Related papers: A Framework for Topological Music Analysis (TMA)
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Audio-based music structure analysis (MSA) is an essential task in Music Information Retrieval that remains challenging due to the complexity and variability of musical form. Recent advances highlight the potential of fine-tuning…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle…
Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…
In this paper, we use topological data analysis (TDA) tools such as persistent homology, persistent entropy and bottleneck distance, to provide a {\it TDA-based summary} of any given set of texts and a general method for computing a…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…
Training data attribution (TDA) for music generation must answer two questions that copyright analysis requires, namely which training songs influence a generated output and along which musical aspects the influence operates. Existing…
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology,…
A new array signal reconstruction and signal-channel DOA estimation method based on TMLA by nonuniform period modulation are proposed. By using non-uniform period modulation, the harmonic component produced by different elements could be…
This paper introduces a simple yet powerful approach based on topological data analysis (TDA) for detecting the true steps in a piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse…
\emph{Topological data analysis} (TDA) has recently emerged as a new technique to extract meaningful discriminitve features from high dimensional data. In this paper, we investigate the possibility of applying TDA to improve the…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Quantitative analysis of commonalities and differences between recorded music performances is an increasingly common task in computational musicology. A typical scenario involves manual annotation of different recordings of the same piece…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…