Related papers: A Framework for Topological Music Analysis (TMA)
Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction.…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…
This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…
We report an approach to obtaining complex networks with diverse topology, here called syntonets, taking into account the consonances and dissonances between notes as defined by scale temperaments. Though the fundamental frequency is…
Persistent homology has been widely used to discover hidden topological structures in data across various applications, including music data. To apply persistent homology, a distance or metric must be defined between points in a point cloud…
Online music databases have increased signicantly as a consequence of the rapid growth of the Internet and digital audio, requiring the development of faster and more efficient tools for music content analysis. Musical genres are widely…
Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Accurate bone strength prediction is essential for assessing fracture risk, particularly in aging populations and individuals with osteoporosis. Bone imaging has evolved from X-rays and DXA to clinical computed tomography (CT), and now to…
This chapter considers how string-based methods might be adapted to address music-analytic questions related to the discovery of musical organization, with particular attention devoted to the analysis of tonal harmony. I begin by applying…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…
We propose an unsupervised learning methodology with descriptors based on Topological Data Analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
We study the topology of several music recommendation networks, which rise from relationships between artist, co-occurrence of songs in playlists or experts' recommendation. The analysis uncovers the emergence of complex network phenomena…
We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…