Modèles de compression et critères de complexité pour la description et l'inférence de structure musicale

Corentin Guichaoua 1
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Abstract : A very broad definition of music structure is to consider what distinguishes music from random noise as part of its structure. In this thesis, we take interest in the macroscopic aspects of music structure, especially the decomposition of musical pieces into autonomous segments (typically, sections) and their characterisation as the result of the grouping process of jointly compressible units. An important assumption of this work is to establish a link between the inference of music structure and information theory concepts such as complexity and entropy. We thus build upon the hypothesis that structural segments can be inferred through compression schemes. In a first part of this work, we study Straight-Line Grammars (SLGs), a family of formal grammars originally used for structure discovery in biological sequences (Gallé, 2011), and we explore their use for the modelisation of musical sequences. The SLG approach enables the compression of sequences, depending on their occurrence frequencies, resulting in a tree-based modelisation of their hierarchical organisation. We develop several adaptations of this method for the modelisation of approximate repetitions and we develop several regularity criteria aimed at improving the efficiency of the method. The second part of this thesis develops and explores a novel approach for the inference of music structure, based on the optimisation of a tensorial compression criterion. This approach aims to compress the musical information on several simultaneous time-scales by exploiting the similarity relations, the logical progressions and the analogy systems which are embedded in musical segments. The proposed method is first introduced from a formal point of view, then presented as a compression scheme rooted in a multi-scale extension of the System & Contrast model (Bimbot et al., 2012) to hypercubic tensorial patterns. Furthermore, we generalise the approach to other, irregular, tensorial patterns, in order to account for the great variety of structural organisations observed in musical segments. The methods presented in this thesis are tested on a structural segmentation task using symbolic data, chords sequences from pop music (RWC-Pop). The methods are evaluated and compared on several sets of chord sequences, and the results establish an experimental advantage for the approaches based on a complexity criterion for the analysis of structure in music information retrieval, with the best variants offering F-measure scores around 70%. To conclude this work, we recapitulate its main contributions and we discuss possible extensions of the studied paradigms, through their application to other musical dimensions, the inclusion of musicological knowledge, and their possible use on audio data.
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Corentin Guichaoua. Modèles de compression et critères de complexité pour la description et l'inférence de structure musicale. Autre [cs.OH]. Université Rennes 1, 2017. Français. ⟨NNT : 2017REN1S053⟩. ⟨tel-01687054⟩



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