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Developed by Carpenter and Grossberg ART1-accept binary data ART2-accept continuous value data ART3-improved ART Fuzzy ART- accept fuzzy data &   j FARTv~g .g0A23z['`NSQX'`/f N Tv OSQX'`vd\OBlRg<Z `  `  GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. 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fDW&cC3___PPT10.+nD' == @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*P D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*P DA' =%(D' =%(D' =A@BBB B0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*P %D' =1:Bvisible*o3>+B#style.visibility<*P %%(D' =-6B'blinds(horizontal)*<3<*P %DA' =%(D' =%(D' =A@BBB B0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*P %=D' =1:Bvisible*o3>+B#style.visibility<*P %=%(D' =-6B'blinds(horizontal)*<3<*P %=DA' =%(D' =%(D' =A@BBB B0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*P =_D' =1:Bvisible*o3>+B#style.visibility<*P =_%(D' =-6B'blinds(horizontal)*<3<*P =_DA' =%(D' =%(D' =A@BBB B0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*P _qD' =1:Bvisible*o3>+B#style.visibility<*P _q%(D' =-6B'blinds(horizontal)*<3<*P _qDA' =%(D' =%(D' =A@BBB B0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*P qD' =1:Bvisible*o3>+B#style.visibility<*P q%(D' =-6B'blinds(horizontal)*<3<*P q+p+0+P 0 ++0+P 0 +. ?0 VN (  ~  s * B( M }     s * C( ; `<$D 0  vr  # o"@ ,$D 0v  # o"@@ ,$D 0  B4G ?"pv ,$D 0 ^ N9SMvsX[ !j_ NO9e   NK ?"MS ,$D 0 \eeQTϑ NsX[!j_      NP ?"p,$D 0 Zv+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*++0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 + @0N0  $$U(  ~  s *xr( M }   F     S (t  7X   3 x"  NƋ+RB\    S { X :C(B)   S x g  :P(T)  N *  *   S l @7 ? 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C D"\B "B S D"V2 # C "f   $ S |$ Z  x|^c6RSpe4 H  0޽h ? 33y___PPT10Y+D=' = @B + A0 0Z(  ~  s *T( M }     s *ස( ; `  *P |H  0޽h ? 33___PPT10e.+D=' = @B +S B0 nf@(  ~  s *( M }     s *<( ; `C <$D 0    c &AS ??  8 $D 0H  0޽h ? 33___PPT10e.+HD' = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>Q%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>QD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>QDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+8+0+0 +9 C0N0 7///PVV.(  x  c $. ( #    &$"7 # #" T ,$D 062  "X + +62  "X / 062  "X 4 t56  "*0+6  "/006   "4056   "4 56   "/ 06   "* +\B   S D" c+c+\B  S D" #5#5\B  S D" C0C0\B  S D"0c+c+\B  S D"0#5#5\B  S D"0C0C0\B  S D" 04\B  S D" c+4\B  S D" +0\B  S D" +#5\B  S D" 0#5\B  S D" c+/\B  S D"0c+/\B  S D"0c+4\B  S D"0+/\B  S D"0+#5\B  S D"004\B  S D"00#5\B  S D"+-\B   S D"|+|-\B ! S D"|0|2\B " S D"02\B # S D"57\B $ S D"|5|7\B % S D"57\B & S D"T5T7\B ' S D"02\B ( S D"T0T2\B ) S D"+-\B * S D"T+T-VB + C D" c+ c+VB , C D" C0p!C0VB - C D" #5$"#5VB . C D" ( c+VB /B C D" ( (VB 0 C D"p!'p!C0VB 1 C D"$"&$"#5VB 2B C D"< 'p!'VB 3B C D"&$"&VB 4 C D" ( c+VB 5 C D"< '< C0VB 6 C D"&#5\B 7 S D"#5X #5\B 8 S D"< C0X C0\B 9 S D" c+X c+z 00F@ : 0@,$D 0 ; N$C  ?"00B* ^rm&  < NI  ?"P? Dr2&  = NM  ?" Dr1&  > NH  ?"#660 DT1&  ? N ?"@@A : Dp1&  @ N ?" @o : Dc1&  A N ?"f` 5T B N$ ?" p j 5B C N8  ?"0@C: DB1&  D N ?"0 P J `x1G1@   E N ?".+/ %  Dp2&  F N| ?" @ :  Dc2&  G N! ?"p  e  ^cn&  H N\& ?"@ G  ^pn&  I N+ ?"`  f YMO G2&  J N<1 ?"`T N  f YMO G2&  K N5 ?"#6  DT2&  L N7 ?"0 f  DTm&  M N0? ?"< r  ^Bm&  N N@D ?" @:  DB2&  O NI ?"  `XnG1@   P NO ?" 6 0  ax2 G1@   Q N,V ?"`z f YMO G2&  R NZ ?"" 6  6&  S NtY ?"B V  6&  T Nb ?"2 F  6&  U Nf ?"F@ NƋ+RB\  V Ntj ?"0 @ : NkB\ H  0޽h ? 336 . ___PPT10 +Po5D ' = @B D ' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*:D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*:+ 0 .T Z(  T  T  0Xr( ip    T c $x( P   * @`H T 0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0N0 .X 0(  X  X  0( ip<$D 0    X c 0A @ 4F_8-2D@ ,$D 0" X 0pL$D 0Ac0H X 0޽h ? fDW&cC3y___PPT10Y+D=' = @B +1 0 " .