Dynamic Clustering Algorithm Based on Immune by xxk47264

VIEWS: 22 PAGES: 5

									       35           8                                                                                                                                         2009   4
    Vol.35        No.8                                      Computer Engineering                                                                               April 2009

    ·                  ·                                    1000       3428(2009)08 0040      04                                    A                                        TP18




                                                 (                                                        710048)




                                            k        n             k




          Dynamic Clustering Algorithm Based on Immune Evolutionary
                        Particle Swarm Optimization
                                                         WANG Lei, JI Huan, LIU Xiao-yong
                                 (School of Computer Science & Engineering, Xi’an University of Technology, Xi’an 710048)

     Abstract    The immune information evolutionary mechanism of artificial immune system is used into Particle Swarm Optimization(PSO)
 algorithm, a new clustering algorithm based on C-means and improved PSO is presented, it can avoid “early ripe” of PSO and traditional clustering
 algorithm. New algorithm chooses the suitable inertia weight for every swarm through the linearly decreasing weight policy, and uses the immune
 evolutionary principle to improve the process of PSO. According to the experiential rule k                          n of classical clustering theory and swarm
 performance cost function, the new swarm is generated above the best particle and then find the best k. Simulation experiments show that this
 method outperforms the classical clustering algorithm in convergence ability and it has the advantages of high accuracy of clustering and good
 clustering ability.
     Key words     immune evolutionary mechanism; Particle Swarm Optimization(PSO); linearly decreasing weight; dynamic clustering


1

                                                                   C-                                                          kmax          n (n                       )
(FCM)                                                                                                                                                          k
                                                                                                                                                              PSO
         [1]
                             FCM
                                                                                                                                                                         FCM


                                                                                 2       C-         (FCM)
                            (Particle Swarm Optimization, PSO)                                            RN               n                              X = {x1 , x2 ,         , xn }
                                                                                                                 /                                            k
                                                                                                                                    U = {uij | i = 1, 2,      , n, j = 1, 2,       , k}
                                                                                                          uij                   i                             j
                                                                                                                 {
                                                                                                            V = v j | v j ∈ R , j = 1, 2,
                                                                                                                                        p
                                                                                                                                                     ,k   }                 vj
                                                                                     j
                PSO                                                                                             U, V
                                                                                                                     2
                           PSO
                                                                                         uij = 1 ∑ ( dij dik )
                                                                                                    c               q −1
                                                                                                                               ∀i, j                                               (1)
                                                                                                   k =1



                                                                                                                                               (60603026)
(Immune Evolutionary Particle Swarm Optimization _ Dynamic                                                  (1972      )
Fuzzy C-Mean, IEPSO_DFCM)
                                                                                               2008-10-11                  E-mail           jihuihuan2002@163.com

    40
                     n
                          q
                    ∑ u ij xi                                                                                                                                         Si + S j
                                              ∀i                                                                                          Ri =        max                                                                                    (8)
        vj =        i =1
                       n
                                                                                                                     (2)                          j =1,2, ,k , j ≠i      dij
                                q
                     ∑ u ij
                     i =1
                                                                                                                                              d ij = ai − a j                              2                                      Ai
        FCM                                                    J(U,V)
                                                                                                                                      i           Ai                          i                                  ai                 i
                     J(U,V)
                                                                                                                                                                        Si = ( ∑ N − ai ) Ai                     ai
        J q (U , V ) = ∑ ∑ u ij q d 2 ij ( x i , v j )
                                     n    c
                                                                                                                     (3)                                                                  N∈Ai
                                    i =1 j =1


              d 2ij ( x i , v j ) =|| xi − v j || A2                                   Rp
                                                                                                                                                                                                 f ( x)
                            xi                            vj                                       Euclidean

                                                                                                                                3.3
3                                                                                                                                                                                                                             c
3.1
                                                                                                       [2]
                                                                ——                                                                                                                                        g(x)
                                                                                                                    PSO                                k                          k
                                                                                                                                          g ( x) = ∑ si − s + ∑ ∑ N − si                                                                     (9)
                                                                                                                                                      i =1                    i =1 N∈Ai

                                                      2                                                                                                                                                     n                            s
                                                                             Pbest                                                                               si                   Ai                         N
                                                                Gbest                                                                     g(x)
                                         D                                                             m
                                                                     i
Xi=(xi1,xi2, ,xid)     i                                                                                                                  Step1                                   k= n                                            [4]
                                                                                                                                                                                                                                        M0
Vi=(vi1,vi2, ,vid) Pid                                    i                                                Gd                             Step2                   k
     Pi(i=1,2, ,m)                                                                                                                                                                               (                            )
                                                                                                                                          Step3 k = k − 1
                                                                                                                                          Step4                                       k
        vid (t + 1) = ωvid + c1r1 (t )( pid (t ) − xid (t )) + c2 r2 (t )( g d (t ) − xid (t )) (4)
        xid (t + 1) = xid (t ) + vid (t + 1)                       1     i      n, 1         d         D              (5)
              c1           c2                                                                      c1 = c2          r1 (t )               Step5
    r2 (t )         [0, 1]                                     ω         0                                                ω                                                           Step2
                                                          ω
                            ω
                                                                                                                                                                                             k
                                                                                      [3]                                       3.4
    (Linearly Decreasing Weight, LDW)
                                                                                                                                                  PSO
        wk = ( wini − wend )( K max − k ) / K max + wend                                                                  (6)
              k                                           Kmax                                          wini
                         wend                                                                                             w
                                                                         LDW                                                                                                                                                [5]




