论文标题
曲线概率主成分分析
Torus Probabilistic Principal Component Analysis
论文作者
论文摘要
分析变量代表方向或角度的非生物信息学，生物学和地质等非欧几里得空间中的数据带来了独特的挑战。在单变量情况下，这种类型的数据称为循环数据，可以称为球形或在多元上下文中的球形。在本文中，我们介绍了针对圆环（或圆环）数据设计的概率主成分分析（PPCA）的新型扩展，称为曲盘概率PCA（TPPCA）。我们提供了用于实施TPPCA的详细算法，并证明了其对圆环数据的适用性。为了评估TPPCA的功效，我们使用仿真研究和三个实际数据集进行了比较分析。我们的发现突出了TPPCA在处理圆环数据中的优势和局限性。此外，我们根据似然比统计数据提出统计测试，以确定组件的最佳数量，从而增强了TPPCA对现实世界应用的实际实用性。
Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed spherical or toroidal in multivariate contexts. In this paper, we introduce a novel extension of Probabilistic Principal Component Analysis (PPCA) designed for toroidal (or torus) data, termed Torus Probabilistic PCA (TPPCA). We provide detailed algorithms for implementing TPPCA and demonstrate its applicability to torus data. To assess the efficacy of TPPCA, we perform comparative analyses using a simulation study and three real datasets. Our findings highlight the advantages and limitations of TPPCA in handling torus data. Furthermore, we propose statistical tests based on likelihood ratio statistics to determine the optimal number of components, enhancing the practical utility of TPPCA for real-world applications.