\ (  \  \  0y ( ip<$D 0    \ c $( u<$D 0   * @`H \ 0޽h ? fDW&cC3..___PPT10a..+."[D-' = @B D-' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\ %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ D' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ 6D' =1:Bvisible*o3>+B#style.visibility<*\ 6%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ 6D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ 6D' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ 6HD' =1:Bvisible*o3>+B#style.visibility<*\ 6H%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ 6HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ 6HD' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ HwD' =1:Bvisible*o3>+B#style.visibility<*\ Hw%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ HwD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ HwD' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ wD' =1:Bvisible*o3>+B#style.visibility<*\ w%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ wD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ wD' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ D' =1:Bvisible*o3>+B#style.visibility<*\ %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ D' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ D' =1:Bvisible*o3>+B#style.visibility<*\ %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ D' =%(D`' =%(D' =A@BBBB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*\ OD' =1:Bvisible*o3>+B#style.visibility<*\ O%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\ OD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\ O+p+0+\ 0 ++0+\ 0 + 0 0.` Z(  `  `  0 ( ip    ` c $(      * @`H ` 0޽h ? fDW&cC3___PPT10e.+D=' = @B +1 0N0 @8@.d (  d  d  0Hƀ( ip<$D 0   X d c 0A  F_8-32d" d 0 Cc0H d 0޽h ? fDW&cC3y___PPT10Y+D=' = @B + 0 P.h Z(  h  h  08ˀ( ip    h c $Հ( `   * @`H h 0޽h ? fDW&cC3___PPT10e.+D=' = @B + D0 80` (   ~   s *8( M }   ~   s *x( ; `     6P   `  Ƌ+RB\QOSc6R 8 0 ' ,, x   0?   `  G2= x1("x2("& ("xn 0              C  H   0޽h ? 33___PPT10e.+D=' = @B +O E0 jbp(  ~  s *p?( M }  ? ~  s *p?( ; `@ ? b  c &AT ??     <!? ?" @ :C=X (2  <0? ?"U 00  P=Tk ci=xi'"pi (2    >  B7? ?"   |_}Tg ]\OhTg 8 18Z2 # C  H  0޽h ? 33___PPT10e.+D=' = @B +e F0 x(  ~  s *G?( M }  ? ~  s *$I?( ; ` ? b  c &AU ?? `  Z  00M? 0   *Xv f[ NhRNk@b_vQ~eQ:N h10Z  C. b  c &AV ??`    <8^? ?" @ JNRN1 RN2 & RNmv[^ TϑB1 B2 & BmNh N TR{| &      H  0޽h ? 33___PPT10e.+D=' = @B +{ G0 &(  ~  s *?( M }  ? x  c $?( 0 @ ? ~  0,?  ` se" S_MRYNoS`vRNk@b[^vBk0Tk:NXv{|h:y s< dkRNk@b[^vBk0Tk N_}Y0WNhX ͑e[~b  08Z"00Z                                C b  c &AW ?? P  H  0޽h ? 33___PPT10e.+D=' = @B + H0 <(  ~  s *ԟ?( M }  ? ~  s *Ԡ?( ; ` ? H  0޽h ? 33___PPT10e.+D=' = @B + I0  <(   ~   s *?( M }  ? ~   s *?( ; ` ? H   0޽h ? 33___PPT10e.+D=' = @B + J0 $6(  $~ $ s *?( M }  ? x $ c $t?(  `` ? H $ 0޽h ? 33___PPT10e.+D=' = @B + K0N0 (<(  (~ ( s *?( M }  ? ~ ( s *?( ; ` ? H ( 0޽h ? 33y___PPT10Y+D=' = @B + L0 ,<(  ,~ , s *E( M }  E ~ , s *E( ; ` E H , 0޽h ? 33___PPT10e.+D=' = @B + M0 0<(  0~ 0 s *!E( M }  E ~ 0 s *)E( ; ` E H 0 0޽h ? 33___PPT10e.+D=' = @B + N0 4<(  4~ 4 s *2E( M }  E ~ 4 s *l8E( ; ` E H 4 0޽h ? 33___PPT10e.+D=' = @B + O0 8Z(  8~ 8 s *LE( M }  E  8 s *OE( ; ` E *,,<H 8 0޽h ? 33___PPT10e.+D=' = @B + P0  <<(  <~ < s *0bE( M }  E ~ < s *fE( ; ` E H < 0޽h ? 33___PPT10e.+D=' = @B + Q0 0@<(  @~ @ s *pE( M }  E ~ @ s *pE( ; ` E H @ 0޽h ? 33___PPT10e.+D=' = @B + R0 @D<(  D~ D s *E( M }  E ~ D s *E( ; ` E H D 0޽h ? 33___PPT10e.+D=' = @B + S0 PH(  H~ H s *E( M }  E ~ H s *E( ; `F  E b H c &AX ??  H H 0޽h ? 33___PPT10e.+D=' = @B + T0 `L(  L~ L s *E( M }  E ~ L s *\E( ; `-  E b L c &AY ??0  H L 0޽h ? 33___PPT10e.