用化学催化原理改进医学信号聚类的非负矩阵分解算法
Chem-NMF: Multi-layer $α$-divergence Non-Negative Matrix Factorization for Cardiorespiratory Disease Clustering, with Improved Convergence Inspired by Chemical Catalysts and Rigorous Asymptotic Analysis
- 借鉴化学反应能量屏障理论设计收敛性更强的多层分解方法
- 在生物信号上提升聚类准确率5.6%±2.7%，人脸图像上提升11.1%±7.2%
- 首次从物理化学角度严格分析NMF收敛性，适合医疗数据分析研究者
非负矩阵分解（NMF）是一种无监督学习方法，在音频处理、生物医学信号分析和图像识别等领域提供低秩表示。将α-散度引入NMF可增强优化灵活性，但扩展至多层架构时收敛性难以保证。为此，我们受化学反应中玻尔兹曼概率与能垒的启发，开展理论收敛性分析，提出新型方法Chem-NMF，引入边界因子以稳定收敛过程。据我们所知，这是首个从物理化学视角严格分析NMF算法收敛行为的研究。基于数学上证明的渐近收敛结果，进一步验证其在真实数据上的有效性。实验表明，该算法在生物医学信号上聚类准确率提升5.6%±2.7%，在人脸图像上提升11.1%±7.2%。
原文摘要 · Abstract (English)
Non-Negative Matrix Factorization (NMF) is an unsupervised learning method offering low-rank representations across various domains such as audio processing, biomedical signal analysis, and image recognition. The incorporation of $α$-divergence in NMF formulations enhances flexibility in optimization, yet extending these methods to multi-layer architectures presents challenges in ensuring convergence. To address this, we introduce a novel approach inspired by the Boltzmann probability of the energy barriers in chemical reactions to theoretically perform convergence analysis. We introduce a novel method, called Chem-NMF, with a bounding factor which stabilizes convergence. To our knowledge, this is the first study to apply a physical chemistry perspective to rigorously analyze the convergence behaviour of the NMF algorithm. We start from mathematically proven asymptotic convergence results and then show how they apply to real data. Experimental results demonstrate that the proposed algorithm improves clustering accuracy by 5.6% $\pm$ 2.7% on biomedical signals and 11.1% $\pm$ 7.2% on face images (mean $\pm$ std).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。