Alternative Local Discriminant Bases Using Empirical Expectation and Variance Estimation

TL;DR

This work extends Local Discriminant Basis methods by introducing discrimination measures based on empirical expectations and variances of expansion coefficients, instead of relying on energy-density alone. It defines two new measures, $\lambda'$ and $\lambda''$, to better capture class separability and intra-class dispersion, and pairs them with a Dyadic Cluster Search Algorithm (DCSA) to build an oracle classifier from multiple LDBs (MLDB). Through three waveform-based experiments, the authors show that using multiple LDBs and combining measures (SLDB/SMLDB) can yield substantial test accuracy gains, with some settings showing clear improvements over the original LDB. The results highlight the practical value of ensemble LDB strategies and the importance of robust feature-discriminability estimates for high-dimensional time–frequency representations.

Abstract

We propose alternative discriminant measures for selecting the best basis among a large collection of orthonormal bases for classification purposes. A generalization of the Local Discriminant Basis Algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.