+D=' = @B + U0 pP<(  P~ P s *(E( M }  E ~ P s *(E( ; ` E H P 0޽h ? 33___PPT10e.+D=' = @B +O V0 jbT(  T~ T s *E( M }  E ~ T s *E( ; ` E b T c &AZ ??@   L T NE ?" M   tki = ci n 0(       C $H T 0޽h ? 33___PPT10e.+D=' = @B + W0 X<(  X~ X s *dE( M }  E ~ X s *xE( ; ` E H X 0޽h ? 33___PPT10e.+D=' = @B + X0N0 \j(  \~ \ s *E( M }  E b \ c &AZ ??`@ y  \ <E ?"  ^-N+T g͑VP[(2 b \ c &A[ ?? 0  H \ 0޽h ? 33y___PPT10Y+D=' = @B + Y0 `<(  `~ ` s *E( M }  E ~ ` s *E( ; ` E H ` 0޽h ? 33___PPT10e.+D=' = @B + Z0 d<(  d~ d s *$N( M }  N ~ d s *$N( ; ` N H d 0޽h ? 33___PPT10e.+D=' = @B + [0 hR(  h~ h s *xN( M }  N  h s *#N( ; ` N "8*VH h 0޽h ? 33___PPT10e.+D=' = @B + \0 l<(  l~ l s *P ( M }  N ~ l s *P ( ; `   H l 0޽h ? 33___PPT10e.+D=' = @B + ]0 p<(  p~ p s * ( M }   ~ p s *` ( ; `   H p 0޽h ? 33___PPT10e.+D=' = @B + ^0 tP(  t~ t s *` ( M }   ~ t s *` ( ; `     t 0_N 9{ &SNART(W~[bT QbeQЏL >AA A$ H t 0޽h ? 33___PPT10e.+D=' = @B + 0 `.l Z(  l  l  0Xx UWc   X H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0 . (      0kZ( ip  Z   c $`rZ( Pp Z * @`B   NA H?1 ?  Hc0  0xZ   0H@8___PPT9 &FParameters: m: dimension of input vector n: number of cluster units  y0 UZ;x0UZ #       G H  0޽h ? fDW&cC3___PPT10e.+D=' = @B +g 0 z. (      0 Z( ip  Z N  C &A art2-1H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0  . (      0Z( ip  Z   c $Z(  Z * @`B   NA I?1 ?0ww Ic0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0  / (      0Z( ip  Z   c $( /' Z * @`B   NA J?1 ? p Jc0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B +E 0 `X/ (      0Z( ip  Z   c $Z( pP  Z * @`B   NA K?1 ?pL  Kc0  0Z   0   e. compute signal to F2:x U    B   NA L?1 ?   Lc0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0   / (      0$Z( ip  Z   c $e( pP  Z * @`B   NA M?1 ?   Mc0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0  0/ (      0e( ip  e   c $e( pP  e * @`B   NA N?1 ?  Nc0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B +; 0 VN@/ (      00e( ip  e   c $7e( pP e * @`B   NA O?1 ? &  Oc0  0      k. Update F1:x U  $  B   NA P?1 ?p 3 Pc0H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + 0 P/ Z(      0Je( ip  e   c $Ne( P  e * @`H  0޽h ? fDW&cC3___PPT10e.+D=' = @B + C0 *p (  p X p C    e p S de @  e  H p 0޽h ? ̙3380___PPT10.ޒH E0 *x (  x X x C    e x S je @  e  H x 0޽h ? ̙3380___PPT10.ޒH F0 *| (  | X | C    e | S  @  e  H | 0޽h ? ̙3380___PPT10.ޒH G0 * (   X  C    e  S Pte @  e  H  0޽h ? ̙3380___PPT10.ޒH H0 * (   X  C    e  S ye @  e  H  0޽h ? ̙3380___PPT10.ޒH I0 + (   X  C    e  S Pe @  e  H  0޽h ? ̙3380___PPT10.ޒH J0 + (   X  C    e  S He @  e  H  0޽h ? ̙3380___PPT10.ޒH K0  + (   X  C    e  S Ċe @  e  H  0޽h ? ̙3380___PPT10.ޒH L0 0+ (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒ:H M0 @+ (   X  C    e  S te @  e  H  0޽h ? ̙3380___PPT10.ޒ:H N0 P+ (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH O0 `+ (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH P0 p+ (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH Q0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH R0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH S0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH T0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH U0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒfH V0 + (   X  C    e  S xe @  e  H  0޽h ? ̙3380___PPT10.ޒfH W0 + (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒfH X0 + (   X  C    e  S de @  e  H  0޽h ? ̙3380___PPT10.ޒfH Y0 , (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH Z0 , (   X  C    e  S \e @  e  H  0޽h ? ̙3380___PPT10.ޒH [0  , (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒH \0 0, (   X  C    e  S \e @  e  H  0޽h ? ̙3380___PPT10.ޒp!H ]0 @, (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒp!H ^0 P, (   X  C    e  S Te @  e  H  0޽h ? ̙3380___PPT10.