Patent Document ID: 7933850
Application ID: 11598608
Patent Flag: 1

Claim One:
1. A method for constructing a functional relationship approximation from a set of data points through nonparametric regression, the method comprising: receiving a training data set in an n-dimensional space, wherein the training data set represents normal system data values from a system, wherein the normal system data values are collected from a system with a known-good behavior pattern; defining a set of regression primitives in the n-dimensional space, wherein a regression primitive in the set passes through N data points in the training data set, wherein N≧n; logically combining the set of regression primitives to produce a convex envelope F, wherein logically combining the set of regression primitives involves using R-function operations by, for each subset of (N−1) data points in the training data set, grouping a subset of regression primitives in the set which pass through the (N−1) data points; and performing an R-conjunction operation on the subset of regression primitives to produce a combined functional relationship associated with the (N−1) data points; and performing an R-disjunction operation on a set of combined functional relationship associated with different subsets of (N−1) data points in the training data set to produce the convex envelope F, such that for each point p in the n-dimensional space: F(p)=0 if p is on the convex envelope, F(p)<0 if p is inside the convex envelope, and F(p)>0 if p is outside the convex envelope; using at least a computer for obtaining the functional relationship approximation by computing an argument of the minimum of F in the n-dimensional space, wherein the functional relationship approximation is constructed based on the training data set, and wherein the functional relationship approximation enables prediction of normal system behavior; and using the functional relationship approximation to classify data from the system.