Meredith Kupinski, Univ. of AZ, Which Measurements Matter? Dimensionality Reduction for Detection and Sensor Design

Abstract: High-dimensional measurements offer rich information, but limited training data can make that information difficult to use. Which features should we retain when the goal is to distinguish between two classes? This talk explores how differences in class means, variances, and correlations can guide both dimensionality reduction and the design of imaging instruments.

 

I will present a supervised framework that learns low-dimensional subspaces by maximizing Jeffreys divergence between class-conditional Gaussian models. The optimization takes place on the Grassmann manifold—the space of fixed-dimensional linear subspaces—and produces compressed measurements for quadratic classification. The resulting projection matrices also provide interpretable rankings of spectral bands, connecting statistical discrimination to practical choices about which wavelengths an instrument should measure. Comparisons with principal component analysis illustrate why directions of greatest variability may differ from those most useful for detection.

 

Using airborne imagery from the FIREX-AQ campaign, I will demonstrate the approach for fire and smoke detection across 50 spectral bands spanning the visible through thermal infrared. For fire pixels, three selected bands achieve an area under the ROC curve of 0.970, compared with 0.993 using all 50 bands. In image-level detection with limited training samples, spectral selection can also improve performance. These results illustrate how class-dependent covariance structure can inform efficient representations, interpretable feature selection, and the design of sensors around specific scientific tasks.