A Functional Data—Analytic Approach to Signal Discrimination

Abstract

Motivated by specific problems involving radar-range profiles, we suggest techniques for real-time discrimination in the context of signal analysis. The key to our approach is to regard the signals as curves in the continuum and employ a functional data-analytic (FDA) method for dimension reduction, based on the FDA technique for principal coordinates analysis. This has the advantage, relative to competing methods such as canonical variates analysis, of providing a signal approximation that is best possible, in an L² sense, for a given dimension. As a result, it produces particularly good discrimination. We explore the use of both nonparametric and Gaussian-based discriminators applied to the dimensionreduced data.

KEY WORDS :

• Basis functions
• Classification
• Dimension reduction
• Discrimination
• Discriminant analysis
• Functional data analysis
• Kernel methods
• Nonparametric density estimation
• Odds ratio
• Radar range profiles
• Signal analysis