Automatic classification of mines using local discriminant bases for broadband sonar data

Abstract

The Local Discriminant Basis (LDB) approach of Saito and Coifman was compared to Principal Components Analysis (PCA) for feature extraction prior to automatic classification. LDB finds an orthonormal basis from a library of local basis vectors (e.g., cosine packets) that maximizes a discriminative measure for the given set of training data. The data consist of broadband sonar data collected from mine-like targets and calibration targets in shallow water on the bottom of Puget Sound in Washington State. The database consists of twelve sequences of data for each of 10 separate objects. Each signal contains 481 samples. The lowest error rate achieved with PCA was 9.2%, or 11 out of 120 errors, using the first 45 principal component vectors and performing classification with Fischer's Linear Discriminant. The corresponding error rate for LDB was also 9.2%, though using fewer (34) coefficients. Comparable results were obtained using CART (Classification Trees) with very few coefficients: 8.3% error rate for LDB with 7 coefficients; 10% for PCA with only 4 coefficients. A modified LDB, which used a robust version of Fisher's separability (the ratio of between-class variation to within- class variation) instead of normalized energy as the discriminative measure, reduced the error rate to 9/120 (7.5%). Another method of improving the basis selection, called 'cycle spinning,' reduced the error rate to 7/120 (5.8%). Thus, LDB yields consistently better classification rates than principal components feature extraction. An added advantage of LDB is speed: it is an O[Nlog(N) 2 ] procedure for cosine packets, while principal components is O(N 3 ).