扩展阿尔法-贝塔散度至复数数据，支持信号处理新应用
The alpha-beta divergence for real and complex data
- 将阿尔法-贝塔散度拓展到复向量，保持数学一致性
- 超参数设为1时退化为欧氏与马哈拉诺比斯距离
- 适用于雷达、通信等复信号处理场景
散度是支撑多数信号处理算法的信息准则基础。阿尔法-贝塔散度家族专为非负数据设计，可参数化并连续插值文献中多种可分离散度。本文将该散度定义扩展至复数数据，特别适用于复向量作为散度输入的情形。该新公式在超参数取1时，退化为经典的欧氏距离和马哈拉诺比斯平方距离。其他超参数选择可得到若干经典散度的可分离与不可分离扩展。在逼近复随机向量的问题中，通过优化阿尔法-贝塔均值失真所获得的中心点具有闭式表达，其解释揭示了散度超参数的不同作用。这些贡献具有广泛潜在应用价值，因许多信号处理领域中的数据本质上为复数。
原文摘要 · Abstract (English)
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously interpolates several separable divergences found in existing literature. This work extends the definition of alpha-beta divergences to accommodate complex data, specifically when the arguments of the divergence are complex vectors. This novel formulation is designed in such a way that, by setting the divergence hyperparameters to unity, it particularizes to the well-known Euclidean and Mahalanobis squared distances. Other choices of hyperparameters yield practical separable and non-separable extensions of several classical divergences. In the context of the problem of approximating a complex random vector, the centroid obtained by optimizing the alpha-beta mean distortion has a closed-form expression, which interpretation sheds light on the distinct roles of the divergence hyperparameters. These contributions may have wide potential applicability, as there are many signal processing domains in which the underlying data are inherently complex.
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。