From c62438ea3f1776332410812c99872895155765cc Mon Sep 17 00:00:00 2001 From: Marc Beninca Date: Sat, 15 Aug 2020 00:46:27 +0200 Subject: [PATCH] wip --- cnam/travaux/probatoire/document/example.tex | 68 ++++++++---------- .../probatoire/document/introduction.tex | 8 ++- .../probatoire/images/ex-nonlinear-linear.png | Bin 121667 -> 119614 bytes 3 files changed, 36 insertions(+), 40 deletions(-) diff --git a/cnam/travaux/probatoire/document/example.tex b/cnam/travaux/probatoire/document/example.tex index 907a312..83ef448 100644 --- a/cnam/travaux/probatoire/document/example.tex +++ b/cnam/travaux/probatoire/document/example.tex @@ -1,68 +1,62 @@ -\section{Exemple} +\section{Exemples} -L’exemple suivant, en 2 parties (linéaire et non linéaire), -illustre bien le propos. +Les 2 cas suivants, +linéaire \cite{ex-linear} et non linéaire \cite{ex-nonlinear}, +illustrent bien le propos. -\textbf{Linéaire} \cite{ex-linear} +\subsection{Linéaire} Une classification est voulue pour pouvoir déterminer si un étudiant sera bon ou non en \gls{ml}, à partir des 2 notes qu’il a obtenu aux examens de Mathématiques et de Statistiques. \fig{}{\Gls{ds} très bien distribué} -{24em}{ex-linear-plot} +{16em}{ex-linear-plot} -… +Avec un tel \gls{ds}, l’identification des \glspl{sv} est aisée, +et une marge la plus large possible est facilement applicable. \fig{}{Séparation à Vaste Marge très nette} -{24em}{ex-linear-svm} - -… - -\fig{}{Anomalies dans le \gls{ds}, violations de marge} -{24em}{ex-linear-out} - -… - -\fig{}{Différentes séparations à marge souple, variation de C} -{28em}{ex-linear-soft} - -… +{16em}{ex-linear-svm} \pagebreak -\textbf{Non linéaire} \cite{ex-nonlinear} +\fig{}{Anomalies dans le \gls{ds}, violations de marge} +{16em}{ex-linear-out} -… +Pour un \gls{ds} avec aberrations, faire varier une marge souple permet +de trouver un compromis entre généralisation et spécialisation. + +\fig{}{Différentes séparations à marge souple, variation de C} +{32em}{ex-linear-soft} + +\pagebreak + +\subsection{Non linéaire} \fig{}{\Gls{ds} inséparable de façon linéaire} -{24em}{ex-nonlinear-plot} +{16em}{ex-nonlinear-plot} -… +Création d’un nouvel espace dimensionnel avec des transformations +non linéaires des variables d’origine. -{\LARGE -$X_{1}=x_{1}^{2}$ - -$X_{2}=x_{2}^{2}$ - -$X_{3}=\sqrt{2} × x_{1} × x_{2}$ +{\large +$X_{1}=x_{1}^{2}$ ; $X_{2}=x_{2}^{2}$ ; $X_{3}=\sqrt{2} × x_{1} × x_{2}$ } -… +Ce nouvel espace permet de trouver une marge et un \gls{hpp} séparateur. \fig{}{\Gls{hpp} séparateur linéaire dans le nouvel espace dimensionnel} {24em}{ex-nonlinear-linear} -… - -\fig{}{Fonction de décision non linéaire dans l’espace d’origine} -{24em}{ex-nonlinear-svm} - -… +\pagebreak \fig{}{Projection de la marge de séparation dans l’espace d’origine} {24em}{ex-nonlinear-sv} -… +Le retour à l’espace de départ permet ainsi marge et séparation non linéaires. + +\fig{}{Fonction de décision finale non linéaire dans l’espace d’origine} +{24em}{ex-nonlinear-svm} \pagebreak diff --git a/cnam/travaux/probatoire/document/introduction.tex b/cnam/travaux/probatoire/document/introduction.tex index 2169ac8..79ef5bd 100644 --- a/cnam/travaux/probatoire/document/introduction.tex +++ b/cnam/travaux/probatoire/document/introduction.tex @@ -24,7 +24,9 @@ pour conserver une capacité de généralisation} choisir les algorithmes les plus pertinents} \end{itmz} -\subsection{Méthodes