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<html><head> <meta HTTP-EQUIV="Content-Type" CONTENT="text/html;charset=ISO-8859-1"> <title>minball.m</title><link rel="stylesheet" type="text/css" href="../../m-syntax.css"></head><body><code><span class=defun_kw>function</span> <span class=defun_out>model </span>= <span class=defun_name>minball</span>(<span class=defun_in>X,options</span>)<br><span class=h1>% MINBALL Minimal enclosing ball in kernel feature space. </span><br><span class=help>%</span><br><span class=help>% <span class=help_field>Synopsis:</span></span><br><span class=help>% model = minball(X)</span><br><span class=help>% model = minball(X,options)</span><br><span class=help>%</span><br><span class=help>% <span class=help_field>Description:</span></span><br><span class=help>% It computes center and radius of the minimal ball</span><br><span class=help>% enclosing data X mapped into a feature space induced </span><br><span class=help>% by a given kernel. The problem leads to a QP problem which is </span><br><span class=help>% solve by 'quadprog' of the MATLAB Optimization toolbox.</span><br><span class=help>% </span><br><span class=help>% <span class=help_field>Input:</span></span><br><span class=help>% X [dim x num_data] Input data.</span><br><span class=help>% options [struct] Control parameters:</span><br><span class=help>% .ker [string] Kernel identifier (default 'linear'). See 'help kernel'.</span><br><span class=help>% .arg [1 x nargs] Kernel arguments.</span><br><span class=help>% .eps [1x1] Multipliers less then eps are set to zero (default 1e-12).</span><br><span class=help>% .mu [1x1] Regularization constant given to diagonal of the </span><br><span class=help>% kernel matrix (default 1e-12).</span><br><span class=help>%</span><br><span class=help>% <span class=help_field>Output:</span></span><br><span class=help>% model [struct] Center of the ball in the kernel feature space:</span><br><span class=help>% .sv.X [dim x nsv] Data determining the center.</span><br><span class=help>% .Alpha [nsv x 1] Data weights.</span><br><span class=help>% .r [1x1] Radius of the minimal enclosing ball.</span><br><span class=help>% .b [1x1] Squared norm of the center equal to Alpha'*K*Alpha.</span><br><span class=help>% .options [struct] Copy of used options.</span><br><span class=help>%</span><br><span class=help>% <span class=help_field>Example:</span></span><br><span class=help>% data = load('riply_trn');</span><br><span class=help>% options = struct('ker','linear','arg',1);</span><br><span class=help>% model = minball(data.X,options);</span><br><span class=help>% [Ax,Ay] = meshgrid(linspace(-5,5,100),linspace(-5,5,100));</span><br><span class=help>% dist = kdist([Ax(:)';Ay(:)'],model);</span><br><span class=help>% figure; hold on; </span><br><span class=help>% ppatterns(data.X); ppatterns(model.sv.X,'ro',12);</span><br><span class=help>% contour( Ax, Ay, reshape(dist,100,100),[model.r model.r]);</span><br><span class=help>%</span><br><span class=help>% See also </span><br><span class=help>% KDIST.</span><br><span class=help>%</span><br><hr><span class=help1>% <span class=help1_field>About:</span> Statistical Pattern Recognition Toolbox</span><br><span class=help1>% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac</span><br><span class=help1>% <a href="http://www.cvut.cz">Czech Technical University Prague</a></span><br><span class=help1>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a></span><br><span class=help1>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a></span><br><br><span class=help1>% <span class=help1_field>Modifications:</span></span><br><span class=help1>% 25-aug-2004, VF, added model.fun = 'kdist' and .diag_add changed to .mu </span><br><span class=help1>% 16-may-2004, VF</span><br><span class=help1>% 15-jun-2002, VF</span><br><br><hr><span class=comment>% process input arguments</span><br><span class=comment>%-----------------------------------------</span><br><span class=keyword>if</span> <span class=stack>nargin</span> < 2, options = []; <span class=keyword>else</span> options=c2s(options); <span class=keyword>end</span><br><span class=keyword>if</span> ~isfield(options,<span class=quotes>'ker'</span>), options.ker = <span class=quotes>'linear'</span>; <span class=keyword>end</span><br><span class=keyword>if</span> ~isfield(options,<span class=quotes>'arg'</span>), options.arg = 1; <span class=keyword>end</span><br><span class=keyword>if</span> ~isfield(options,<span class=quotes>'eps'</span>), options.eps = 1e-12; <span class=keyword>end</span><br><span class=keyword>if</span> ~isfield(options,<span class=quotes>'mu'</span>), options.mu = 1e-12; <span class=keyword>end</span><br>[dim,num_data] = size(X);<br><br><span class=comment>% kernel matrix with regularization</span><br><span class=comment>%-----------------------------------------</span><br>K = kernel( X, options.ker, options.arg )+...<br> eye(num_data,num_data)*options.mu;<br><br><span class=comment>% set up QP problem</span><br><span class=comment>%-----------------------------------------</span><br>f = -diag(K);<br><br>H=2*K;<br><br>Aeq = ones(1,num_data);<br>beq = 1;<br><br>LB = zeros(num_data,1);<br>UB = inf*ones(num_data,1);<br><br><span class=comment>% optimization</span><br><span class=comment>%----------------------------</span><br>qp_options=optimset(<span class=quotes>'Display'</span>,<span class=quotes>'off'</span>);<br>model.Alpha=quadprog(H,f,[],[],Aeq,beq,LB,UB,zeros(num_data,1),qp_options);<br><br><span class=comment>% take non-zero Alpha's</span><br><span class=comment>%---------------------</span><br>inx= find(model.Alpha > options.eps);<br>model.Alpha = model.Alpha(inx);<br><br><span class=comment>% compute radius</span><br><span class=comment>%---------------------</span><br>K = K(inx,inx);<br>model.b = model.Alpha'*K*model.Alpha;<br>model.r = sum( sqrt( diag(K) - 2*K*model.Alpha + model.b ))/length(inx);<br><br><span class=comment>% setup model</span><br><span class=comment>%---------------------</span><br>model.sv.X= X(:,inx);<br>model.nsv = length(inx);<br>model.options=options;<br>model.fun = <span class=quotes>'kdist'</span>;<br><br><span class=jump>return</span>;<br><span class=comment>% EOF</span><br></code>?? 快捷鍵說明
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