Compression-based geometric pattern discovery in music

The purpose of musical analysis is to find the best possible ex-planations for musical objects, where such objects may range from single chords or phrases to entire musical corpora. Kol-mogorov complexity theory suggests that the best possible ex-planation for an object is represented by the shortest possible description of it. Two compression algorithms, COSIATEC and SIATECCOMPRESS, are described that take point-set representations of musical objects as input and generate com-pressed encodings of these point sets as output. The algo-rithms were evaluated on a task in which 360 folk songs were classified into tune families using normalized compression distance, a 1-nn classifier and leave-one-out cross-validation. COSIATEC achieved a success rate of 84 % on this task, compared with a success rate of 13 % for a general-purpose compressor. Variants of the algorithms incorporating modi-fications that have been suggested in the literature were also run on the task and the results were compared

Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes

I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more non-random, non-arbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers, artists, dancers, comedians, yourself, and (since 1990) artificial systems.Comment: 35 pages, 3 figures, based on KES 2008 keynote and ALT 2007 / DS 2007 joint invited lectur

Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Improving the running time of repeated pattern discovery in multidimensional representations of music

Methods for discovering repeated patterns in music are important tools in computational music analysis. Repeated pattern discovery can be used in applications such as song classification and music generation in computational creativity. Multiple approaches to repeated pattern discovery have been developed, but many of the approaches do not work well with polyphonic music, that is, music where multiple notes occur at the same time. Music can be represented as a multidimensional dataset, where notes are represented as multidimensional points. Moving patterns in time and transposing their pitch can be expressed as translation. Multidimensional representations of music enable the use of algorithms that can effectively find repeated patterns in polyphonic music. The research on methods for repeated pattern discovery in multidimensional representa- tions of music is largely based on the SIA and SIATEC algorithms. Multiple variants of both algorithms have been developed. Most of the variants use SIA or SIATEC directly and then use heuristic functions to identify the musically most important patterns. The variants do not thus typically provide improvements in running time. However, the running time of SIA and SIATEC can be impractical on large inputs. This thesis focuses on improving the running time of pattern discovery in multidimensional representations of music. The algorithms that are developed in this thesis are based on SIA and SIATEC. Two approaches to improving running time are investigated. The first approach involves the use of hashing, and the second approach is based on using filtering to avoid the computation of unimportant patterns altogether. Three novel algorithms are presented: SIAH, SIATECH, and SIATECHF. The SIAH and SIATECH algorithms, which use hashing, were found to provide great improvements in running time over the corresponding SIA and SIATEC algorithms. The use of filtering in SIATECHF was not found to significantly improve the running time of repeated pattern discovery

Using point-set compression to classify folk songs

Thirteen different compression algorithms were used to calculate the normalized compression distances (NCDs) between pairs of tunes in the Annotated Corpus of 360 Dutch folk songs from the collection Onder de groene linde. These NCDs were then used in conjunction with the 1-nearest-neighbour algorithm and leave-one-out cross-validation to classify the 360 melodies into tune families. The classifications produced by the algorithms were compared with a ground-truth classification prepared by expert musicologists. Twelve of the thirteen compressors used in the ex-periment were based on the discovery of translational equivalence classes (TECs) of maximal translatable patterns (MTPs) in point-set representations of the melodies. The twelve algorithms con-sisted of four variants of each of three basic algorithms, COSI-ATEC, SIATECCOMPRESS and Forth’s algorithm. The main difference between these algorithms is that COSIATEC strictly partitions the input point set into TEC covered sets, whereas the TEC covered sets in the output of SIATECCOMPRESS and Forth’s algorithm may share points. The general-purpose compressor, bzip2, was used as a baseline against which the point-set com-pression algorithms were compared. The highest classification success rate of 77–84 % was achieved by COSIATEC, followed by 60–64 % for Forth’s algorithm and then 52–58 % for SIATE-CCOMPRESS. When the NCDs were calculated using bzip2, the success rate was only 12.5%. The results demonstrate that the effectiveness of NCD for measuring similarity between folk-songs for classification purposes is highly dependent upon the actual compressor chosen. Furthermore, it seems that compres-sors based on finding maximal repeated patterns in point-set rep-resentations of music show more promise for NCD-based mu-sic classification than general-purpose compressors designed for compressing text strings. 1

Understanding and Compressing Music with Maximal Transformable Patterns

We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. 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, $E=\left\lbrace\left\langle P_1, T_1\right\rangle,\left\langle P_2, T_2\right\rangle,\ldots\left\langle P_{\ell}, T_{\ell}\right\rangle\right\rbrace$, where each $\langle P_i,T_i\rangle$ consists of a maximal pattern, $P_i\subseteq D$, and a set, $T_i\subset F$, of transformations that map $P_i$ 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

An approach for identifying salient repetition in multidimensional representations of polyphonic music

SIATEC is an algorithm for discovering patterns in multidimensional datasets (Meredith et al., 2002). This algorithm has been shown to be particularly useful for analysing musical works. However, in raw form, the results generated by SIATEC are large and difficult to interpret. We propose an approach, based on the generation of set-covers, which aims to identify particularly salient patterns that may be of musicological interest. Our method is capable of identifying principal musical themes in Bach Two-Part Inventions, and is able to offer a human analyst interesting insight into the structure of a musical work