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.
(6) 6. . . . 221)30 41 .!$!15,01 -( %J ! P O % - &% J ( & ( , J%2 &%N J - + + - % &% 1.5+ QJ % P& + &- J & ( ( + % O % + & + QJ%2 . 221)30 41,6 ,1$!15,01 #. J % & @ P& QJ ( % % 2 -& QJ%& J & * P& 2 & @ &%& J & )SQJ J ( % *& & 2 &  & % *& & & % QJ % 2 , " %J- 2 & QJ% &J 2 % & ( P " 2 . 272.0,$.0 %-& &%+ % & # O ! + & 4#+O - &J% ' ( 2 J & %-& O J % % &% P + &O KLKL2 % - &% QJ % %P + QJ* N% &* 2 .
(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 ( & .
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(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 & %-& + % . .
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(18) 18. & %%P ( -QJ O % OO % &% + +$4$+1$',0^! .+'!!^=$+).$ 2$ & %-& J& &* -J - QJ% 2 S QJ - J -& P ( -+ S& QJ QJ O - % J @ NJ &%% &- &% ( - + @ = +0% 0 +& 0 & M+J &% QJO N N ` IH P &%2 &- % &% % !# N ( &* %QJM QJ 7 %J + QJ & J S& &%2 S& &% ( J PJ 72 &%+* &%% 0JQJ +!,$+ ;%J R% &- * &%0JQJ +!#+ ;%J 2QJO O &%% % +O % 2 J &J J &%+ QJ + QJ / &% &- & & M2 )*+,-'./01 & SERIES DE TIEMPO PARA FRANCIA 0,12. 01. <= 18 (4:3) - LCD-DISPLAY. 0,1. 02. <= 18 (16:9) - LCD-DISPLAY. UNIDADES VENDIDAS (MILLONES). 03. 19-20 (16:9) - LCD-DISPLAY 04. 21-23 (16:9) - LCD-DISPLAY 05. 19-23 (4:3) - LCD-DISPLAY. 0,08. 06. 24-29 - LCD-DISPLAY 07. 30-32 - LCD-DISPLAY 07. 30-32 - PLASMA-DISPLAY 08. 33-39 - LCD-DISPLAY. 0,06. 08. 33-39 - PLASMA-DISPLAY 09. 40-44 - LCD-DISPLAY 09. 40-44 - PLASMA-DISPLAY 10. 45-49 - LCD-DISPLAY. 0,04. 10. 45-49 - PLASMA-DISPLAY 11. 50-55 - LCD-DISPLAY 11. 50-55 - PLASMA-DISPLAY. 0,02. 12. > 55 - LCD-DISPLAY 12. > 55 - PLASMA-DISPLAY. 200803. 200709. 200703. 200609. 200603. 200509. 200503. 200409. 200403. 200309. 0. TIEMPO (MESES). Z# +QJ&J / &%QJJ &- !,$ !# & - 2 &* P& %J72 ! - %J J &J P & +QJ %QJM+ % * J S % %% & % & 2.
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(23) 23. $ & - & OJ J P @ &%&( %&!B5++.9C% J -@ #d2I 4U`&-" % % 2Ie#d2 4U`2&-" & % % 2 e#e 4U`&-" &J- % % 2 ' &% @ N *% -4f4f47f4 ` # *% -72e4f4f47f4 e7 ) *% -7d4f4f47f4 e & *% -d4f4f47f4 e J * &* % P ( % -J & QJ& " %J- 2 ! J & J &% B " C &J % )2 . 27201#$09.;#?A . & 0 U ;# M - QJ J &% { xi } + QJ. %( J & *&+ - [ xt , xt −τ ,...., xt − ( m −1)τ ] J g %(+%J % xt +1 & g 2, - & ( ( % % % g S& &*N& K7L2 . 2 20)!, # .01$!1#A01$1 J J % 2+QJ J PQJ P % & QJ " % % 2 . 2 22 #A01$1B'. 4 $1C = 4- J 7 &%2B 7 P + J P & & M J % C2&& 7PJ P 2 , %@ % % J ( PJJ QJ J PJ ( .
