# An Analysis of Rhythmic Patterns with Unsupervised Learning
## 1 Introduction
### Related Work
#### Models for Music Understanding  
Next to MIREX-type tasks, several researchers explored modeling of musical rhythm, where the focus is on the model and understanding of the modeled structures. These models often rely on analyses of human cognitive processes, and the perception of music and language. One of the more recently established and frequently used music theories was proposed by [PERSON] [13; 14], based on six perceptual principles. He empirically shows that many of the commonly known music rules have their basis in the perceptual principles. Inspired by [PERSON]'s work, [PERSON] and [PERSON] [15] proposed a simple Markov chain model for rhythm modeling, to explore interconnections between entropy rate and aesthetic value. They applied the proposed model to two pieces of minimalist music and showed that their rather simplistic model produces a similar analysis to one provided by a human expert. [PERSON] et al. [16] proposed a generative model for characterization of musical rhythms by using transformations, which provide a musically meaningful encoding of patterns, focusing on the syncopation in rhythmic patterns. The model incorporates [PERSON]'s metrical expectation principle of weak-strong bonds to model syncopation. The authors demonstrated the model's performance on a pop music piece by [PERSON]. They argue the proposed model's explicitness and usability for analysis, by providing \"musically and perceptually meaningful and detailed characterization\" (p. 126). The proposed model extends beyond the analysis of rhythm with its generative nature. In contrast to models based on human perception, data-driven models learn implicit rules by extracting knowledge from large datasets. For example, [PERSON] et al. [17] proposed a model based on probabilistic context-free grammars trained on quantized MIDI files from music21 ([[http://web.mit.edu/music21/doc/about/referenceCorpus.html](http://web.mit.edu/music21/doc/about/referenceCorpus.html)]([http://web.mit.edu/music21/doc/about/referenceCorpus.html](http://web.mit.edu/music21/doc/about/referenceCorpus.html))) and EWLD [18] datasets. Starting with unweighted acyclic grammars, this approach builds minimal parse trees from the music input. By adding additional restrictions and limiting the amount of all possible rules to be learned from the input, the model produces meaningful representations of rhythm structure and rhythmic notation. [PERSON] [19] proposed a unified model for polyphonic music analysis, including metrical analysis. In this later work, [PERSON] [20] focused on the rhythmic modality and compared six probabilistic models of rhythm on two datasets, the Essen Folksong Collection, and the corpus of [PERSON] and [PERSON] string quartets, to explore ways of modelling rhythm perception. The author argues that the perception of common-practice rhythm is governed by general principles. There are several hypotheses discussed, each arguing one of the six models presented: the Uniform Position Model, the Zeroth-Order Duration Model, the Metrical Position Model, the Fine-Grained Position Model, the First-Order Metrical Duration Model and the Hierarchical Position Model. The latter is based on the hypothesis that \"the common-practice rhythms are generated in a hierarchical manner\" (p. 358). Among the six models, the Hierarchical Position Model and the First-Order Metrical Duration Model achieved the lowest cross-entropy, with the Hierarchical Position Model being severely less complex than the First-Order Metrical Duration Model. Since rhythm in non-Western music contains a more extensive variety of different meters, several works are explicitly dedicated to exploration and rhythm modeling of non-Western music. [PERSON] [21] observed the rhythmic patterns (usul) in Turkish Makam music. He investigated how these patterns are related to note events and how the patterns are related to the meter as a latent mental construct.