Spherical Principal Curves
This paper presents a new approach for dimension reduction of data observed in a sphere. Several dimension reduction techniques have recently developed for the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted to implement principal curves on Riemannian manifolds. However, this approach uses approximations to deal with data on Riemannian manifolds, which causes distorted results. In this study, we propose a new approach to construct principal curves on a sphere by a projection of the data onto a continuous curve. Our approach lies in the same line of Hastie and Stuetzle (1989) that proposed principal curves for Euclidean space data. We further investigate the stationarity of the proposed principal curves that satisfy the self-consistency on a sphere. Results from real data analysis with earthquake data and simulation examples demonstrate the promising empirical properties of the proposed approach.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionSimilar Papers 제목 키워드 기반
Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. Principal curves act as a nonlinear generalization of PCA and the pres…
Dimensionality ReductionAn Elliptic Curve Based Solution to the Perspective-Three-Point Problem
The Perspective-Three-Point Problem (P3P) is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the c…
Manifold unwrapping using density ridges
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of pri…
Lower Dimensional Spherical Representation of Medium Voltage Load Profiles for Visualization, Outlier Detection, and Generative Modelling
This paper presents the spherical lower dimensional representation for daily medium voltage load profiles, based on principal component analysis. The objective is to unify and simplify the tasks for (i) clustering visual…
ARCClusteringOutlier DetectionMultiple penalized principal curves: analysis and computation
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are…