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Implementación de un predictor de series de tiempo utilizando Support Vector Regression para el mercado de los televisores en el continente europeo

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pg 22-24.

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

(7) 7.           %  O  J  %    J    &%  -   J PJ  QJ "&% &       PJ   J     2    -     J   QJ  %   OO QJ+  J  &  J +  J  J    R    +  J%      QJ      %    %      %   O   S  %  %   %QJ O -     2  . 224# . . 222,1.,01)8 ,1    % O   PJ    &%%&  4#+ &% J % & & &* +QJ-* & QJ%  J 2 !  &*QJ   % "   &       &%    & +   QJ     %         ;   B   &          &  PJ  C2@ ( x1, y1 ) ,...,( xn , yn ) ∈ Ȥ x ¡ m Q2BC      T  J   J  ;(             N  +    JJ &      &   R       &  QJ 2 !        ( ; &  + QJ  y ∈ ¡ + (   J2,&&   & +%-& -* &      J PJ  QJ   &*N&%-  QJ %&  J PJ       f ( x ) ≈ y.   !  4#O %&  J O%%     @ f ( x, w ) = w ⋅ x +b BC   QJ w , x ∈ ī, b ∈ ¡     &      &* &  +QJJ   P  2 !  P  &*&%   * +QJ  J J PJ     (  2  PJ      4 % U " V;  (  P   @  0 ­ si y − f (x,w ) ≤ ε E (x, y, f ) = y − f (x,w ) ε = ®  de lo contrario ¯ y − f (x, w ) − ε  1& .

(8) 8. E (x, y, f ) = max ( 0, y − f (x,w ) − ε ) .  !QJ&% QJ PJ  J    P   % O&   & QJV2   +  P  & QJV  P  J &2 (  V  QJ &J  "      PJ  +    ( %PJ   % " QJ*       2  . 222). , 1  ! 4# J  J  PJ   WBNC QJ (     %     X QJ   J  &    &*   QJ  %   +   J    O        P  KL2 %  " J    +&    BC2 !(   % ( WBNC - P@ 2 & P J &   &   % J%J  X@ 2 k ( x,x' ) := x , x' = ĭ ( x ) ,ĭ ( x' )  P  S KL2 2 &       %   & & +  %    %& J    &  % " J  -   &   2 72 ! -   PJ  WBNC%& M J  (   PJ   &   &  % " 2  . 2272!9.!    &- +  & N&"    PJ   -(  ( J    PJ     + QJ *J % J%J  ĭ( x ),ĭ ( xi ) KL   J  %     &   2   *J   &J +    J  JJ & J J U %( P  # QJ@ ĭ ( x ),ĭ ( xi ) = k ( x, xi )   % %  - +U %&QJ%J  J % J%J   &    % X+   &  X+ QJ&    T2!      U J-   S    # O !   KL2  . 22 24  ! &  %  % "     &%   J PJ    J %QJMB    & C@ R[ f ] = ³ c( f, x, y )dP(x, y )  2. Capítulo 1.

(9) 9. $  &   %- - QJ J&PJ %  -        -(  +          2   &%      J   QJ   %J  & &"   &  PJ     S  +%JQJ  $2 JJ +    &J    Q2 BC       -  J   B     "  C %QJM& &" PJ   J " @  İ RREG [ f ] = Ω[ f ] +C ⋅ Remp [ f ]  $  Ω[ f ] & J " + J  -&@ 1 2 İ RREG [ f ] = w +C ⋅ Remp [ f ] 2    &%B   & C* %@ m İ Remp [ f ] := 1 ¦ | yi − f (xi )|İ  m i=1 % *&,   QJ & -   % "  w2 +% J* &*    %J222  . 222! 1 0#1$:;4   & :;4  J   P&    & V;4+ QJ   &%   %   PJ      " V;  (  J  & 2%-&  V;4 J   J &  @ . (. w∈Γ , ȟ ∈¡. ). IJ w, ȟ (*) =. mi nimizar (*) m , b∈¡. (. sujeto a. 1 1 m 2 w +C ⋅ ¦ ( ȟi + ȟi* ), 2 m i=1. w , xi +b ) − yi ≤ İ + ȟi ,. . yi − ( w , xi +b ) ≤ İ + ȟi* , *.  22221)!# #!    &*N% :;4+ &* %%&"  J * @ mi (*)nimizar m. w∈Γ , ȟ ∈¡. ,ε , b∈¡. (. *. ȟ i( ) ≥ 0, ȟi( ) = ȟi* , ȟi .. donde. *. ). % J  J %-& . 1 1 m § · 2 w +C ⋅ ¨ υ İ + ¦ ( ȟi + ȟi* ) ¸ m 2 i=1 © ¹  ( w , xi +b ) − yi ≤ İ + ȟi ,. IJ w,ȟ ( ) ,İ =. sujeto a. yi − ( w , xi +b ) ≤ İ + ȟi* , donde. ȟ i(*) ≥ 0, İ ≥ 0, ȟi(*) = ȟi* , ȟ i ..

