Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.13595

Persistent Homology of Music Network with Three Different Distances

Eunwoo Heo·Byeongchan Choi·Myung ock Kim·Mai Lan Tran·Jae-Hun Jung
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.SDcs.CGeess.AS

Keep this discovery

BibTeXRIS

Eunwoo Heo, Byeongchan Choi, Myung ock Kim, Mai Lan Tran, Jae-Hun Jung. 2025-06-16. Persistent Homology of Music Network with Three Different Distances. https://doi.org/10.1080/17459737.2025.2568844

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Xiaomi-CocktailASR-1 Technical Report

Recently, large language model (LLM) based ASR models have achieved significant progress, yet they generally lack support for multi-speaker scenarios, where the cocktail party problem remains a critical bottleneck for further advancing ASR. Existing TS-ASR methods, including end-to-end architectures with speaker embeddings and latest LLM-based explorations suffer from degraded single-speaker performance and the inability to reject when the target speaker is absent. In this paper, we propose Xiaomi-CocktailASR-1, an LLM-based end-to-end TS-ASR architecture. By utilizing reference speech as voiceprint prompts, it directly transcribes the target speaker's speech without requiring speech separation. Xiaomi-CocktailASR-1 maintains competitive performance in single-speaker scenarios, comparable to mainstream ASR models. It also features a negative sample rejection capability, outputting empty text when the target speaker is absent from the mixed speech. Additionally, Xiaomi-CocktailASR-1 supports a Chain-of-Thought (CoT) reasoning mode to provide explicit reasoning steps. Extensive experiments on various synthetic and real-world multispeaker benchmarks demonstrate that Xiaomi-CocktailASR-1 achieves state-of-the-art performance, effectively addressing the cocktail party problem through a unified architecture that balances multispeaker and single-speaker recognition accuracy, along with rejection capability.

cs.SD↗
arXiv2026

EConv-TasNet: Efficient Conv-TasNet for Effective Speech Separation

Conv-TasNet has served as a strong baseline for time-domain speech separation, and many studies have extended it with advanced architectures such as dual-path networks, U-Nets, and attention mechanisms. However, these methods often introduce high computational cost and complexity, limiting their deployment in resource-constrained scenarios. To address this issue, we propose eConv-TasNet, an efficient variant of Conv-TasNet that improves both effectiveness and efficiency without relying on resource-intensive modules. The proposed model consists of a group-wise early-splitting (GES) module and a multi-group feature aggregation (MGFA) module. GES generates discriminative speaker embeddings at intermediate stages, while MGFA progressively aggregates these group-level representations for refined mask estimation. Experimental results show that eConv-TasNet reduces model size by 22.4%, accelerates inference by 18.9%, and improves SI-SNRi by 14.0%-28.0% across three public benchmarks. Moreover, it achieves competitive performance compared with state-of-the-art methods while requiring significantly fewer parameters and lower inference cost. These results demonstrate a favorable efficiency-effectiveness trade-off for edge deployment.

cs.SD↗