Langrangian SVM的使用~·

转自：http://bbs.sciencenet.cn/forum.php?mod=viewthread&tid=523129

 http://research.cs.wisc.edu/dmi/lsvm/

function [iter, optCond, time, w, gamma] = lsvm(A,D,nu,tol,maxIter,alpha,
...
       perturb,normalize);
% LSVM Langrangian Support Vector Machine algorithm
%   LSVM solves a support vector machine problem using an iterative
%   algorithm inspired by an augmented Lagrangian formulation.
%
%   iters = lsvm(A,D)
%
%   where A is the data matrix, D is a diagonal matrix of 1s and -1s
%   indicating which class the points are in, and 'iters' is the number
%   of iterations the algorithm used.
%
%   All the following additional arguments are optional:
%
%   [iters, optCond, time, w, gamma] = ...
%     lsvm(A,D,nu,tol,maxIter,alpha,perturb,normalize)
%
%   optCond is the value of the optimality condition at termination.
%   time is the amount of time the algorithm took to terminate.
%   w is the vector of coefficients for the separating hyperplane.
%   gamma is the threshold scalar for the separating hyperplane.
%
%   On the right hand side, A and D are required. If the rest are not
%   specified, the following defaults will be used:
%     nu = 1/size(A,1), tol = 1e-5, maxIter = 100, alpha = 1.9/nu,
%       perturb = 0, normalize = 0
%
%   perturb indicates that all the data should be perturbed by a random
%   amount between 0 and the value given. perturb is recommended only
%   for highly degenerate cases such as the exclusive or.
%
%   normalize should be set to 1 if the data should be normalized before
%   training.
%
%   The value -1 can be used for any of the entries (except A and D) to
%   specify that default values should be used.
%
%   Copyright (C) 2000 Olvi L. Mangasarian and David R. Musicant.
%   Version 1.0 Beta 1
%   This software is free for academic and research use only.
%   For commercial use, contact [email protected].

  % If D is a vector, convert it to a diagonal matrix.
  [k,n] = size(D);
  if k==1 | n==1
    D=diag(D);
  end;

  % Check all components of D and verify that they are +-1
  checkall = diag(D)==1 | diag(D)==-1;
  if any(checkall==0)
    error('Error in D: classes must be all 1 or -1.');
  end;

  m = size(A,1);

  if ~exist('nu') | nu==-1
    nu = 1/m;
  end;
  if ~exist('tol') | tol==-1
    tol = 1e-5;
  end;
  if ~exist('maxIter') | maxIter==-1
    maxIter = 100;
  end;
  if ~exist('alpha') | alpha==-1
    alpha = 1.9/nu;
  end;
  if ~exist('normalize') | normalize==-1
    normalize = 0;
  end;
  if ~exist('perturb') | perturb==-1
    perturb = 0;
  end;
  
  % Do a sanity check on alpha
  if alpha > 2/nu,
    disp(sprintf('Alpha is larger than 2/nu. Algorithm may not converge.'));
  end;

  % Perturb if appropriate
  rand('seed',22);
  if perturb,
    A = A + rand(size(A))*perturb;
  end;
  
  % Normalize if appropriate
  if normalize,
    avg = mean(A);
    dev = std(A);
    if (isempty(find(dev==0)))
      A = (A - avg(ones(m,1), : ) )./dev(ones(m,1), : ) ;
    else
      warning('Could not normalize matrix: at least one column is constant.')
;
    end;
  end;
  
  % Create matrix H
  [m,n] = size(A);
  e = ones(m,1);
  H = D*[A -e];
  iter = 0;
  time = cputime;
  
  % "K" is an intermediate matrix used often in SMW calclulations
  K = H*inv((speye(n+1)/nu+H'*H));
  
  % Choose initial value for x
  x = nu*(1-K*(H'*e));
  
  % y is the old value for x, used to check for termination
  y = x + 1;
  
  while iter < maxIter & norm(y-x)>tol
    % Intermediate calculation which is used twice
    z = (1+pl(((x/nu+H*(H'*x))-alpha*x)-1));
    y = x;
    % Calculate new value of x
    x=nu*(z-K*(H'*z));
    iter = iter + 1;
  end;
  
  % Determine outputs
  time = cputime - time;
  optCond = norm(x-y);
  w = A'*D*x;
  gamma = -e'*D*x;
  disp(sprintf('Running time (CPU secs) = %g',time));
  disp(sprintf('Number of iterations = %d',iter));
  disp(sprintf('Training accuracy = %g',sum(D*(A*w-gamma)>0)/m));
  
  return;
  
function pl = pl(x);
  %PLUS function : max{x,0}
  pl = (x+abs(x))/2;
  return;
  
举例：A =

    41   250
    42   238
    26   196
    63   368
    45   350
    55   316
    57   400
    66   402
    64   424
    38   254
    40   350
    54   318
    55   348
    54   362
    59   428
    74   452
    63   468
    70   484
    56   366
    38   238
    45   328
    61   418
    91   576
    61   346
    66   462
    50   292
    63   430
    51   350
    24   170
    64   410
    64   410
    53   342
    43   270
    79   602
    44   332
    79   536
    58   392
    68   392
    18   104
    64   434
    59   390
    40   246
    40   228
    43   364
    89   602
    23   146
    47   308
    76   492
    52   348
    89   520
    76   596
    77   576
    81   624
    74   580
    70   482
    70   576
    76   616
    52   354
    42   272
    81   634
    56   446
   102   696
    86   584
    88   694
   109   826
    57   468
    61   614
    61   532
    61   430
   101   796
    96   850
    64   526
    94   798
    51   342
    61   538
    68   586
    84   710
   127   974
    93   700
    94   730
    90   680
    66   558
    66   598
    85   748
   102   732
    94   886
    83   730
    89   658
    79   556
    66   536
    83   740
    90   816
    97   756
    80   742
    76   676
   116   952
    86   768
    64   468
    89   668
    73   724

D =

     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
    -1
>> [iter, optCond, time, w, gamma] = lsvm(A,d,nu,tol,maxIter,alpha, perturb,normalize)

;
Running time (CPU secs) = 0
Number of iterations = 70
Training accuracy = 0.83
>> w

w =

    0.0993
   -0.0140

>> x=[1:140];
>> y=(0.0993.*x - gamma)./0.0140;
>> plot(X(1:50),Y(1:50),'ob')
>> hold on
>> plot(X(51:100),Y(51:100),'or')
>> plot(x,y,'k')