用相关性映射揭示复杂数据中的规律，区分不同物理区域。
Mapping correlations and coherence: adjacency-based approach to data visualization and regularity discovery
- 基于斯托克斯参数构建相关性地图，捕捉空间上变化的相关模式。
- 可将区域划分为具有不同相关类型的小区域，对应物理或气候区。
- 方法简单高效，适合物理系统、气候等复杂数据的规律发现。
科学的发展不断重塑人类对自然的认知。有效观察数据中的结构与模式是发现规律、构建理论的关键步骤。随着数据日益复杂，系统性揭示规律成为挑战。相关性是描述数据规律的常用且有效手段，但复杂模式下的空间非均匀性和复杂性常会削弱相关性。本文提出一种算法，通过全面考虑相关矢量的双重对称性（利用斯托克斯参数），生成反映相关性类型与强度的地图。该方法能实现物理量间相关性的空间解析，使一个区域常被划分为具有不同相关类型的子区域。这些子区域对应于物理系统中的物理态，或气候图中的气候带。方法简洁，适用于多种数据，尤其在揭示物理系统等复杂体系的规律方面极具价值。作为新且高效的可视化方法，有望推动规律发现的计算方法发展。
原文摘要 · Abstract (English)
The development of science has been transforming man's view towards nature for centuries. Observing structures and patterns in an effective approach to discover regularities from data is a key step toward theory-building. With increasingly complex data being obtained, revealing regularities systematically has become a challenge. Correlation is a most commonly-used and effective approach to describe regularities in data, yet for complex patterns, spatial inhomogeneity and complexity can often undermine the correlations. We present an algorithm to derive maps representing the type and degree of correlations, by taking the two-fold symmetry of the correlation vector into full account using the Stokes parameter. The method allows for a spatially resolved view of the nature and strength of correlations between physical quantities. In the correlation view, a region can often be separated into different subregions with different types of correlations. Subregions correspond to physical regimes for physical systems, or climate zones for climate maps. The simplicity of the method makes it widely applicable to a variety of data, where the correlation-based approach makes the map particularly useful in revealing regularities in physical systems and alike. As a new and efficient approach to represent data, the method should facilitate the development of new computational approaches to regularity discovery.
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