Clustering of volume reverberation spectra: An application of correspondence analysis

Abstract

Correspondence analysis was 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-derivation matrix with essentially similar results. The correspondence analysis technique has several clear-cut advantages: the clustering is quickly displayed in a 2-dimensional plot; eigenvectors computed in the analysis are spectral curves which are characteristic of extremum environments in the data set (they are called volume reverberation environments and their possible indentitication with preponderant fish species is discussed); those frequencies which most directly serve as indicators of a particular cluster of spectra are identified; and 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; it is broadly applicable to the problem of identifying and classifying spectra in many disciplines. The governing equations of correspondence analysis are summarized and a geometrical interpretation relating the original spectra, eigenvectors and factor scores is given.