Sensitivity analysis of fuzzy Goldman typical testors

摘要

In the framework of supervised classification problems, the estimation of feature relevance and the search of all discriminating sub-descriptions of objects have great practical significance. Solving this problem in real situations is not always an easy task, because of the computational cost. The problems due to the size of matrix representation of objects, the computational complexity of algorithms, the non-standard object descriptions like mixed incomplete, which appear very frequently in Soft Sciences, and also the presence of fuzzy characteristics in the class descriptions or in the similarity measure used in the modeling of the problem in question have a big influence on the computational cost. Here, real valued similarity measures between feature values will be considered. Fuzzy Goldman typical testors are useful for estimating feature relevance and for searching all discriminate sub-descriptions of objects, but the computational complexity of algorithms to compute all Fuzzy Goldman typical testors is too high. Modifications of the training matrix very frequently appear in real world problems. Any modification to the training matrix can change the set of all Fuzzy Goldman typical testors, so this set must be computed again after each modification. This paper analyzes one of the sensitivity problems in Pattern Recognition: how does the set of all Fuzzy Goldman typical testors change after modifications of the training matrix. Four theorems about the behavior of the set of all Fuzzy Goldman typical testors are proposed and proved. An alternative method for calculating all Fuzzy Goldman typical testors of the modified matrix, more efficient than any traditional testor finding algorithm, is proposed. The new method's complexity is analyzed and some experimental results are shown.