(10) 10. ,&  %J  (+       & J( J&* &  V2  ! J   J  J( PQJ %-& +%JQJ   NJ  &    V+ QJ   & M J-2  22221)!#$'!  J QJ  %-&   :;4  J  %-&  J *+      "   %-&  J 2    & !   +  J &J%  !    J9 +%-& (  J &  @ m. maximizar W (α (*) ) = ¦ (α i* − α i ) yi − (*) m α ∈¡. i =1. 1 m ¦ (αi* − αi )(α j* − α j ) k ( xi , x j ) 2 i , j =1. m. ¦ (α. sujeto a. i =1. i. − α i* ) = 0,. . ª Cº. α (*) ∈ «0, » , ¬ m¼ m. ¦ (α. donde. i =1. i. + α i* ) ≤ C ⋅υ , α i(*) = α i* , α i ..  22272'., 1.$  <.    J   %   -%-&  J +-  J PJ     @ m. f ( x) = ¦ (α i* − α i ) k ( xi , x) + b  i =1.   J  &     QJ 2 . "  QJ  %JQJ  JU .  229.!      +        9  %   &%M  &+  %   &J&% J *2  J  &J   " % J +%  &%&  9  J NJ( & 2  . 2229.! ' .1  9 . J *   J &  @. 2 § ·  k ( x, x ') = exp ¨ − x − x2' ¸ donde γ = 1 2 . ¨ ©. 2σ. ¸ ¹. 2σ.  J 9 %( P  +J &% QJ J (   & .

(11) 11. %(2  & U   %  &  QJ+  J  O JP & %QJM+%J   P     J  S& -  &       & +%  QJ J    P  K L72   "  QJ%  +%   & & +JP & - & %     J   %& %  J     %-& 2  . 2229.!$ 0,= 1.> 09.  , P   &%  %-      9 +-JJ U  QJ%J &%&  -  +% &  P  &  72 K/L J9  O >U +%%J IH%  J   J  (  J &-  9 2  '  (      * &J(   %%  J  U % J%  O  * & J (     (  -    J 2  U (  @  x − xi y − yi 1 n f ( x, y ) = ¦ K ( ) B( ) n i =1 h1 h2  9 -J U   J+%&% J +) -J U ) & 2  % OO %( O 2  J QJ% QJ9  J   P&   QJ  &  7+% U    O  %-   P  2!      &    O  %   J   %+  J  PJ   J  9     %  - 2  . 22721019.!  K L &J  QJ   & "  9  &  %J    %(  P        JN J  &QJ  9  J 2  KL&J QJO J  &%  &  9  J    J 9 !  2  % +9  & +    J -J  &%M+%J J    B&% *& 9 CO  PJ  J& +QJ (   J&   &%J  2    &*&% 9 +P  %J27+ 2 + 272 KL2    3. pg 150..

(12) 12. 2724#0.$',0 41        %J %   %J 4#%J J " 2    4#PJ  - &J &     % % " J%(" 2  &- NJ (        J(  4#+ & P     J( + QJ PJ P&J   &  % 4 % UK7L2)* &  % -   OO QJ   J & QJ S&J -J %      B P    J( C+ %        J  &  QJ %  - %   J  %P      & 2&   N  &  KL+ KLKL2 4  %    QJN J % *&QJ%J  (   %2 1   U  J  γ = 2 2σ 2    PJ   %&"   - &@  1 m 1 u min Ω ( h ) + C L ( h ( x ), y ) + C ' L(h( xm +i ), y*m +i )  ¦ ¦ i i y*m+i , i =1...u m i =1 u i =1  %J  (  ,B% *& %     & C,YB% *& %     %J- C2   &ZBQJ J &     QJ  %J- C+J  % *&QJ - & M  O%P QJ    J QJ * N    &  QJ  J *  %   &   &Z+ %J  O -   (   %  Φ ( x ) 2  ! J  %-& %&  -  J &  @  W = (I N + CXXT + C ' X'X'T )−1 (CXY + C ' X'Y')  $ [ & "QJ& &"  PJ   %&"   P& &  KL +\      & +\Y  %J- +5 QJ +5Y QJ  %J-     & 2 $ &   J *   J @ X 'T W  $   % &   (   &  QJ  &    J  %-&   +  J &% QJ J   ( & 4# J(2  . 2 2#$ $$$#?1 . 2 22,1 ., $#1$!1@  0  4. pg 6.    J     &     %-& +    %     .  .

(13) 13. (  -QJ PJ -& +JJ &    &%M- %   &  %% 2  #+J %& +  (     (  % O   (   2      +   &   #+ &   %  2   # P   J &  @ m. ¦ (x. i. − pi ). 2. i=1.  m & S&  + (  +  ( % O2 MSE =. $  =J-   &    &%M QJ  J(    J   (  QJ  &      (   &  QJ   -      &  2  &     QJ   ,   ,PP  B,,C  #  -J  B#C+ QJ  P    J &  @   m. SCC =. m. ¦ ( x i − p i )2. ¦ |x. i=1 m. i=1. ¦ (x. MAE = i−k. − xi ). 2. i. − pi |. m. . i=1.  !  # (   QJ  (     &&  '#  PJ     S& (  O    &&  2!    ( O  &&  QJO   PJ      & (  2    #% &&    QJ#+N%%QJ   &   P + QJ (  J  2 % +,,J  QJ   P&      J &    (   2P (    &  P +    QJ      J %P &   2 . 2 22 ,1#, <. ,'.0 00 4 $ !1 $ .0 #A01$1     &%     P & J  &  2    J#.#$+ P    J &  @  RMS RMS = MSE NRMSD =  RANGO  $ . 1O  J     + P  &  P   &  & 2   J   &        P   &%   -&   J  QJ   &    %     J       &%   %    &   & 2.

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