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zLqS3?K{Gi;H8nv(G&MOzLpV7;AUrlOGeI>lL^nb)K}AMGK|(M=GdV>yH9E3vmdyb!^8YO>U?r5GOXFA9e6R|N&<(3KDNp%e4XlMTumRR- z(%0|P9#{`sU@L5c?NEkZ=z|?lfnnGQyI{AbrFq}CN7JE3PkS}JGU{ocrqi>Y_G|iL z($fJ=KR@x*uj!9rPX{%fpYb%Hp>EvMpoXS7PeU4d>pdOPF!9dQJ7EpgoA%+ZzA>)< zHg5biZv8VRdyG3(<6hagpBPhbjR#MSnQ32e7S6$WxBwU75?t2skoC{TWC3n?m;aXx OA_+A&3MC~)PeuxI3%=+8 diff --git a/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex b/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex index 79680e5a..1abeaf21 100644 --- a/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex +++ b/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex @@ -51,9 +51,9 @@ \left ( \xv^T \xtil + b \right)^2 &= \left ( \mat{ x_1 \\ x_2} \cdot (\xt_1 \ \xt_2) + b \right) \cdot \left ( \mat{ x_1 \\ x_2} \cdot (\xt_1 \ \xt_2) + b \right) \\[10pt] &= (x_1 \xt_1 + x_1 \xt_2 + x_2 \xt_1 + x_2 \xt_2 + b) \cdot \\ & \ \ \ \ \ \ (x_1 \xt_1 + x_1 \xt_2 + x_2 \xt_1 + x_2 \xt_2 + b) \\[10pt] - &= x_1^2 \xt_1^2 + x_2^2 \xt_2^2 + 2 x_1 \xt_1 x_2 \xt_2 + 2 x_1 \xt_1 + 2 x_2 \xt_2 + b^2 \\[10pt] - &= ( x_1^2 , x_2^2 , \sqrt{2b} x_1 x_2 , \sqrt{2b} x_1 , \sqrt{2b} x_2 , b ) \cdot \\ - & \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2b} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b ) \\[10pt] + &= x_1^2 \xt_1^2 + x_2^2 \xt_2^2 + 2 x_1 \xt_1 x_2 \xt_2 + 2 b x_1 \xt_1 + 2 b x_2 \xt_2 + b^2 \\[10pt] + &= ( x_1^2 , x_2^2 , \sqrt{2} x_1 x_2 , \sqrt{2b} x_1 , \sqrt{2b} x_2 , b ) \cdot \\ + & \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b ) \\[10pt] &= \phix \cdot \phixt \end{aligned} \end{equation*} From 6ca36980713bd2145976a03c65f11cb768a3f9d0 Mon Sep 17 00:00:00 2001 From: "patricio.massaro" Date: Sun, 5 Mar 2023 18:01:48 +0100 Subject: [PATCH 3/5] Adding missing Transpose --- slides-pdf/slides-nonlinsvm-kernel-poly.pdf | Bin 825386 -> 825394 bytes .../slides-nonlinsvm-kernel-poly.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/slides-pdf/slides-nonlinsvm-kernel-poly.pdf 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a/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex +++ b/slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex @@ -52,9 +52,9 @@ &= (x_1 \xt_1 + x_1 \xt_2 + x_2 \xt_1 + x_2 \xt_2 + b) \cdot \\ & \ \ \ \ \ \ (x_1 \xt_1 + x_1 \xt_2 + x_2 \xt_1 + x_2 \xt_2 + b) \\[10pt] &= x_1^2 \xt_1^2 + x_2^2 \xt_2^2 + 2 x_1 \xt_1 x_2 \xt_2 + 2 b x_1 \xt_1 + 2 b x_2 \xt_2 + b^2 \\[10pt] - &= ( x_1^2 , x_2^2 , \sqrt{2} x_1 x_2 , \sqrt{2b} x_1 , \sqrt{2b} x_2 , b ) \cdot \\ - & \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b )^T \\[10pt] - &= \phix \cdot \phixt + &= ( x_1^2 , x_2^2 , \sqrt{2} x_1 x_2 , \sqrt{2b} x_1 , \sqrt{2b} x_2 , b )^T \cdot \\ + & \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b ) \\[10pt] + &= \phix^T \cdot \phixt \end{aligned} \end{equation*} \end{vbframe} From 70158b9d8bb208707654c3a22834857d16f1f902 Mon Sep 17 00:00:00 2001 From: "patricio.massaro" Date: Sun, 5 Mar 2023 22:23:37 +0100 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