Eigenbeam analysis of the diversity in bat biosonar beampatterns

A quantitative analysis of the interspecific variability in the biosonar beampatterns of bats has been performed on a data set that consisted of 267 emission and reception beampatterns from 98 different species. The beampatterns were aligned using a pairwise optimization framework defined by a rotation for which a cost function is minimized. The cost function was defined by a p-norm computed over all direction and summed across a discrete set of evenly sampled frequencies. For a representative subset of beampatterns, it was found that all pairwise alignments between beampatterns result in a global minimum that fell near the plane bisecting the mean direction of each beampattern and containing the origin. Following alignment, the average beampattern was found to consist of a single lobe that narrowed with increasing frequency. Variability around the average beampattern was analyzed using principle component analysis (PCA) that resulted in “eigenbeams”: The first three “eigenbeams” were found to control the beamwidth of the beampattern across frequency while higher rank eigenbeams accounted for symmetry breaks and changes in lobe direction. Reception and emission beampattern could be differentiated based on their PCA scores using only a small number of eigenbeams.