arXiv subjects

Byeongchan Choi

Publications and source records attributed to Byeongchan Choi.

3 recordsLinked to original sources

arXiv2026

Zipf-Mandelbrot Scaling in Korean Court Music: Universal Patterns in Music

Zipf's law, originally discovered in natural language and later generalized to the Zipf-Mandelbrot law, describes a power-law relationship between the frequency of a Zipfian element and its rank. Due to the semantic characteristics of this law, it has also been observed in musical data. However, most such studies have focused on Western music, and its applicability to non-Western music remains not well investigated. We analyzed 43 Korean court music pieces called Jeong-ak, spanning several centuries and written in the traditional Korean musical notation Jeongganbo. These pieces were transcribed into Western staff notation, and musical data such as pitch and duration were extracted. Using pitch, duration, and their paired combinations as Zipfian units, we found that Korean music also fits the Zipf-Mandelbrot law to a high degree, particularly for the paired pitch-duration unit. Korean music has evolved collectively over long periods, smoothing idiosyncratic variations and producing forms that are widely understandable among people. This collective evolution appears to have played a significant role in shaping the characteristics that lead to the satisfaction of Zipf-Mandelbrot law. Our findings provide additional evidence that Zipf-Mandelbrot scaling in musical data is universal across cultures. We further show that the joint distribution of two independent Zipfian data sets follows the Zipf-Mandelbrot law; in this sense, our result does not merely extend Zipf's law but deepens our understanding of how scaling laws behave under composition and interaction, offering a more unified perspective on rank-based statistical regularities.

stat.AP↗

arXiv2025

Persistent Homology of Music Network with Three Different Distances

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 or between nodes in a graph network. These definitions are not unique and depend on the specific objectives of a given problem. In other words, selecting different metric definitions allows for multiple topological inferences. In this work, we focus on applying persistent homology to music graph with predefined weights. We examine three distinct distance definitions based on edge-wise pathways and demonstrate how these definitions affect persistent barcodes, persistence diagrams, and birth/death edges. We found that there exist inclusion relations in one-dimensional persistent homology reflected on persistence barcode and diagram among these three distance definitions. We verified these findings using real music data.

cs.SD↗

arXiv2025

Persistent Homology with Path-Representable Distances on Graph Data

Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their interpretations. In this paper, we define a class of distances on graphs, called path-representable distances, and investigate structural relationships between their induced persistent homologies. In particular, we identify a nontrivial injection between the 1-dimensional barcodes induced by two commonly used graph distances: the unweighted and weighted shortest-path distances. We formally establish sufficient conditions under which such embeddings arise, focusing on a subclass we call cost-dominated distances. The injection property is shown to hold in 0- and 1-dimensions, while we provide counterexamples for higher-dimensional cases. To make these relationships measurable, we introduce the total persistence difference (TPD), a new topological measure that quantifies changes between filtrations induced by cost-dominated distances on a fixed graph. We prove a stability result for TPD when the distance functions admit a partial order and apply the method to the SNAP EU Research Institution E-Mail dataset. TPD captures both periodic patterns and global trends in the data, and shows stronger alignment with classical graph statistics compared to an existing PH-based measure applied to the same dataset.

math.AT↗