Analysing Music with Point-Set Compression Algorithms

Several point-set pattern-discovery and compression algorithms designed for analysing music are reviewed and evaluated. Each algorithm takes as input a point-set representation of a score in which each note is represented as a point in pitch-time space. Each algorithm computes the maximal translatable patterns (MTPs) in this input and the translational equivalence classes (TECs) of these MTPs, where each TEC contains all the occurrences of a given MTP. Each TEC is encoded as a ⟨pattern,vector set⟩ pair, in which the vector set gives all the vectors by which the pattern can be translated in pitch-time space to give other patterns in the input dataset. Encoding TECs in this way leads, in general, to compression, since each occurrence of a pattern within a TEC (apart from one) is encoded by a single vector, that has the same information content as one point. The algorithms reviewed here adopt different strategies aimed at selecting a set of MTP TECs that collectively cover (or almost cover) the input dataset in a way that maximizes compression. The algorithms are evaluated on two musicological tasks: classifying folk song melodies into tune families and discovering repeated themes and sections in pieces of classical music. On the first task, the best-performing algorithms achieved success rates of around 84%. In the second task, the best algorithms achieved mean F1 scores of around 0.49, with scores for individual pieces rising as high as 0.71.