Margin-based Refinement for Linear Discriminant Analysis

For the two classes supervised learning problem, we present a refinement method for increasing the classification accuracy of an initial separating hyperplane in the feature space Rd. The main idea corresponds to dimensionality reduction of, e.g. LDA separation, however not in its original form R$^{d}$ ! R but rather as dimensionality reduction R$^{d}$ ! R$^{j}$ for some j 1. The method combines discriminant and margin-based properties of the separation. Due to efficiency reasons, we define rules for fast calculation of the refinement. Furthermore, we discuss theoretical fundamentals of our method and show its high performance by cross-validation tests on datasets from the UCI Machine Learning Repository with different numbers of features and objects. Due to the margin-based origin, the method is suitable for not well-balanced datasets. Cross-validation tests for not well-balanced data are given as well

Fuzzy-Pattern-Classifier Training with Small Data Sets

It is likely in real-world applications that only little data isavailable for training a knowledge-based system. We present a method forautomatically training the knowledge-representing membership functionsof a Fuzzy-Pattern-Classification system that works also when only littledata is available and the universal set is described insufficiently. Actually,this paper presents how the Modified-Fuzzy-Pattern-Classifier’s member-ship functions are trained using probability distribution functions