non supervisées} +\subsection{Méthodes} + +\subsubsection{Méthodes non supervisées} Ces premières méthodes permettent de travailler avec un ensemble d’éléments ne disposant pas d’étiquetage préalable, elles mettent ainsi en place @@ -42,7 +44,7 @@ Exemples d’algorithmes : \item{Apriori} \end{itmz} -\subsection{Méthodes semi-supervisées} +\subsubsection{Méthodes semi-supervisées} Ces méthodes autorisent l’utilisation d’un ensemble d’éléments hétérogène, certains étant ayant déjà été étiquetés au préalable, alors que d’autres non. @@ -55,7 +57,7 @@ Exemples d’algorithmes : \item{autoencodeurs} \end{itmz} -\subsection{Méthodes supervisées} +\subsubsection{Méthodes supervisées} Ces méthodes utilisent 2 sous-ensembles d’éléments intégralement étiquetés, ayant une valeur de sortie pour plusieurs valeurs de variables en entrée. diff --git a/cnam/travaux/probatoire/images/ex-nonlinear-linear.png b/cnam/travaux/probatoire/images/ex-nonlinear-linear.png index b1817799345c913949185a7e45af7dabc9000881..761083acb99764333f8ab6b71721af59317295fd 100644 GIT binary patch literal 119614 zcmZU4Ra6|o7U1CSuEB!4ySsaEcbCE4EfCxtf&>fhZUKV36WrYiutVN^yC2)<%$b_% z+f}!&%XE~oq7)K5K0E*bK$4LbR|NndJOKc3Em&~SO!wk!765>E;jOL(R5kV>adL6A zu(mTN0eU%^lbCy2TL1u_D^;0a66twdB;IS`8Nr+m_k=T@Ve|wiB`n;!HT&_{-0$cT z@bH41oWsc1p7P$i&buFL9u4$H8&eFT54z{nntPeX1Kv(9d@hgt0^aBMcOK@2I?i2g z?)}*eW=OAIg07zMplc2`g)UuVncpAVY&ShB{giI~b`C;SzASvduZh`pd+8vac@Tf~ z^{45aH%#LdI=MaZ+0q?-Fs#gLf8>dJbMNkor&U?WC@NfzB7J`7^wUHYdWU|;-xT{z zc(6&w;ywKBH=Yn3DM>&}XI|dMJAS?pgsF6 z_gOQW+OFG?){nkl)#+<@2w2oDaNZ;0o&%>s@ZJ5?z1Ho0BlP6*K)Xpwon9>Hi*ENr zFSX$J5ua2-yi>Q=7*mgs;pXj&A-vr8Om2B&hqbNC8`tQJ{)ImcHfv)-wx6@^R2@$6;GRkyaT-B8ySC(6+@!tP4Oa?I<=RW;5VNX0NT zuE|zZHEu{Y6ZiJ4$<=h;Z45JWwM=d4h3vr8$Y(j1WLRdnH7y@#B~QxI)zlr^RMgbk z4XE8+N^gRE9Y&oSMrH z&u`WZRa7tJsX_M2Xioe}|1LaK!7410<+86UJ(A3`_uHe0rmpr^D2^zQePZ_So=QUn0S(WxzYu+_E>o#Xf zLVV2NGUv=x0+=Z+kTOfMuc$mu4inyqOFwUG%Zf&WOb2Ep1DAwZyyf&VGKJi}mhe{Djhd9i=2AbC;$DU z#j6pOC*kZr)xCIHB3}tTwIG_!;J%|O5kx6t)M*|FJYlfWan%gje%3GTkQ1ez_{b{;6qQl~Iqn5*N?dynw$5;_v$>Wmb-5?YHCWjh*BQ z5(dh40`k?yvXS<17*jXDnR!Nt^gOkWlT+r24|mmV5?QUop1ECE_^Dk)xS+AGH&wNuN$R)HxW`(RYCF~ln^9X<6Z|>++1s=e0|s3| zQePQYi+|Ta6Pg}XT8L{x5!FZ$c#Hybu=&(9w$BJELF~9-@VguPQm$b84 zP{lIeCT?c(tMLYYH1sEei8yfHwXBqtJW|47hF2^-r>JcqV(w3&Yc-BmQ55kZ;KNil z0>?<7n=n3`mY$(Q5xoLE4l&~O8+Wo$&*CY5{9q~*&}M#vOvOp@fAEQ6q8cvf3Anu(O#Uclb#4wncl#oIjrC# zYm|cfh5JP_SY&5$oE4UPS*LgmoCvJZlbWn5DQYpQV|Yfri_s2$;k=;<#gev$lXl?leuFk8CB)~tL<2*>p6tYGKqttDDC1V~_dfZ6h;EN&L zF!aB^U@3ZTQD!l`ELn$Q(pGEA0Y*NqUlvA(q4Fl_TE# z*T9P>0fn=P@K3^)*OD*|rR}X!vQ;8yMzK=1x88?5*f_5uqcDsa!-RZcqJJj@FYj%V zTTK+hB4l$MsMvWbcNm~jRBeA5nfl|p(7{&e!aZ5Y>6-AX{bHG^Z2T&oNl;sQlyg`J zH%9O|huA@vdmG)!>>Zyu5JxzYb|(W^5gaB{({o4H3N^skOM~S*yFuf=O8^fW6-yb6 zQH)Lb*+kT;!OdV+j<+*9rV5O4j;sS(!KpdBT|XTjOWcs*+4i3JX#-t~>^n7HU6@+1 zJ}JWa0d!KInCZ2M)Tg9I*P#NAG4Rhyg@32-xlSZG|E!mN&C_ddfvxx96bTT8%5-KZdcj;=1>mZXETYu7SQvh^oUjE=Yybf zb$Zz;;|XkK6)T)m(zQf;=`hAbg@c-g&UV9Y`}sR(CeFC{NGBxb^mK~t+Np?nnp`7a zs!NAf6#07Udp4|TAZaT#n3ieKIzX0eyuMXzamK@k%*P$iLo$Vf5XE<B#3Ctthl^Jera3}h=PE zivg%9aM84_vcK*)U$ilGN_oT#b4?H~xoztCB^l;Wmtszd)KMDOJ#6W|t06@iB0QY^ z3hcHJYuOZbyQLq+B96EdFa37R3XexWgD<^3_Y3YP>y*ErDzUTF;TyD*nh8-$Ss=AU zOxR_Wz>l!c-r!XUEoc+muUFjqT}P;m`q#0IJbIKd96z4m62GBS)bq%d%oDLvWp*X~%Fr$Zy!{W<4qiYpBxNh z)I%*dXI;WSBdldPzzL3DL7_37RS!R6!j6)!O!YHTtMs0#n)v&CD8Bkah+PtC(K<<; 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