztwiOjwÕxUyz,{!dŽwṕ shd¨ií)s|eXqtv7ztwp­yxÌx¼djƒqtÿ z<br />

¨·Œ*®kd¨®Ozmd.d¨iOs6R·|Š0{+wd¨g*c·<br />

wƒztp·knoi\£E¬O±G·0©*wv7z·7noiOx ·Yf¦ztyŽj~·¦¥X7p·K … ŠGcÕn ˆ f¦ztwṕ pŠ …†~†~†<br />

diYd¨gu7ṕ<br />

·Œ*®kd¨®Ozmd.d¨iOs56¦·|Š;:*s|iŽqty~i¹ŒÒ· · ˆ ®kwÊ +c dg|}~ÿ ztsuqt®O xUyz)s|eXqtv7ztwp*yx0xUd¨jƒqtyz§d¨iYdguOṕ wKztp·<br />

…<br />

:X·ŒEzmdÕcŠGc;dgh¬Oy~ikd~¬7yÔf— Š7¸ôs|g|ṕ y~i°cŠYcÕjÓ©*d¨vk}¨®Žqty~i{E· ˆ wKq´ztyX¬Owp.dztlºw¬Ogu)s|)¯7zty±~w<br />

¥ŽOp·P … ŠGcÕn ˆ f¦ztwṕ pŠ …¨†~†¨†<br />

) ·ÌÑEw¬kdh©Ò·|ŠP©Ìd¨l¨d¨iOy8¡·|Š²Œ*®Yd¨®7zmd¨.diksF6¦·|ŠG:*s|iŽqty~i¹ŒÒ· · b¥kc\ 0c d¨g|}~yzts|qt®OæxUyz)s|eXqtv7ztw<br />

a<br />

b<br />

c<br />

d<br />

e<br />

f<br />

g<br />

h<br />

i<br />

j<br />

k<br />

32 64 96 128<br />

32 64 96 128<br />

QRJ.-FSM0/jU”¤ÛÚÜ–”21”¤SbLNX<br />

@ BEH#FÌ57I°I > áNá 6Aà2T3<br />

ö¢1 V 8)÷ aƒbN=K< > `7b¹`7= 5X6 a H M ; /Oü0/03 ; Q<br />

".+54¿+€ÚK+€Ø§Þb+B<br />

ˆ wƒjK®Oiks|jd¨g¡EwƒḠÿ ź qEÚ¡³ŒEÎ ˆ ¡³Î%< ‡ ί~Š ÿ w¯7q·Oyx0+y~)Ā·¢¥Xjs¼·|ŠYÑ*iOs|±N·7yx ˆ ÿ ztÿ iŽqtyOŠ–=

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!