ޒp!H _0 `, (   X  C    e  S e @  e  H  0޽h ? ̙3380___PPT10.ޒP `0 p, (   X  C    e  S Te @  e  H  0޽h ? ̙3380___PPT10.ޒP a0 , (   X  C    p  S p @  p  H  0޽h ? ̙3380___PPT10.ޒP b0 , (   X  C    p  S P p @  p  H  0޽h ? ̙3380___PPT10.ޒP c0 , (   X  C    p  S dp @  p  H  0޽h ? ̙3380___PPT10.ޒP d0 , (   X  C    p  S 4p @  p  H  0޽h ? ̙3380___PPT10.ޒP e0 , (   X  C    p  S p @  p  H  0޽h ? ̙3380___PPT10.ޒP-h0 -@ ((  @ ^ @ S     @ c $ @    H @ 0޽h ? ̙3380___PPT10.x`xKh@ͤnڵHQ=(Ҋ-VUZy0֬el75RAEy(7BO"*oT Ůo&uU/J_x;޼{of_>*["+5m07fP绞iq,s}\b'$v:3'ӓ~{cO\nr鋫uԝ̀RM{XT: :RbW@|=,(6NGkQٹw/}pvg9Ʈwlu3ձ5WjGFO: 'ki4ZdٓfkoikњvyiOg ր{0& xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!]3K!Ff V30d'2b`bDD`;PtGC  ?k?H}& i@c?^7XgAe>;Tl oωF`*a悤=/$|3Jv>WX@څsG6yz+#TVrz"NPٓCQS e= xUM/Q=MSB'X4?@HYX)MdVM4~MYHD-lu7}LFؠgr;yz{:>?PP41i.ivڬW#ж:f';J)]h(y[Ro>t4(\1E֔c&N'Tp朏:`hQl8Z3FBŜ;IB# /~Q}$sumME-ʻ履)c1ߌ =ׯ?^_Bcsx"IA_og W#P3|tC,cAƃa¥ʌ)LeJӲ Pвk]tdEFedm.X^#+f 4Kȱd/ e,lP(R ) L./O+Qع^c=k(ZXX 8z _,7fJ PN/+^leed$3032pY,f1uyy LmJ x=A<i9A,* ' ' #4C#? ?X?(RYh*rz" !F!T F~LxW]h\E>3?ٛ4iCkn,Ul%)kOv{w{k>h! 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Developed by Carpenter and Grossberg ART1-accept binary data ART2-accept continuous value data ART3-improved ART Fuzzy ART- accept fuzzy data &   j FARTv~g .g0A23z['`NSQX'`/f N Tv OSQX'`vd\OBlRg<Z `  `  GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>?@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<b 0 `/ Z(      0rp( ip     c $< e( P  p * @`H  0޽h ? fDW&cC3___PPT10e.+D=' = @B +riaэ# Ea  ( :  iEquation Equation.30 Microsoft lQ_ 3.0t Equation.30  ՜.+,D՜.+,D    Ļʾbjpuip y;$' RTimes New RomanArial WingdingsFranklin Gothic Medium κ _GB2312 _GB2312 пTahomaSymbol PMingLiUArial Unicode MS MS MinchoGungsuhImpactPPTģ壭3Microsoft ʽ 3.0Microsoft ʽ݋ 3.0Microsoft Equation 3.0MathType 4.0 Equation Ϣѧ Ŀ ¼ӦгӦгӦгARTṹͼ ARTĽṹ ARTĽṹȽϲʶART ArchitectureART ArchitectureART ArchitectureART ArchitectureART Architecture ART Architecture Ƚϲźſ Ƚϲ ʶ ϵͳλ ARTijʼ ARTʵ ARTʵȽ Ƚ   ѵ ѵ ѵ ѵ ѵ ѵ ѵ ѵѵART ImplementationART ImplementationART ImplementationART AlgorithmART AlgorithmART AlgorithmART AlgorithmART2 ART2ART2ART2ART2ART2 ART2ART2ART2 YZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4GdGdFЖF0Jppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =B;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR8 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddee  >0 (  ~  s *L( M }     s *( ; `<$ 0  ,dH  0޽h ? 33  ___PPT10l .+2D ' != @B D ' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*U%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*UD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*UD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*U%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*UD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*U+8+0+0 +m d0 / (   ~  s *Z( M }  p   s *;N( ; `<$ 0 p ,dH  0޽h ? 33___PPT10.+2D' 2N= @B DP' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Q%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* QD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* QD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Qg%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* QgD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* QgD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* g%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* gD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* gD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +8+0+ 0 +m e0 / (   ~  s *( M }     s *d. ( ; `<$ 0  ,dH  0޽h ? 33___PPT10.+2D' = @B DP' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* !