(24) 24. % + QJ P& QJ O && ( && ' #PJ S& ( 2N% J P& @ at + k = f (at , at −1 ,..., at − m +1 ) , - " %J 2272+J ( :H&2 &*+ O J PJ % #+ QJ PJ % & PJ % &2 . 2 22 #A01$1B,'!1 C %J QJ& J %JQJ% QJO ( &% P 2% O 4- % B P C2 J PJ QJ &% & & & M % 2! PJ 7N% %QJ& 2 , %@ -J % P & % % ( &%%& J && PJ 2 MJ - QJ " & - & & M 2 +O J J& % %- & M (B S ( - 4 )!C+J J& % %- B @!,$!#C2 &* J& &%+J M &2! J& M J & @ n añon = # total años QJ%&%% MBQJ%& M QJ C+ `2$ P& &- J QJS& MB/ C( 2! J& & O QJ ;& & ( c2 &% & & QJ( c`2 HHI& &-QJ( c`2 ! - H J& B & + + &%C2 , - J J& QJ% J& & M J + J ( % & M2 ( P 2 ' &% J % - %J ( J PJ @ '()' & ?1 27 2H. # 2 HI 2. . _`/B @7C . ;7B @7C . . " ! . ; . !,$ . h h h. d . !# .
(25) 25. !%J J% (&J QJO & & + S - % 2 ! %& - &J M +& # +(!,$ & M & / %J P& B @7C2 ! J &J M + & 3J + (!# &* %J 2 ! BQJ C %(QJ S& ( ( % QJ - - 2 )*+,-'./01 3 MERCADO SUIZO. UNIDADES VENDIDAS (MILLONES). 0,06. 0,05. 12. > 55 11. 50-55 10. 45-49 09. 40-44. 0,04. 08. 33-39 07. 30-32 06. 24-29. 0,03. 05. 19-23 (4:3) 04. 21-23 (16:9) 03. 19-20 (16:9). 0,02. 02. <= 18 (16:9) 01. <= 18 (4:3). 0,01. 200802. 200711. 200708. 200705. 200702. 200611. 200608. 200605. 200602. 200511. 200508. 200505. 200502. 200411. 200408. 200405. 200402. 200311. 200308. 200305. 0. TIEMPO(MESES). Z ! PJ 7&J & J & % +&J" + J QJ&% & & &J J " ( + (QJ( % & M( 2 - QJJ ( % & + & M N( & + % &% - &* ( & %J 2 &- & J % & & MJ% & J( 2 && & &*( & & M7;7%J %QJJ% &J - P & &S J% 2 &- + J QJ & + ( ( & %J O % P ( (&* & % S& &2 %& % QJ PJ * & J ( J & J& ( 2. . 2 272 #A01$17B,'!!,1.0 ..0C & + & & J + &- % &% QJ % - 2= 4 - - BJ C2 J PJ QJ &% & & % + & & M2%J QJJ PJ .
(26) 26. % & (J%2 , %@ % && %QJ & P QJ QJO J - +&* O QJ & 2 - QJ &* H J& - + J J& % J % 2 QJ - Hf ` J& +J /7 2 !& 7%J !BS P %KHLC%JQJ PJ QJ * P &%%& J &- ( & 2 . 2 2 2 #A01$1 B4#0.$',0 41C , P PQJ %-& &%& J % & & %KL+ P QJ - O"( J" % *&2 ! P& QJ & PJ J ( + & # + J &% QJ 7 PJ P BJ % &%C2 , %@ JN% %J272 .
(27) 27. . 228#01,+:+D %J+ J QJ P& O % & + J- %QJ QJ # O ! J + %J QJ J % *& -J & + % & J 2 J & & O %J& % %J % J& 2 . 222 8#01, 2222 016 % *&,QJ& %J22 +22H22H2+ & +% *& 2)* & PJ % *& &- J J " 2 " PJ + %@ 1 2 İ RREG [ f ] = w +C ⋅ Remp [ f ] 2 %J % QJ% J & 2. İ % Remp [ f ] C &% & B % w C2 % " QJ%J ( %-& 22H2QJ &J% ! ,c&2 4 % QJ &% & &- P J & 4,+ QJ &- %J QJ % *& , & - & & 4, & 2 2222,1#.$, 1. KL O -J , &J-J J B( &*% *&20 &- & QJ &JO O J -SQJ P -( ,2 +( ,& %(- 2P2KLH O -J ,`% J %-& P + -J J + J QJ O 2 . B. 5 6. Capítulo 9.3 – 9.6 pg 6.
