Transformation of song data into syllable similarity-space.

(A) To transform data from a given bird into similarity-space we first segment all syllables from a set of songs produced by that bird and compute their corresponding PSDs. (B) Three examples of segmented syllables, each of a different type, and their corresponding PSDs. (C) For each of 3000 sample syllables from the song to be analyzed, similarity of PSDs is calculated relative to a basis set of PSDs for 50 syllables randomly drawn from the same song. This creates an M (number of basis syllables) by N (number of sample syllables) similarity matrix. (D) Visualization of how transformation of raw syllable data into the syllable similarity-space results in a clustering of syllables by type. Each point in the plot indicates the similarity between the PSD for one sample syllable and two basis PSDs (‘basis PSD1’ and ‘basis PSD2’) from the set of 50 basis PSDs. For clarity of exposition, only data that fall into one of three regions of high density are plotted here. Each of these regions corresponds approximately to multiple instances of one syllable type (which cluster near each other because of the similarity in their PSDs). In practice, there were more than three regions of syllable clustering (corresponding approximately to the number distinct syllable types in the bird’s song), and these regions were represented in the 50 dimensional space defined by the basis set of PSDs (only two of which are illustrated here). The regions of high density in this similarity-space were fit with a Gaussian mixture model, in which the optimal number of Gaussian mixtures was determined by Bayesian Information Criteria. Individual data points here are color-coded by their assignment to one of three Gaussian mixtures. For clarity of presentation, data from only three of the 9 total Gaussian mixtures are shown. In any single dimension (top and right) data points assigned to each Gaussian mixture were approximately normally distributed. (E) Similarity matrix shown in C, reordered so that data are grouped by assignment to each of 9 Gaussian mixtures fit to the data (represented by colored blocks at the right of the similarity matrix). In this reordered representation, it is apparent that syllables assigned to each Gaussian mixture have a shared ‘bar code’ reflecting a shared pattern of PSD similarity values relative to the basis PSDs. The spectrograms at the right illustrate that syllables assigned to a given Gaussian mixture tend to be of the same type.