%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* !D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* !D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* !3%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* !3D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* !3D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 3J%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 3JD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 3JD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* JX%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* JXD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* JXD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* Xs%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* XsD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Xs+8+0+ 0 +0 / ((   ^  S    p  c $IN @  p  H  0޽h ? ̙3380___PPT10.ޒH0 / ((   ^  S      c $8 @    H  0޽h ? ̙3380___PPT10.ޒHr$Đ՟b@6G# e  ( :  iEquation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0BA.ART Architecture (4/20)NC:490,9,ART Architecture (6/18)DDEquation Equation.30(Microsoft e z_}/hV 3.0EEEquation Equation.30,Microsoft Equation 3.0FFEquation Equation.30,Microsoft Equation 3.0GGEquation Equation.DSMT40*MathType 4.0 EquationHHEquation Equation.30,Microsoft Equation 3.0IIEquation Equation.30,Microsoft Equation 3.0JJEquation Equation.30,Microsoft Equation 3.0KKEquation Equation.30,Microsoft Equation 3.0LLEquation Equation.DSMT40*MathType 4.0 EquationMMEquation Equation.30,Microsoft Equation 3.0NNEquation Equation.30,Microsoft Equation 3.0OOEquation Equation.30,Microsoft Equation 3.0PPEquation Equation.30,Microsoft Equation 3.04/ 0XDTimes New Roman00sF0D[SOes New Roman00sF0 DArialNew Roman00sF0"0DWingdingsRoman00sF0@DFranklin Gothic MediumF0"PDNSeeOlin Gothic MediumF0`DfNOlin Gothic MediumF01pDN[_GB2312othic MediumF01DwiSO_GB2312othic MediumF01DNSeLwi2312othic MediumF0DTahoma12othic MediumF0"DўSOoma12othic MediumF01DSymbol12othic MediumF0DPMingLiUothic MediumF0DArial Unicode MSediumF0"DMS Minchoode MSediumF01DGungsuhoode MSediumF0DImpactoode MSediumF0"fB3x(.U  @n?" dd@  @@`` 11 2b= <.=  .;CDDIIX(((F D67  :":AD + 2 b 0 4U %W>@ B%CDEWFGHIJKLMNOPQRSTUVWXYZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$2$D纉ﵯjI2$)yNv$02$fUH)E_Z2$Ɩ2L]nE2$2_-&H 2$!`c&܏_Cԯ'2$̀H=2>-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4GdGdFЖF0Jppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =B;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR8 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddeer;I# Le  ( :  iEquation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0BA.ART Architecture (4/20)NC:490,9,ART Architecture (6/18)DDEquation Equation.30(Microsoft e z_}/hV 3.0EEEquation Equation.30,Microsoft Equation 3.0FFEquation Equation.30,Microsoft Equation 3.0GGEquation Equation.DSMT40*MathType 4.0 EquationHHEquation Equation.30,Microsoft Equation 3.0IIEquation Equation.30,Microsoft Equation 3.0JJEquation Equation.30,Microsoft Equation 3.0KKEquation Equation.30,Microsoft Equation 3.0LLEquation Equation.DSMT40*MathType 4.0 EquationMMEquation Equation.30,Microsoft Equation 3.0NNEquation Equation.30,Microsoft Equation 3.0OOEquation Equation.30,Microsoft Equation 3.0PPEquation Equation.30,Microsoft Equation 3.04/ 0XDTimes New Roman00sF0D[SOes New Roman00sF0 DArialNew Roman00sF0"0DWingdingsRoman00sF0@DFranklin Gothic MediumF0"PDNSeeOlin Gothic MediumF0`DfNOlin Gothic MediumF01pDN[_GB2312othic MediumF01DwiSO_GB2312othic MediumF01DNSeLwi2312othic MediumF0DTahoma12othic MediumF0"DўSOoma12othic MediumF01DSymbol12othic MediumF0DPMingLiUothic MediumF0DArial Unicode MSediumF0"DMS Minchoode MSediumF01DGungsuhoode MSediumF0DImpactoode MSediumF0"fB3x(.U  @n?" dd@  @@`` 11 2b= <.