(28) 28. 222 8#01: 2222016 % *&: J &J ( & ε 2 S $ ;+ KL+ -QJ PJ % *&: J @ 2:J J%% P B %J QJ* %PJ J-C2 2:J P% P 4 %2Z 72, %- - + & :J P 4 % P 2 Z %P 4 % S& 4 %- S& ( 2222 ,1#.$, 1. :` %&" %J O QJ ε " - & +% %J & + &- QJ 25J &J QJ - - J % *&2 ' :&* %&&*%J %PJ J-+ &% & O &* %QJM2 + % &% &%J .7+ . S& 4 %2 QJ O J : - QJ & J S& ( % &- O QJ &PJ &**% & K7L2 . 2272 8#01D 22722016 % *& & U 9 J * % . J 2 . QJ . § x − x' 2 · 1 k ( x, x ') = exp ¨ − ¸ donde γ = 2 ¨ ¸ 2σ 2σ 2 © ¹. J -* & J PJ J J & P 2 &- + % *&i&J J( " + QJ &* ( &*a O b* J 2 $ & + D ( i - QJ &* %QJM J *&* 2 22722 ,1#.$, 1. + J D JP & %QJM+ %J P J S&.
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(31) 31. QJ S& & - % % O J -J - % 2 S& & ( % QJ % -+ &- + %& J H7 % &%2 2 222#A01$1 % & J H & %J- + & %( J" 2 +% J% &% % + + QJO % - &%2 2 2272#A01$17 &% + &- O % % &%2&% & % & & B &J QJ " J C+O %J- % H& %J- & 2 )*+,-'./01 # . . MERCADO DE LOS 6 PAISES MAS SIGNIFICATIVOS 3,5. UNIDADES (EN MILLONES). 3. 2,5. SPAIN. 2. NETHERLANDS ITALY GREAT BRITAIN GERMANY. 1,5. FRANCE. 1. 0,5. TIEMPO (MESES). 200802. 200711. 200708. 200705. 200702. 200611. 200608. 200605. 200602. 200511. 200508. 200505. 200502. 200411. 200408. 200405. 200402. 200311. 200308. 200305. 0. Z PJ &J QJNJ & & 2!%% $&-%JQJ ( J& 2 & # 3J&%O J & ( % &QJ 2% QJ % %J J % P % 2 %J ( J % %J 22722.
(32) 32. J % ( - QJ &J J &J 2, J - QJ&& % & ( + QJ&& % & %J- +P & %J % -+ QJ & % &QJ ( 2 . 221,$ # .014 .! % & J J & - % & %%J%K7L2A -* & J @ 2 0 P& P& J Pj 4#2 J - ! )4#KL+& & & 2 2 & &% ( & 2 & " O"S %%J%K/L+ J &*N& J & & 2 72 J K7L7+ - ( %J 2 &%& 9 J 2 2 ' ( J" BN% %J272C&% &% *&,+:D2 2 ' &&- % *&% QJ % B & f( C2 H2 " J- % J %J- % J 2 I2 , &- & ( (J % 2 /2 ' &&- % *& & M & ( + QJ % B & f ( f%J- C2 2 , - & % + & % P & ( P " 2 Z0 -SQJ &&- % *&,+D+: " & ) O>)J N% %J2222 &) O>)J J S % QJJ *& 2$ & + +%&%,`k + O J -SQJ J D:+ +D`kK;+;7+;++7L:`K+2+2 h2/+L2 %J QJ J &#+O J -SQJ &* ( 2&%+&#* D#`k; :#`2 O D`kK;H2+;H2+;2+;+; 2+; L:`K+2+27+27+2 +2 +2+2L2 J QJ J ? & 2 QJ ) O > )J ( % & J %QJ -SQJ &*%QJM QJ -SQJ %J J & J & -SQJ %JQJ* J -SQJ 2! -SQJ B C & OJ 2. 12 13. pg 17 pg 4.
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