NUSVO

Support Vector Optimiser: NU algorithm, low-level routine

    [V,J,NU,C] = NUSVO(K,NLAB,NU,OPTIONS)

Input
K	Similarity matrix
NLAB	Label list consisting of -1/+1
NU	Regularisation parameter (0 < NU < 1): expected fraction of SV (optional; default: 0.01)
OPTIONS
.PD_CHECK	force positive definiteness of the kernel by adding a small constant  to a kernel diagonal (default: 1)
.BIAS_IN_ADMREG	it may happen that bias of svc (b term) is not defined, then  if BIAS_IN_ADMREG == 1, b will be taken from its admissible  region (if the region is bounded, the midpoint will be used);  if BIAS_IN_ADMREG == 0 the situation will be considered as  an optimisation failure and treated accordingly (deafault: 1)
.ALLOW_UB_BIAS_ADMREG	it may happen that bias admissible region is unbounded  if ALLOW_UB_BIAS_ADMREG == 1, b will be heuristically taken  from its admissible region, otherwise(ALLOW_UB_BIAS_ADMREG == 0) the situation will be considered as an optimisation failure and  treated accordingly (deafault: 1)
.PF_ON_FAILURE	if the optimisation is failed (optimiser did not converge, or there are  problems with finding of the bias term and PF_ON_FAILURE == 1,  then Pseudo Fisher classifier will be computed,  otherwise (PF_ON_FAILURE == 0) an error will be issued (default: 1)

Output
V	Vector of weights for the support vectors
J	Index vector pointing to the support vectors
NU	NU parameter (useful when NU was automatically selected)
C	C regularisation parameter of SVC algorithm, which gives the same classifier

Description

A low level routine that optimises the set of support vectors for a 2-class  classification problem based on the similarity matrix K computed from the  training set. SVO is called directly from SVC. The labels NLAB should indicate  the two classes by +1 and -1. Optimisation is done by a quadratic programming.  If available, the QLD function is used, otherwise an appropriate Matlab routine.

NU is bounded from above by NU_MAX = (1 - ABS(Lp-Lm)/(Lp+Lm)), where  Lp (Lm) is the number of positive (negative) samples. If NU > NU_MAX is supplied  to the routine it will be changed to the NU_MAX.

If NU is less than some NU_MIN which depends on the overlap between classes  algorithm will typically take long time to converge (if at all).  So, it is advisable to set NU larger than expected overlap.

Weights V are rescaled in a such manner as if they were returned by SVO with the parameter C.

See also

nusvc, svo, svc,