Clustering of volume reverberation spectra: An application of correspondence analysis

Correspondence analysis has been applied to 34 spectral curves of volume reverberation to cluster the spectra into groups. The clustering is compared with an earlier grouping of the spectra based on the cross-standard-deviation matrix with essentially similar results. However, the correspondence analysis technique has a number of clear-cut advantages: (1) the clustering is quickly displayed in a two-dimensional plot; (2) eigenvectors computed in the analysis are spectral curves which are characteristic of extremum environments in the data set (we call them volume reverberation environments and discuss their possible indentification with preponderant fish species); (3) those frequencies which most directly serve as indicators of a particular cluster of spectra are identified; and (4) the examination of the relationship of environmental parameters and the factor scores computed in the analysis provide a basis for extrapolation of the spectra to their appearance in unmeasured conditions. The volume reverberation spectra (known as column strengths) are chosen as a particular example of the application of correspondence analysis; we believe it is broadly applicable to the problem of identifying and classifying spectra in many disciplines. As an aid to the reader in understanding the technique, we have summarized the governing equations of correspondence analysis and given a geometrical interpretation relating the original spectra, eigenvectors, and factor scores. Subject Classification: 60.20; 30.40.