=  .;CDDIIX(((F D67  :":AD + 2 b 0 4U %W>@Root EntrydO) a@PicturesCurrent UserASummaryInformation(ȩ B%CDEWFGHIJKLMNOPQRSTUVWXYZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4GdGdFЖF0Jppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =B;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR8 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddeerI# \e  ( :  iEquation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0BA.ART Architecture (4/20)NC:490,9,ART Architecture (6/18)DDEquation Equation.30(Microsoft e z_}/hV 3.0EEEquation Equation.30,Microsoft Equation 3.0FFEquation Equation.30,Microsoft Equation 3.0GGEquation Equation.DSMT40*MathType 4.0 EquationHHEquation Equation.30,Microsoft Equation 3.0IIEquation Equation.30,Microsoft Equation 3.0JJEquation Equation.30,Microsoft Equation 3.0KKEquation Equation.30,Microsoft Equation 3.0LLEquation Equation.DSMT40*MathType 4.0 EquationMMEquation Equation.30,Microsoft Equation 3.0NNEquation Equation.30,Microsoft Equation 3.0OOEquation Equation.30,Microsoft Equation 3.0PPEquation Equation.30,Microsoft Equation 3.04/ 0XDTimes New Roman00sF0D[SOes New Roman00sF0 DArialNew Roman00sF0"0DWingdingsRoman00sF0@DFranklin Gothic MediumF0"PDNSeeOlin Gothic MediumF0`DfNOlin Gothic MediumF01pDN[_GB2312othic MediumF01DwiSO_GB2312othic MediumF01DNSeLwi2312othic Medium6F0DTahoma12othic MediumF0"DўSOoma12othic MediumF01DSymbol12othic MediumF0DPMingLiUothic MediumF0DArial Unicode MSediumF0"DMS Minchoode MSediumF01DGungsuhoode MSediumF0DImpactoode MSediumF0"fB3x(.U  @n?" dd@  @@`` 11 2b= <.=  .;CDDIIX(((F D67  :":AD + 2 b 0 4U %W>@ B%CDEWFGHIJKLMNOPQRSTUVWXYZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4GdGdFЖF0Jppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =B;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR8 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddeerI#  e ( :  Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~ Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0BA.ART Architecture (4/20)NC:490,9,ART Architecture (6/18)DDEquation Equation.30(Microsoft e z_}/hV 3.0EEEquation Equation.30,Microsoft Equation 3.0FFEquation Equation.30,Microsoft Equation 3.0GGEquation Equation.DSMT40*MathType 4.0 EquationHHEquation Equation.30,Microsoft Equation 3.0IIEquation Equation.30,Microsoft Equation 3.0JJEquation Equation.30,Microsoft Equation 3.0KKEquation Equation.30,Microsoft Equation 3.0LLEquation Equation.DSMT40*MathType 4.0 EquationMMEquation Equation.30,Microsoft Equation 3.0NNEquation Equation.30,Microsoft Equation 3.0OOEquation Equation.30,Microsoft Equation 3.0PPEquation Equation.30,Microsoft Equation 3.04/ 0XDTimes New Roman00@ B%CDEWFGHIJKLMNOPQRSTUVWXYZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4AdAdF1ЖF0ppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =@;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR6 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i                          ! " # $ % & ' ( ) * + 6 . Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddee >0 \(  ~  s *( M }     s *( ; `  ,dH  0޽h ? 33___PPT10e.+D=' {= @B + d0 / \(   ~  s *X {( M }  {   s *1( ; ` { ,dH  0޽h ? 33___PPT10e.+D=' {= @B + e0 / \(   ~  s *$L{( M }  {   s *S{( ; ` { ,dH  0޽h ? 33___PPT10e.+D=' {= @B +/ C0N0 ..PVV_.(  x  c $*7( #   ` &$"7 # #" T 62  "X + +62  "X / 062  "X 4 t56  "*0+6  "/006   "4056   "4 56   "/ 06   "* +\B   S D" c+c+\B  S D" #5#5\B  S D" C0C0\B  S D"0c+c+\B  S D"0#5#5\B  S D"0C0C0\B  S D" 04\B  S D" c+4\B  S D" +0\B  S D" +#5\B  S D" 0#5\B  S D" c+/\B  S D"0c+/\B  S D"0c+4\B  S D"0+/\B  S D"0+#5\B  S D"004\B  S D"00#5\B  S D"+-\B   S D"|+|-\B ! S D"|0|2\B " S D"02\B # S D"57\B $ S D"|5|7\B % S D"57\B & S D"T5T7\B ' S D"02\B ( S D"T0T2\B ) S D"+-\B * S D"T+T-VB + C D" c+ c+VB , C D" C0p!C0VB - C D" #5$"#5VB . C D" ( c+VB /B C D" ( (VB 0 C D"p!'p!C0VB 1 C D"$"&$"#5VB 2B C D"< 'p!'VB 3B C D"&$"&VB 4 C D" ( c+VB 5 C D"< '< C0VB 6 C D"&#5\B 7 S D"#5X #5\B 8 S D"< C0X C0\B 9 S D" c+X c+F 00F@ : 0@ ; N@D7 ?"00B* ^rm&  < N,J7 ?"P? Dr2&  = NN7 ?" Dr1&  > NL7 ?"