                                                                                                                                                                                                                          3

                                              PSO
3.2
    FCM                                                                                                                         3.4.1
IEPSO_DFCM
    D                                              N = { N i , i = 1, 2,       , n}            n                                                                                                                      IEPSO_DFCM
                                                                                                       k
                                                                                      xi = (ai1 , ai 2 ,        , aik )                                                                                               50%
              aij                        i                       j                                 i
                                                                                                                                                                                                                                   [6]
         j
                                                                                                                                                                  D                                                   m
                                                                                                                                           f ( xi )
                                                                                                                                                                       m
                  1 k                                                                                                                     P ( xi ) = f ( xi ) ∑ f ( x j )
        f ( x) = 1 ∑ Ri                                                                                                   (7)
                                                                                                                                                                       j =1
                                                                                                                                                                                                                                         (10)
                  k i=1

                                                                                                                                                                                                                                         41
                                                                                                                                                                                   k


3.4.2                                                                                                                                     Else                                             k+1
                                                                                                                                End If
                                                                                                                                If    (                                  min(g(x)k+1 )               )then
                                                            Pi                                                                                            M   2
                                                                                                                                                                                       m
                                                                                                                                k=k-1
                        f(xi)                                                                     Pi                            End If
                                                                                                                                t=t+1;
                                                           10−1
               ⎛ max ( f ( x ) ) − f ( xi ) ⎞
                                                                                                                                If    (                           ) then
          Pi = ⎜                            ⎟                                                                      (11)
                    max ( f ( x ) )
                                                                                                                                                                         k+1
               ⎜                            ⎟
               ⎝                            ⎠                                                                                   End If
                     xi = ( ai1 , ai 2 , , aik )                                       aij             i                        End
          j                               i                                    j                                                End
                                                                                                                          4
    Step1                                                                                                                 4.1
    Step2                                                            Pi
    Step3                                                                                                        [Umin,                          3
Umax]                                                                                                                                                (3.0, 7.0), (7.0, 3.0)            (7.0, 8.0)
                        aij                   xi                                                                          50                                        150
          aij ' = U min + r (U max − U min )                                                                      (12)                                                k = 150 ≈ 12
              r        [-1      1]                                                                                                                    m=100                                ωini = 0.8
3.4.3                                                                                                                                ωend = 0.3                            c1 = c2 = 2
                                                                                       (           )                      Dmax = 100
  (                      )                                                                                                                                                                 1~    3

                                                                   IEPSO_DFCM                                                                        1                         k       5, 4, 3




3.5      IEPSO-DFCM
        IEPSO-DFCM
      Procedure
      Begin
      Initialize                              n                           k=       n                             w ini
                            w end                      c 1 ,c2                          D max                     t=1
                       ε>0                                       M                           m    k=k-1
      While(                                               ||    ( min(J(t)) − min(J(t − 1))                   ε ) ) do
      Begin
                                                                          f(x)         /*                                                                   1      k=5
  (7)             */
                                                                               (IMS)
                                                                                                           (
      )
                   /*               (4)            (5)*/


  M1          /*                      (11)            (12)            */


  min(g(x) k )
                                                                     min(J(t))               /*
  (3)             */
                   If       ( ( min(J(t)) − min(J(t − 1)) < ε ) ) then
                  If    (                                             min(g(x) k+1 )               )then                                                    2      k=4

  42
                                                                                                                      2        IEPSO-DFCM                               FCM
                                                                                                                                                                                                       /(%)
                                                                                                                                    FCM                      3             87.526                81.6
                                                                                                            Wine
                                                                                                                              IEPSO-DFCM                     3             55.210                95.2
                                                                                                                                    FCM                      3            156.223                63.7
                                                                                                            Iris
                                                                                                                              IEPSO-DFCM                     3             78.941                81.1

                                                                                                                      3       IEPSO-DFCM
                                                                                                                                                                                                    /(%)
                                                                                                                                 PSO-FCM                         3       140                   93
                                                                                                            Wine
                                                                                                                               IEPSO-DFCM                        3       146                   97
                                                                                                                                 PSO-FCM                         3       101                   74
                                                                                                             Iris
                                                                                                                               IEPSO-DFCM                        3       133                   89


                                              3    k=3
                                                                                                      5

                                       1      k=5, 4, 3

           k
                                           (5.407 2,4.820 8), (8.016 8,8.025 0), (2.290 4,4.326 2),
       5                2.561 2
                                                     (3.657 1,8.675 1), (7.990 8,2.802 8)
                                           (7.142 0,3.405 5), (7.938 1,7.914 9), (2.964 4,4.580 6),
       4                2.085 5
                                                              (3.797 5,8.537 9)
       3                1.912 2            (6.627 4,3.296 9), (7.372 9,8.204 4), (2.991 9,6.524 0)




4.2
                              k
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                                    FCM                           3                                                           , 2003.
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