Separable Classification Problems Research Articles

Unified dual for bi-class SVM approaches

SVM theory was originally developed on the basis of a separable binary classification problem, and other approaches have been later introduced. In this paper, we demonstrated that all these approaches admit the same dual problem formulation.

Coevolutionary genetic fuzzy systems: a hierarchical collaborative approach

In this paper a coevolutionary genetic approach is devised to support hierarchical, collaborative relations between individuals representing different parameters of Takagi–Sugeno fuzzy models. The coevolutionary approach assumes species to mean partial solutions of fuzzy modeling problems organized into four hierarchical levels. Individuals at each hierarchical level encode membership functions, individual rules, rule-bases and fuzzy systems, respectively. A shared fitness evaluation scheme is used to measure the performance of each individual. Constraints are observed and particular targets are defined throughout the hierarchical levels, with the purpose of promoting the occurrence of valid individuals and inducing rule compactness, rule base consistency, and partition set visibility. The performance of the approach is evaluated via an example of function approximation with noisy data, and a nonlinearly separable classification problem.

New methods for testing linear separability

If two sets are linearly separable (LS), then there exists a single layer perceptron feedforward neural network that classifies them. We propose three methods for testing linear separability. The first method is based on the notion of convex hull, the second on a halting upper bound for the perceptron learning algorithm, and the third one, called the class of linear separability algorithm, is based on the characterization of the set of points by which passes a hyperplane that linearly separates two classes. We also study the treatment of nonlinearly separable (NLS) classification problems. We propose two solutions for handling NLS problems. The first solution is an approximation of an NLS classification problem by means of an LS one. We prove that the problem of finding the best approximation is NP-complete. The second solution is an NLS to LS transformation algorithm which can be used for building a multilayer feedforward neural networks called the Recursive Deterministic Perceptron (RDP). This neural network model can be used for solving any two class classification problems even if the two classes are NLS. We prove that the construction of an RDP linearly separating two classes X and Y can be done in less than n steps where n is the cardinal of the set X∪ Y. The geometrical halting upper bound for the perceptron algorithm and the class of linear separability algorithm are the principal results of this paper.

Case Studies on Modeling Manufacturing Processes Using Artificial Neural Networks

The modeling capability of an artificial neural network is studied through three different manufacturing processes. The first case study is a linear separable pattern classification problem in manufacturing process diagnosis. The performance between the neural network and the probability voting classifier is compared. The second case study uses a design of experiment to study an SMC compression molding process. Modeling and predicting performances between a regression model and a neural network model are compared in linear as well as nonlinear cases. The third case study investigates correlation models between the operating conditions and product quality defects of an automotive painting process. Results from a neural network model are compared with those of a probability voting classifier. An ad hoc modification named focused learning paradigm on the back-propagation algorithm is also introduced to speed up network learning.