On the Architecture of layered Neural Network for Land use Classification of Satellite Remote Sensing Image
Shimizu, Eihan and le, Van Trung
Deparment of Civil Engineering, University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan
Tel : 03-3812-2111 ext. 6126 FAX : 03-3812-4977
E-mail : [email protected]
Abstract
Layered Neural Network (LNN) have been proposed recently as a non-parametric classification method suitable for the efficient analysis of satellite remote sensing images. Most of the studies in this field, however, have been empirical and LNNs have been applied just like “black box” estimation machines. When a non-parametric function is trained with {0,1} binary target by the least squares, the output of the calibrated function is considered an estimate of a posterior probability. The accuracy of this estimate mainly depends on the network structure, the activation function form as well as he learning paradigm and the number of training data sued in learning. This paper discusses the application of LNN to remotely sensed data classification. We provide a theoretical interpretation for the LNN Remotely Sensed Data Classification. We provide a theoretical interpretation for the LNN classifier in comparison with the conventional classification methods. The most important part is the derivation of a generalized form of LNN classifier based on the maximum entropy principle. According to the generalized form, we discuss the relationship between the familiar type of LNN classifier employing the igmodial activation function and the other types of discriminate models such as the Multinomial Logit Mode.
1. Introduction
Layered Neural Networks (LNN) have been broadly applied in classification, prediction and other modeling problems. Hill et al.. (1994) gave a full review of studies comparing LNNs and conventional statistical models. With the exception of comparisons with regression analysis, however, there have so far been few studies to provide a theoretical interpretation for the application of LNN.
This paper will show how LNNs approximate the Bayes optimal discriminate function when used for classification of satellite remote sensing image, and discuss the relationship between the familiar type of LNN classifier employing the sigmodial activation function and the other types of discriminate models such as the Multinomial Logit Model.
2. Basic Formulating of LNN Classifier
Let x represent a feature vector which is to be classified. Let he possible classes be denoted by wj(i=1,2.J). If we consider the discriminate function dj(x), then the decision rule is
