Music genre profiling based on Fisher manifolds and Probabilistic Quantum Clustering
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ORIGINAL ARTICLE
Music genre profiling based on Fisher manifolds and Probabilistic Quantum Clustering Rau´l V. Casan˜a-Eslava2 • Ian H. Jarman1 • Sandra Ortega-Martorell1 • Paulo J. G. Lisboa1 Jose´ D. Martı´n-Guerrero2
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Received: 17 June 2019 / Accepted: 28 October 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Probabilistic classifiers induce a similarity metric at each location in the space of the data. This is measured by the Fisher Information Matrix. Pairwise distances in this Riemannian space, calculated along geodesic paths, can be used to generate a similarity map of the data. The novelty in the paper is twofold; to improve the methodology for visualisation of data structures in low-dimensional manifolds, and to illustrate the value of inferring the structure from a probabilistic classifier by metric learning, through application to music data. This leads to the discovery of new structures and song similarities beyond the original genre classification labels. These similarities are not directly observable by measuring Euclidean distances between features of the original space, but require the correct metric to reflect similarity based on genre. The results quantify the extent to which music from bands typically associated with one particular genre can, in fact, crossover strongly to another genre. Keywords Fisher metric Manifold structure Multidimensional scaling Probabilistic quantum clustering Music information retrieval
1 Introduction A unique property of probabilistic classifiers stems from the fact that the metric is induced in either the space of model parameters, or the space of data. This does not apply to classifiers arising from computational learning theory, & Rau´l V. Casan˜a-Eslava [email protected] Ian H. Jarman [email protected] Sandra Ortega-Martorell [email protected] Paulo J. G. Lisboa [email protected] Jose´ D. Martı´n-Guerrero [email protected] 1
Liverpool John Moores University, 3 Byrom Street, Liverpool, Merseyside L3 3AF, UK
2
Departament d’Enginyeria Electro`nica - ETSE, Universitat de Vale`ncia (UV), Av. Universitat, SN, 46100 Burjassot, Vale`ncia, Spain
for instance Support Vector Machines, which work on the basis of discriminant vector spaces. The metric is linked to the Fisher information matrix which is calculated directly from the conditional probabilities inferred from the model. This property is most often ignored, but it holds the key to derive important properties about the data structure, which provide insights on the question addressed by the classifier. In binary or multinomial classification, the question addressed by the classifier is the probability of class membership of any given test point. Therefore, the metric will make explicit the similarity structure of the data, by weighting each input variable precisely according to the information it contains about class membership. New questions may be asked by changing the class labels and so the data structure w
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