Summary
Logistic Regression (LR) has become a widely used and accepted method to analyze binary or multiclass outcome variables, since it is a flexible tool that can predict probability for the state of a dichotomous variable. A recently proposed LR method is based on the hybridization of a linear model and Evolutionary Product Unit Neural Network (EPUNN) models for binary classification. This produces a high number of coefficients, so two different methods for simplifying the structure of the final model by reducing the number of initial or PU covariates are presented in this paper, both being based on the Wald test. The first method is a Backtracking Backward Search (BBS) method, and the other is similar, but it is based on the standard Simulated Annealing process for the decision steps (SABBS). In this study, we used aerial imagery taken in mid-May to evaluate the potential of two different combinations of LR and EPUNN (LR using PUs (LRPU), as well as LR using Initial covariates and PUs (LRIPU)) and the two presented methods of structural simplification of the final models (BBS and SABBS) used for discriminating Ridolfia segetum patches (one of the most dominant, competitive and persistent weed in sunflower crops) in a naturally infested field of southern Spain. Then, we compared the performance of these methods to six commonly used classification algorithms; our proposals obtaining a competitive performance and a lower number of coefficients.
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Extract
Structural Simplification of Hybrid Neuro-Logistic Regression Models in Multispectral Analysis of Remote Sensed Data
1. Introduction
Classification problems attempt to solve the task of deciding the class membership y of an unknown data item ? based on a data set D = {(x^sub i^, y^sub i^)} i = 1, ..., n of data items x^sub i^ with known class membership. The x^sub i^ are usually k-dimensional feature vectors, whose components are called covariates or independent variables. In most problem domains, there is no functional relationship between y and x. In this case, the relationship has to be described more generally by a probability distribution P(x;y); one then assumes that the data set D contains independent samples from P. From statistical decision theory, it is well known that the optimal class membership decision is to choose the class label y that maximizes posteriori distribution P(y/x). Therefore there are different approaches to data classification: One which considers only one distinction between the classes previously defined and which assigns a class label to an unknown data item, and another which attempts to model P(y/x). This latter attempt yields not only a class label for a data item, but also a probability of class membership. Logistic Regression (LR), Artificial Neural Networks (ANNs), and decision trees all follow the latter approach, although they vary considerably in building an approximation to P(y/x) from data. However, in spite of the great number of techniques developed to solve classification problems, there is no optimum methodology or technique to solve specific problems. This point has enc...See the full content of this document
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