2015/11/16 by Benjamin Eltzner, Eltzner, Benjamin, Stephan Huckemann +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #62H30 #FOS: Biological sciences #FOS: Computer and information sciences #Methodology (stat.ME) #Quantitative Methods (q-bio.QM) #RNA Research and Splicing #RNA and protein synthesis mechanisms #RNA regulation and disease #msc:62H30 #q-bio.QM #stat.ME
paper · pdf · doi:10.48550/arxiv.1511.04993
35 pages, 19 figures
arxiv created 2015/11/16 · openalex publication_date 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produces a variety of non-winding, non-dense descriptors. This is achieved by deforming tori into spheres and then using a variant of the recently developed principle nested spheres analysis. This PCA analysis involves a step of small sphere fitting and we provide an improved test to avoid overfitting. However, deforming tori into spheres creates singularities. We introduce a data-adaptive pre-clustering technique to keep the singularities away from the data. For the frequently encountered case that the residual variance around the PCA main component is small, we use a post-mode hunting technique for more fine-grained clustering. Thus in general, there are three successive interrelated key steps of torus-PCA in practice: pre-clustering, deformation, and post-mode hunting. We illustrate our method with two recently studied RNA structure (tori) data sets: one is a small RNA data set which is established as the benchmark for PCA and we validate our method through this data. Another is a large RNA data set (containing the small RNA data set) for which we show that our method provides interpretable principal components as well as giving further insight into its structure.