SVM Support Vector Machine (2) simplified SMO algorithm for machine learning algorithm python implementation

1. Background knowledge

In the last section, we introduce the Lagrange boarding to obtain the support vector machine deformation formula. Detailed reform can refer to the Great God's blog-address

Reference to Lagrange formula F (x1,x2,... λ) =f (x1,x2,...) -λg (x1,x2 ...). We have transformed the above formula to:

The constraint becomes:

The following is based on the minimal optimization algorithm SMO (sequential minimal optimization). Find the nearest point of the distance divider, which is the support vector set. Shown in the blue dots of the following figure.

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2. Code

Import Matplotlib.pyplot as PLT from numpy Import * to time import sleep def loaddataset (fileName): DA Tamat = [];  
        Labelmat = [] fr = open (fileName) for line in Fr.readlines (): Linearr = Line.strip (). Split (' t ') Datamat.append ([Float (linearr[0]), float (linearr[1])]) labelmat.append (float (linearr[2))) return DA  
        Tamat,labelmat def selectjrand (i,m): j=i #we want to select any J. equal to I (j==i):  
    j = Int (Random.uniform (0,m)) return J def Clipalpha (aj,h,l): if aj > H:aj = H  
    If l > Aj:aj = l return AJ def smosimple (Datamatin, Classlabels, C, Toler, Maxiter): Datamatrix = Mat (Datamatin); Labelmat = Mat (Classlabels). Transpose () b = 0; M,n = shape (datamatrix) Alphas = Mat (Zeros ((m,1))) iter = 0 while (ITER < Maxiter): Alphapair  
          schanged = 0 for I in range (m):  FXi = float (multiply (alphas,labelmat). T* (Datamatrix*datamatrix[i,:]. T) + b Ei = Fxi-float (Labelmat[i]) #if checks if an example violates KKT conditions if (lab  
                Elmat[i]*ei <-toler) and (Alphas[i] < C)) or ((Labelmat[i]*ei > Toler) and (alphas[i) > 0)): j = Selectjrand (i,m) FXJ = float (multiply (alphas,labelmat). T* (Datamatrix*datamatrix[j,:]. T)) + b Ej = Fxj-float (labelmat[j]) Alphaiold = Alphas[i].copy ();  
                Alphajold = Alphas[j].copy (); if (Labelmat[i]!= labelmat[j]): L = max (0, Alphas[j]-alphas[i]) H = min (C,  
                    C + alphas[j]-alphas[i]) else:l = max (0, Alphas[j) + alphas[i]-C) H = min (C, alphas[j] + alphas[i]) # if L==h:print "L==h"; Continue ETA = 2.0 * datamatrix[i,:]*datamatrix[j,:]. T-datamatrix[i,:]*daTamatrix[i,:]. T-datamatrix[j,:]*datamatrix[j,:]. T if ETA >= 0:print "eta>=0";                  Continue alphas[j]-= labelmat[j]* (Ei-ej)/eta alphas[j] = Clipalpha (alphas[j],h,l) # if (ABS (Alphas[j]-Alphajold) < 0.00001): print "J not moving Enough";  
                                                                        Continue alphas[i] + = labelmat[j]*labelmat[i]* (Alphajold-alphas[j]) #update I by the same amount as J  
                #the update is in the oppostie direction B1 = b-ei-labelmat[i]* (Alphas[i]-alphaiold) *datamatrix[i,:]*datamatrix[i,:]. t-labelmat[j]* (Alphas[j]-alphajold) *datamatrix[i,:]*datamatrix[j,:]. T b2 = b-ej-labelmat[i]* (Alphas[i]-alphaiold) *datamatrix[i,:]*datamatrix[j,:]. t-labelmat[j]* (Alphas[j]-alphajold) *datamatrix[j,:]*datamatrix[j,:]. T if (0 < alphas[i]) and (C > Alphas[i]): b = B1 elif (0 < AlphaS[J]) and (C > Alphas[j]): b = B2 Else:b = (B1 + b2)/2.0 alphapairschanged = 1 # Print "ITER:%d i:%d, pairs changed%d"% (iter,i,alphapairschanged) if (alphapairschanged = 0):  
      
ITER + + 1 else:iter = 0 # print "Iteration number:%d"% iter return B,alphas def matplot (datamat,lablemat): Xcord1 = []; Ycord1 = [] Xcord2 = []; Ycord2 = [] Xcord3 = [];  
           Ycord3 = [] for I in range (MB): if Lablemat[i]==1:xcord1.append (datamat[i][0) Ycord1.append (Datamat[i][1]) else:xcord2.append (datamat[i][0]) ycord2.append (Datamat I  
             [1]) B,alphas=smosimple (datamat,labelmat,0.6,0.001,40) for J in Range (MB): if alphas[j]>0: Xcord3.append (Datamat[j][0]) ycord3.append (datamat[j][1]) FIG = plt.figure ( ) ax = Fig.add_subplot (111) ax.scatter (Xcord1, Ycord1, s=30, c= ' Red ', marker= ' s ') Ax.scatter (Xcord2, Ycord2, s=30, c= ' green ') ) Ax.scatter (Xcord3, Ycord3, s=80, c= ' Blue ') Ax.plot () Plt.xlabel (' X1 ');  
    Plt.ylabel (' X2 ');  
Plt.show () If __name__== ' __main__ ': Datamat,labelmat=loaddataset ('/users/hakuri/desktop/testset.txt ') # b,alphas=smosimple (datamat,labelmat,0.6,0.001,40) # print b,alphas[alphas>0] Matplot (datamat,l Abelmat)

Author: csdn Blog Rae Garvin