Torus Principal Component Analysis with an Application to RNA Structures
نویسندگان
چکیده
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.
منابع مشابه
An application of principal component analysis and logistic regression to facilitate production scheduling decision support system: an automotive industry case
Production planning and control (PPC) systems have to deal with rising complexity and dynamics. The complexity of planning tasks is due to some existing multiple variables and dynamic factors derived from uncertainties surrounding the PPC. Although literatures on exact scheduling algorithms, simulation approaches, and heuristic methods are extensive in production planning, they seem to be ineff...
متن کاملDevelopment of a cell formation heuristic by considering realistic data using principal component analysis and Taguchi’s method
Over the last four decades of research, numerous cell formation algorithms have been developed and tested, still this research remains of interest to this day. Appropriate manufacturing cells formation is the first step in designing a cellular manufacturing system. In cellular manufacturing, consideration to manufacturing flexibility and productionrelated data is vital for cell formation....
متن کاملMultivariate geostatistical analysis: an application to ore body evaluation
It is now common in the mining industry to deal with several correlated attributes, which need to be jointly simulated in order to reproduce their correlations and assess the multivariate grade risk reasonably. Approaches to multivariate simulation which remove the correlation between attributes of interest prior to simulate and then re-impose the relationship afterward have been gaining popula...
متن کاملSparse Structured Principal Component Analysis and Model Learning for Classification and Quality Detection of Rice Grains
In scientific and commercial fields associated with modern agriculture, the categorization of different rice types and determination of its quality is very important. Various image processing algorithms are applied in recent years to detect different agricultural products. The problem of rice classification and quality detection in this paper is presented based on model learning concepts includ...
متن کامل