Statistical Shape Analysis & Modeling Group

Alignment, Modeling, and Classification of Elastic Functional Data

The task of clustering and modeling underwater objects using acoustic spectrum is complicated by the uncertainties in aspect angles at different data collections. Small changes in the aspect angles introduce compositional noise in the signals. The traditional alignment techniques are based on energy functions that are not proper distances, and necessitate a separate (and thus suboptimal) choice of distance to compare the aligned functions.

We present a comprehensive technique, for removing compositional noise and aligning functions that: (1) uses a single cost function for data alignment, (2) combines the data and smoothness in natural fashion, and (3) leads to a proper distance between aligned functions. It is based on establishing re-parameterization orbits of functions under the warping group and defining a distance between orbits using the Fisher-Rao metric. Using this metric we can compute a proper covariance and perform functional principal component analysis. From the principal components we can develop models of the y variability (aligned data) and x variability (warping functions) and perform classification. We investigate the use of this framework in modeling and classification of spectral signatures in acoustic data and demonstrate improvements in signal classification using this framework, over current methods.