TY - GEN
T1 - Understanding and Compressing Music with Maximal Transformable Patterns
AU - Meredith, David
N1 - Conference code: 11
PY - 2023/7/9
Y1 - 2023/7/9
N2 - We present a polynomial-time algorithm that discovers all maximal patterns in a point set, 𝐷⊂ℝ𝑘, that are related by transformations in a user-specified class, 𝐹, of bijections over ℝ𝑘. We also present a second algorithm that discovers the set of occurrences for each of these maximal patterns and then uses compact encodings of these occurrence sets to compute a losslessly compressed encoding of the input point set. This encoding takes the form of a set of pairs, 𝐸={⟨𝑃1,𝑇1⟩,⟨𝑃2,𝑇2⟩,…⟨𝑃ℓ,𝑇ℓ⟩}, where each ⟨𝑃𝑖,𝑇𝑖⟩ consists of a maximal pattern, 𝑃𝑖⊆𝐷, and a set, 𝑇𝑖⊂𝐹, of transformations that map 𝑃𝑖 onto other subsets of 𝐷. Each transformation is encoded by a vector of real values that uniquely identifies it within 𝐹 and the length of this vector is used as a measure of the complexity of 𝐹. We evaluate the new compression algorithm with three transformation classes of differing complexity, on the task of classifying folk-song melodies into tune families. The most complex of the classes tested includes all combinations of the musical transformations of transposition, inversion, retrograde, augmentation and diminution. We found that broadening the transformation class improved performance on this task. However, it did not, on average, improve compression factor, which may be due to the datasets (in this case, folk-song melodies) being too short and simple to benefit from the potentially greater number of pattern relationships that are discoverable with larger transformation classes.
AB - We present a polynomial-time algorithm that discovers all maximal patterns in a point set, 𝐷⊂ℝ𝑘, that are related by transformations in a user-specified class, 𝐹, of bijections over ℝ𝑘. We also present a second algorithm that discovers the set of occurrences for each of these maximal patterns and then uses compact encodings of these occurrence sets to compute a losslessly compressed encoding of the input point set. This encoding takes the form of a set of pairs, 𝐸={⟨𝑃1,𝑇1⟩,⟨𝑃2,𝑇2⟩,…⟨𝑃ℓ,𝑇ℓ⟩}, where each ⟨𝑃𝑖,𝑇𝑖⟩ consists of a maximal pattern, 𝑃𝑖⊆𝐷, and a set, 𝑇𝑖⊂𝐹, of transformations that map 𝑃𝑖 onto other subsets of 𝐷. Each transformation is encoded by a vector of real values that uniquely identifies it within 𝐹 and the length of this vector is used as a measure of the complexity of 𝐹. We evaluate the new compression algorithm with three transformation classes of differing complexity, on the task of classifying folk-song melodies into tune families. The most complex of the classes tested includes all combinations of the musical transformations of transposition, inversion, retrograde, augmentation and diminution. We found that broadening the transformation class improved performance on this task. However, it did not, on average, improve compression factor, which may be due to the datasets (in this case, folk-song melodies) being too short and simple to benefit from the potentially greater number of pattern relationships that are discoverable with larger transformation classes.
KW - SIA
KW - data compression
KW - maximal transformable patterns
KW - music analysis
KW - parsimony principle
KW - pattern discovery
KW - point-set patterns
UR - http://www.titanmusic.com/papers/public/MeredithHCII2023.pdf
UR - http://www.scopus.com/inward/record.url?scp=85169058924&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-34732-0_24
DO - 10.1007/978-3-031-34732-0_24
M3 - Article in proceeding
SN - 978-3-031-34731-3
T3 - Lecture Notes in Computer Science
SP - 309
EP - 325
BT - Culture and Computing
A2 - Rauterberg, Matthias
PB - Springer
CY - Cham, Switzerland
T2 - C&C: International Conference on Culture and Computing
Y2 - 23 July 2023 through 28 July 2023
ER -