A scale-free distribution of false positives for a large class of audio similarity measures

The "bag-of-frames" approach (BOF) to audio pattern recognition models signals as the long-term statistical distribution of their local spectral features, a prototypical implementation of which being Gaussian Mixture Models of Mel-Frequency Cepstrum Coefficients. This approach is the most predominant paradigm to extract high-level descriptions from music signals, such as their instrument, genre or mood, and can also be used to compute direct timbre similarity between songs. However, a recent study by the authors shows that this class of algorithms when applied to music tends to create false positives which are mostly always the same songs regardless of the query. In other words, with such models, there exist songs-which we call hubs-which are irrelevantly close to very many songs. This paper reports on a number of experiments, using implementations on large music databases, aiming at better understanding the nature and causes of such hub songs. We introduce two measures of "hubness", the number of n-occurrences and the mean neighbor angle. We find that in typical music databases, hubs are distributed along a scale-free distribution: non-hub songs are extremely common, and large hubs are extremely rare-but they exist. Moreover, we establish that hubs are not a property of a given modelling strategy (i.e. static vs dynamic, parametric vs non-parametric, etc.) but rather tend to occur with any type of model, however only for data with a given amount of "heterogeneity" (to be defined). This suggests that the existence of hubs could be an important phenomenon which generalizes over the specific problem of music modelling, and indicates a general structural property of an important class of pattern recognition algorithms.