| EKOZINEC | |
Kozinec's algorithm for eps-optimal separating hyperplane.
Synopsis:
model = ekozinec(data)
model = ekozinec(data,options)
model = ekozinec(data,options,init_model)
Description:
This function is implementation of the Kozinec's algorithm
with eps-optimality stopping condition [SH10]. The algorithm
finds the eps-optimal separating hyperplane.
model=ekozinec(data) the Kozinec's rule is used to find the closest
points w1, w2 from the convex hulls of the vectors from the first and
the second class. The found points determine the optimal separating
hyperplane.
model=ekozinec(data,options) specifies stopping conditions of
the algorithm in structure options:
.eps [1x1] ... controls how close is the found solution to
the optimal hyperplane in terms of margin
(default eps=0.01). The options for eps are:
eps > 0 ... eps-optimal hyperplane is sought for.
eps == 0 ... algorithm converges to the optimal hyperplane (but it
does not have to stop in finite number of iterations).
eps < 0 ... algorithm stops when the separating hyperplane
is found (zero training error) regardless the margin
so it solves the same task as the ordinary Perceptron.
.tmax [1x1]... maximal number of iterations.
model = ekozinec(data,options,init_model) specifies initial model
which must contain:
.W1 [dim x 1] ... Vector from the first convex hull.
.W2 [dim x 1] ... Vector from the second convex hull.
Input:
data [struct] Labeled (binary) training data.
.X [dim x num_data] Input vectors.
.y [1 x num_data] Labels (1 or 2).
options [struct]
.eps [real] Controls how closeness to the optimal hypeprlane (see above).
.tmax [1x1] Maximal number of iterations (default tmax=inf).
init_model [struct] Initial model; must contain items
.W1 [dim x 1], .W2 [dim x 1] see above.
Output:
model [struct] Binary linear classifier:
.W [dim x 1] Normal vector of hyperplane.
.b [1x1] Bias of hyperplane.
.W1 [dim x 1] The nearest vector of the first convex hull.
.W2 [dim x 1] The nearest vector of the second convex hull.
.margin [1x1] Margin of the found hyperplane.
.exitflag [1x1] 1 ... eps-optimality condition satisfied or separating
hyperplane has been found
0 ... number of iterations exceeded tmax.
.t [1x1] Number of iterations.
Example:
data = genlsdata( 2, 50, 1);
model = ekozinec(data, struct('eps',0.01));
figure; ppatterns(data); pline(model);
See also
PERCEPTRON, MPERCEPTRON, LINCLASS.
About: Statistical Pattern Recognition Toolbox
(C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
19-may-2004, VF
3-may-2004, VF
17-Sep-2003, VF
17-Feb-2003, VF
16-Feb-2003, VF
21-apr-2001, V.Franc, created