In almost every scientific field, measurements are performed over time. These observations lead to a collection of organized data called time series. The purpose of time series data mining is to try to extract all meaningful knowledge from the shape of data. Even if humans have a natural capacity to perform these tasks, it remains a complex problem for computers. In this paper we intend to provide a survey of the techniques applied for time series data mining. The first part is devoted to an overview of the tasks that have captured most of the interest of researchers. Considering that in most cases, time series task relies on the same components for implementation, we divide the literature depending on these common aspects, namely representation techniques, distance measures and indexing methods. The study of the relevant literature has been categorized for each individual aspects. Four types of robustness could then be formalized and any kind of distance could then be classified. Finally, the study submit various research trends and avenues that can be explored in the near future. We hope that this paper can provide a broad and deep understanding of the time series data mining research field.
Archived PDF is a preprint.International audienceThis paper defines homometry in the rather general case of locally-compact topological groups, and proposes new cases of its musical use. For several decades, homometry has raised interest in computational musicology and especially set-theoretical methods, and in an independent way and with different vocabulary in crystallography and other scientific areas. The link between these two approaches was only made recently, suggesting new interesting musical applications and opening new theoretical problems. We present some old and new results on homometry, and give perspective on future research assisted by computational methods. We assume from the reader's basic knowledge of groups, topological groups, group algebras, group actions, Lebesgue integration, convolution products, and Fourier transform
Archived PDF is a preprint.International audienceThis paper describes phase-retrieval approaches in music by focusing on the particular case of the cyclic groups (beltway problem). After presenting some old and new results on phase retrieval, we introduce the extended phase retrieval for a generalized musical Z-relation. This concept is accompanied by mathematical definitions and motivations from computer-aided composition. We assume from the reader basic knowledge of groups, topological groups, group algebras, group actions, Lebesgue integration, convolution products, and Fourier transform
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