#660 DT1&  ? N({ ?"@@A : Dp1&  @ N${ ?" @o : Dc1&  A N{ ?"f` 5T B Nl7 ?" p j 5B C N<{ ?"0@C: DB1&  D N{ ?"0 P J `x1G1@   E N{ ?".+/ %  Dp2&  F ND ?" @ :  Dc2&  G N@ ?"p  e  ^cn&  H N ?"@ G  ^pn&  I N\ ?"`  f YMO G2&  J Np ?"`T N  f YMO G2&  K N@ ?"#6  DT2&  L N ?"0 f  DTm&  M N ?"< r  ^Bm&  N NH% ?" @:  DB2&  O NX+ ?"  `XnG1@   P N/ ?" 6 0  ax2 G1@   Q NX7 ?"`z f YMO G2&  R N; ?"" 6  6&  S NX? ?"B V  6&  T NTC ?"2 F  6&  U NtA ?"F@ NƋ+RB\  V N(K ?"0 @ : NkB\ H  0޽h ? 33y___PPT10Y+D=' {= @B + 0  .\ Z(  \  \  0~( ip    \ c $( u  * @`H \ 0޽h ? fDW&cC3___PPT10e.+D=' {= @B +r,  # D+ @ [ b % ( L#  ] e ( :  Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0Equation Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0t Equation.30 Microsoft lQ_ 3.0BA.ART Architecture (4/20)NC:490,9,ART Architecture (6/18)DDEquation Equation.30(Microsoft e z_}/hV 3.0EEEquation Equation.30,Microsoft Equation 3.0FFEquation Equation.30,Microsoft Equation 3.0GGEquation Equation.DSMT40*MathType 4.0 EquationHHEquation Equation.30,Microsoft Equation 3.0IIEquation Equation.30,Microsoft Equation 3.0JJEquation Equation.30,Microsoft Equation 3.0KKEquation Equation.30,Microsoft Equation 3.0LLEquation Equation.DSMT40*MathType 4.0 EquationMMEquation Equation.30,Microsoft Equation 3.0NNEquation Equation.30,Microsoft Equation 3.0OOEquation Equation.30,Microsoft Equation 3.0PPEquation Equation.30,Microsoft Equation 3.04/ 0XDTimes New Roman00@ B%CDEWFGHIJKLMNOPQRSTUVWXYZ[\]^_`     b$9oX-ݴAy-hb$E|&I$/_ "-hb$L{O᪯7kFJ98R$@eC:}a0e@B)uɝR$eIf18͸3a >z2$?BsNA5IL)<2$&*3bO\CUF7r2$ٔE,2{e2$sApjH 2$ˣ rM鯊cL#Žb$۫*mZ0e|(PS2$ g[Զ$Ng52$=D.?%K`2$2nf2$tc;&] m2$AIHO4|r V!*2$5o:藉k2$zx-mK2$Zi&s<*02$]5l"/悿c-sP 0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 3&Y@89:EN ʚ;.b8ʚ;g4AdAdF1ЖF0ppp@ <4!d!d@00r<4dddd@00r ___PPT10D[SOes New Roman00TF0TDTimes New Roman00TF0T pp&___PPT9CoV ppswy<z<? +O =@;h ^y~Oo`f[ (&6( C v U_.g633Aj1 ARTv~g 2 ARTvRYS 3 ARTv[s Ƌ+R0k 0g~b 0~ 4 ART2  AAAAAAa A a a Aa F E^/ct,g0A^qQ/ctART(Adaptive Resonance Theory)!jW/fVBoston'Yf[vSGrossbergTACarpenet(W1976t^cQv0 ART/fNy~~^y~Q~~g /feYe^vf[`NQ~0S_(W^y~Q~TsX gNN\O(ue [sXOo`vxOS0W(W^y~Q-NNu R:N^y~Q~(WۏL~~;mR0ART1\/fُ7hNy~~0WNu[sXƋxv^y~Q~t!jW0Q~vSQX'`v4yR6 c C  K'b^/ct,g0AGrossbergNv[N{|v_tTƋ;mRatQ NgW4YNُebvxvzv^ ^g(upef[eg;RRN{|ُy;mR ^zN{|v_tTw;mRvNy~Nvpef[!jWTt0 ART!jW/fWN NRvBl cQv 1[NN*Nf[`N|~ Bl[ g^'`S3z['` ^'`SNT^͑NN 3z['`SNX[P͑NN0ُy|~v0 2f[`Ne S gvOo`TeOo`YUOYt OYu g(uwƋ c~ewƋvsQ|YUOS㉳Qv0 3[YLuOo`NSX[PvOo`~Tv^QV{v0<gZZQ\ I9,c^/ct,g0AARTt]cQN Ny!jW~g sSARTt ART2 ART30 ART1(uNYtNۏ6ReQvOo` ART2(uNYtNۏ6RT!jbOo`ُ$NyN ART3(uNۏLR~d"}0 ARTtSN(uN0Ɖɉ0UɉTW[&{Ƌ+RI{W0 !Rs GART;`SO~gV . g0A H ARTv~gg0X=(x1 x2 & xn) R=(r1 r2 & rm) C=(c1 c2 & cn) P=(p1 p2 & pn) Ti=(ti1 ti 2 & ti n) Bi=(b1i b2i & bni)RAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAAIAAAAIAIAIAAIAAAAIAIAIAAIAAAAIAn  I ARTv~g g0tijh:yƋ+RB\v,{i*N^y~CQ0RkB\v,{j*N^y~CQvTcCg bijh:ykB\v,{i*N^y~CQ0RƋ+RB\v,{j*N^y~CQvTcCg pi:NkB\v,{i*N^y~CQvQ~eQ$QZAIAA AA AAIAA AA AAIAA A     JkB\TƋ+RB\g0 >jART Architecture"!  Functions of each models: Comparison layer: -accept binary input X -initially pass X to C . So C = X -binary vector R is produced from recognition layer to modify C C1  ?kART Architecture"!   @lART Architecture"!   -each neuron in the comparison layer has 3 inputs: X: input vector Pj: weighted sum of recognition layer output Gain 1: same signal to all neurons -use  two-third rule => at least two of a neuron s three inputs must be one, otherwise, the output is zero. -initially, Gain 1 is set to one and R are set to 0.OZ8 )BR"&J   AmART Architecture"!  