Radar Theory
theHigh Range Resolution Radar Extensions to Rough Set Theory for Automatic Target Recognition
Dale E. NELSON Target Recognition Branch Sensors Directorate, Air Force Research Laboratory Wright-Patterson AFB, OH 45433 USA and Janusz A. STARZYK Department of Computer and electrical Engineering Ohio University, Russ College of Engineering & Tech., Athens, OH 45701 USA
ABSTRACT Rough Set Theory (RST) is a recent development in the area of data mining and knowledge discovery. RST is an emerging Automatic Target Recognition (ATR) methodology for determining features and then classifiers from a training data set. RST guarantees that once the training data has been labeled all possible classifiers (based on that labeling) will be generated. The primary limitation is that the operation of finding all the classifiers (reducts) has been shown to be N-P hard. This means that for any realistically sized problem the computational time for finding the classifiers will be prohibitive. In this paper we extend RST by defining new terms: a focused information system, a focused reduct, and a power information system. Using these concepts we develop a means to create a classifier capable of acceptable performance on a six target class HRR problem. Our method, in addition to making a robust classifier, creates a method which can extract useful knowledge from incomplete or corrupted data. This is accomplished through the partitioning of the data. Each partition will have multiple classifiers. We then introduce a method to fuse all these classifiers to yield a robust classifier with a probability of correct classification of 92% and a probability of declaration of 99%. Keywords: Rough Set Theory, Reduct, High Range Resolution Radar, Automatic Target Recognition, Fusion. 1. INTRODUCTION Classification of High Range Resolution (HRR) radar signals is difficult. A typical HRR signal contains 128 range bins with values between 0-255 representing the signal strength. A 3-D object is now
Dale E. NELSON Target Recognition Branch Sensors Directorate, Air Force Research Laboratory Wright-Patterson AFB, OH 45433 USA and Janusz A. STARZYK Department of Computer and electrical Engineering Ohio University, Russ College of Engineering & Tech., Athens, OH 45701 USA
ABSTRACT Rough Set Theory (RST) is a recent development in the area of data mining and knowledge discovery. RST is an emerging Automatic Target Recognition (ATR) methodology for determining features and then classifiers from a training data set. RST guarantees that once the training data has been labeled all possible classifiers (based on that labeling) will be generated. The primary limitation is that the operation of finding all the classifiers (reducts) has been shown to be N-P hard. This means that for any realistically sized problem the computational time for finding the classifiers will be prohibitive. In this paper we extend RST by defining new terms: a focused information system, a focused reduct, and a power information system. Using these concepts we develop a means to create a classifier capable of acceptable performance on a six target class HRR problem. Our method, in addition to making a robust classifier, creates a method which can extract useful knowledge from incomplete or corrupted data. This is accomplished through the partitioning of the data. Each partition will have multiple classifiers. We then introduce a method to fuse all these classifiers to yield a robust classifier with a probability of correct classification of 92% and a probability of declaration of 99%. Keywords: Rough Set Theory, Reduct, High Range Resolution Radar, Automatic Target Recognition, Fusion. 1. INTRODUCTION Classification of High Range Resolution (HRR) radar signals is difficult. A typical HRR signal contains 128 range bins with values between 0-255 representing the signal strength. A 3-D object is now
References: [1] [2] [3] [4] [5] [6] A. Nakamura and G. Jian-Miang, “A modal logic for similarity-based data analysis”, Hiroshima Univ. Technical. Report., 1988. Z. Pawlak, “Information systems - theoretical foundations”, Information Systems, Vol. 6, pp.205-218, 1981. Z. Pawlak, Rough Sets - Theoretical Aspects of Reasoning About Data, Kluwer Academic Publ., 1991. J. A. Starzyk, D. E. Nelson, and K. Sturtz, "Reduct Generation in Information Systems", Bulletin of International Rough Set Society, 1999, 3(1/2). J.A. Starzyk, D.E. Nelson, and K. Sturtz, " A Mathematical Foundation for Improved Reduct Generation in Information Systems", Journal of Knowledge and Information Systems, March 2000. A. Skowron, C. Rausser, “The Discernibility Matrices and Functions in Information Systems, Fundamenta Informaticae, 15(2), pp.331-362, 1991.