SMO算法伪代码Word文档下载推荐.docx

1、% PLATT, J.C. （1998）.% Fast training of support vector machines using sequential minimal% optimization. In Schlkopf, B., Burges, C., and Smola, A.J., editors,% Advances in Kernel Methods: Support Vector Learning, chapter12, % pages 185-208. MIT Press, Cambridge, Massachusetts.% History : May 15/2001

2、 - v1.00if size（Y, 2） = 1 | isreal（Y）error（y must be a real double precision column vector）;endn = size（Y, 1）;if n = size（X, 1）x and y must have the same number of rowsif （nargin7） % check correct number of argumentshelp svcreturn;end;if nargin = 4 & isa（C, svc）net = C;C = get（net,Ckernel = get（net,

3、kernelelseif nargin 4, C = Inf; end; 5, kernel = linear;NOBIAS = 0;switch nargincase 5if ischar（kernel） & strcmp（kernel,NOBIAS = 1;case 6if ischar（alpha_init） & strcmp（alpha_init,） case 7if ischar（bias_init） & strcmp（bias_init,if nargin = 7if n = size（alpha_init, 1）alpha must be a real double precis

4、ion column vector with the same size as yif any（alpha_init 0） | examineAllif examineAll%Loop sobre todos los puntosfor i = 1:ntpnumChanged = numChanged + examineExample（i）;%Loop sobre KKT points%Solo los puntos que violan las condiciones KKTif （SMO.alpha（i）SMO.epsilon） & （SMO.alpha（i）（SMO.C-SMO.epsi

5、lon）if （examineAll = 1）examineAll = 0;elseif （numChanged = 0）examineAll = 1;epoch = epoch+1;% trerror = 1; %100*sum（error）0: %d, 0alphaSMO.epsilon）;function RESULT = nonBoundLagrangeMultipliers;RESULT = sum（SMO.alpha （SMO.alpha SMO.epsilon） & （alpha2 （SMO.C-SMO.epsilon）e2 = SMO.error（i2）;e2 = fwd（i2

6、） - y2;% r2 0. r2 = f2*y2-1r2 = e2*y2;%KKT conditions:% r20 and alpha2=0 （well classified）% r2=0 and 0alpha2C （support vectors at margins）% r20 and alpha2=C （support vectors between margins）% Test the KKT conditions for the current i2 point. % If a point is well classified its alpha must be 0 or if%

7、 it is out of its margin its alpha must be C. If it is at margin% its alpha must be between 0C.%take action only if i2 violates Karush-Kuhn-Tucker conditionsif （r2 SMO.tolerance） & （alpha2 SMO.epsilon）% If it doenst violate KKT conditions then exit, otherwise continue.%Try i2 by three ways; if succe

8、ssful, then immediately return 1;RESULT = 1;% First the routine tries to find an i1 lagrange multiplier that% maximizes the measure |E1-E2|. As large this value is as bigger % the dual objective function becames.% In this first test, only support vectors will be tested.POS = find（SMO.alpha （SMO.alph

9、a （SMO.alpha（i1） %no progress possibleRESULT = 0;function RESULT = takeStep（i1, i2, e2）% for a pair of alpha indexes, verify if it is possible to execute% the optimisation described by Platt.if （i1 = i2）, return;% compute upper and lower constraints, L and H, on multiplier a2alpha1 = SMO.alpha（i1）;

10、alpha2 = SMO.alpha（i2）;x1 = SMO.x（i1）; x2 = SMO.x（i2）;y1 = SMO.y（i1）;C = SMO.C; K = SMO.Kcache;s = y1*y2;if （y1 = y2）L = max（0, alpha2-alpha1）; H = min（C, alpha2-alpha1+C）;L = max（0, alpha1+alpha2-C）; H = min（C, alpha1+alpha2）;if （L = H）, return;if （alpha1 （alpha1 % e2 = SMO.error（i2）;%else% e2 = fw

11、d（i2） - y2;%end;%compute etak11 = K（i1,i1）; k12 = K（i1,i2）; k22 = K（i2,i2）;eta = 2.0*k12-k11-k22;%recompute Lagrange multiplier for pattern i2if （eta 0.0）a2 = alpha2 - y2*（e1 - e2）/eta;%constrain a2 to lie between L and Hif （a2 H）a2 = H;%When eta is not negative, the objective function W should be%e

12、valuated at each end of the line segment. Only those terms in the%objective function that depend on alpha2 need be evaluated. ind = find（SMO.alpha0）;aa2 = L; aa1 = alpha1 + s*（alpha2-aa2）;Lobj = aa1 + aa2 + sum（-y1*aa1/2）.*SMO.y（ind）.*K（ind,i1） + （-y2*aa2/2）.*SMO.y（ind）.*K（ind,i2）;aa2 = H;Hobj = aa1

13、 + aa2 + sum（-y1*aa1/2）.*SMO.y（ind）.*K（ind,i1） + （-y2*aa2/2）.*SMO.y（ind）.*K（ind,i2）;if （LobjHobj+SMO.epsilon）elseif （LobjHobj-SMO.epsilon）a2 = alpha2;if （abs（a2-alpha2） （a1 （a2SMO.bias = b2;SMO.bias = （b1 + b2）/2;% update error cache using new Lagrange multipliersSMO.error = SMO.error + w1*K（:,i1） + w2*K（:,i2） + bold - SMO.bias;SMO.error（i1） = 0.0; SMO.error（i2） = 0.0;% update vector of Lagrange multipliersSMO.alpha（i1） = a1; SMO