Patent Document ID: 20080109389
Application ID: 11934569
Patent Status: 0

Claim One:
1. A training system for classifying a physical condition, the system comprising: a) an input module configured to receive n labeled data points {(a 1 , y 1 ),. .. ,(a n , y n )}, at least one of said n labeled data points describing at least one physical parameter for a physical phenomenon, said n labeled data points including vectors a i ε and markers y i ε {−1,1}, each of said n labeled data points placed in one of two sets I + ={i:(a i ,1)} and I − ={i:(a i ,−1)}; b) a mathematical formulation module configured to use said n labeled data points to model said physical phenomenon as a mathematical formulation, said mathematical formulation including: i) variables x=(w,b,Δ), where w ε , b ε , Δ ε ; ii) an objective function ƒ(x)=Δ; and iii) a plurality of constraints, said plurality of constraints including: 
 c i ( x )≡ c i ( w,b, Δ)=( w,a i )− b−Δ≧ 0, iεI + ;   (1) 
 c i ( x )≡ c i ( w,b, Δ)=−( w,a i )+ b−Δ≧ 0, iεI − ; and   (2) 
 ∥w∥ 2 =1;   (3) c) a transformer module configured to build a specific function L(w,b,Δ,λ,γ,τ) using: i) said mathematical formulation; ii) Lagrange multipliers λ=(λ 1 ,. .. , λ n ); iii) scaling parameters γ, τ, k; iv) a class of transformation functions with a predefined set of properties; and v) said n labeled data points, said n labeled data points further including a nonlinear resealing part; d) a Lagrange multipliers updater module configured to calculate updated Lagrange multipliers {circumflex over (λ)}=({circumflex over (λ)} 1 ,. .. , {circumflex over (λ)} n ); e) a scaling parameters updater module configured to calculate updated scaling parameters {circumflex over (γ)}, {circumflex over (τ)}, {circumflex over (k)}; and f) an iterative solver module configured to generate a classification rule using: i) said specific function; ii) said Lagrange multipliers updater module; iii) said scaling parameters updater module; iv) a general stopping criteria verifier module; and v) an accuracy parameter (ε).