Recognition layer: -compute dot product of B and C -the neuron with largest output wins -the winning neuron is set to one others are set to zero. Gain 2 -OR of components of X "  &Y"f  BnART Architecture "!   CoART Architecture "!  Gain 1 OR of X components G2 OR of R G1 ---------------------------------------------------- 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 h "  " g                KkB\QOSc6R . g0A BG1= %(r1("r2("& ("rm) '" (x1("x2("& ("xn) ~"AAAIAAIAAAAIAAAIAAIAAAAIA, LkB\ ,g0AfgbL2/3ĉR ci= 1 xi+pi+G1e"2 ci= 0 xi+pi+G1< 2b(AAAIAAAIAIAAAIAAAIAIAA@MƋ+RB\ ,g0A,Ƌ+RB\[szN:g6R BkNC gg'Yvpy lZ ` AIAAA.  N|~ YMOc6R ,g0AXNCvv0.5e bRN11\ Nn|^Bl dkeQ~1\ۏeQg~b]\O6k 10 RN1܀ 20CS @bN[Q~ۏL~T2=C0 >f6q vQSQ~vR{|v^ N/fNb NSv ~~O(u NbOP[-NveQTϑ SL=6 RYSOBv@b gCQ }GWSZAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAA AAIAAIAIAAA     e~2g0g0f50Q~ۏeQ~T20B2O9e T2=1 0 0 1 0 B2=6/7 0 0 6/7 0 60S_Q!keQX2e RN1 0RN2@b_vQ~eQR+R:N1T12/7 ُQ!k[RN2oS0FO/f dkeƋ+RB\~kB\vT2=1 0 0 1 0 0N gs=2/3 Yg|~v YMOc6RSpe>2/3 dke|~O͑e:NX3 bN*Nev^y~CQ T"ZZZAAIAAIAAIAAAAAAAAAAAAAIAAAAAAAAAAAAAAIAAIAAAI AAAAAAIAAIAAAAAAAAAAAAA AA AAI A0   QpART Implementation  8Initialization Tj, Bj, Vigilance level r Bj: 0< bij < L/(L-1+m) for all i, j m: # of components in the input vector L: as constant > 1 (L=2, typically) all bij are the same value Tj: tij=1 for all i, j : 0<<1 coarse distinction at first, fine distinction at last.  " Z    ##+# # ######'######+##+##+ ####  #  =#        n      W RqART Implementation  2. Recognition NETj = (BjC) OUTj=1 NETj>T 0 otherwise 3. Comparison Q           t        & SrART Implementation  '5. Training If the input X is matched,B(Z      ( Ts ART Algorithm  :Initialization L > 1, 0<<1 0< bij < L/(L-1+m) for all i, j tij=1 for all i, j 2. While stopping condition is false, do 3-12: 3. For each training pattern(X), do 4-11: 4. Set R = 0, C = X 5. For each node in recognition layer that is not inhibited (r-1):HV " ZZc ccckc c cccckc ccccc.ccccccc""""L" "@"     Ut ART Algorithm   6. If rj -1, rj = (BjC) 7. While Reset is true 8. Find winning neuron j, If rj -1 then this pattern cannot be clustered. 9. Let P =TJ, compute C PZcc"ckc ckcc    :  c"ckc  1                     t       F  h Vu ART Algorithm   10., c   Wv ART Algorithm   XwART2   4Several sublayers replace F1 layer Update functions:,5 " Z# &   $ YxART2   ZyART2  fParameters(continue): a, b: fixed weight in F1, cannot be zero. c: fixed weight used in testing for Reset, 0<c<1. d: output activation of F2, e: a small parameter to prevent division by zero when norm of a vector is zero. q : noise suppression parameter a: learning rate r: vigilance level4 " Z '  5    V  0    4 [zART2  8Algorithm: a. Initialization: a, b, c, d, e, q, a, r b. perform # of epochs of training c. For each input pattern, S, do d. to m. d. update F1 "     Z  !    \{ART2   d. update F1 again&    ]|ART2   g f. While Reset is true, do g. to h. g. Find winning neuron J in F2 h. Check for Reset:RhZ ?  $   h ^}ART2   i) If ||R|| < r - e, then yJ = -1 (inhibit J) Reset is true; repeat f. ii) If ||R|| >= r - e, then          9      &(  f _~ART2  [ i. Do j. to l. for # of learning iterations. j. update weight for neuron J `\  I     \ `ART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k aART2   j l. Test stopping condition for weight updates. m. Test stopping condition for # of epochs.$kj   k /<>@ABCDEFG H!I"J#K$L%M&N'O(P)Q*R+S,T-U.V/W0X1Y2Z3[4\5]6^<bddee B0 @(  ~  s *( M }   ~  s *( ; `C   b  c &AS ??   H  0޽h ? 33___PPT10e.+D=' ~= @B +r^ *m J# ] -p e       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()89:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~   8       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~ART2  õʾĸģǶ OLE  õƬ;0 8@ _PID_HLINKSA 618,10,ART Architecture (4/20)490,9,ART Architecture (6/18)#_Ep shizhongzhishizhongzhi