Principal Boundary on Riemannian Manifolds. Issue 531 (2nd July 2020)
- Record Type:
- Journal Article
- Title:
- Principal Boundary on Riemannian Manifolds. Issue 531 (2nd July 2020)
- Main Title:
- Principal Boundary on Riemannian Manifolds
- Authors:
- Yao, Zhigang
Zhang, Zhenyue - Abstract:
- Abstract: We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to acquire a classification boundary for the classes with labels, using the intrinsic metric on the manifolds. Motivated by finding an optimal boundary between the two classes, we invent a novel approach—the principal boundary. From the perspective of classification, the principal boundary is defined as an optimal curve that moves in between the principal flows traced out from two classes of data, and at any point on the boundary, it maximizes the margin between the two classes. We estimate the boundary in quality with its direction, supervised by the two principal flows. We show that the principal boundary yields the usual decision boundary found by the support vector machine in the sense that locally, the two boundaries coincide. Some optimality and convergence properties of the random principal boundary and its population counterpart are also shown. We illustrate how to find, use, and interpret the principal boundary with an application in real data. Supplementary materials for this article are available online.
- Is Part Of:
- Journal of the American Statistical Association. Volume 115:Issue 531(2020)
- Journal:
- Journal of the American Statistical Association
- Issue:
- Volume 115:Issue 531(2020)
- Issue Display:
- Volume 115, Issue 531 (2020)
- Year:
- 2020
- Volume:
- 115
- Issue:
- 531
- Issue Sort Value:
- 2020-0115-0531-0000
- Page Start:
- 1435
- Page End:
- 1448
- Publication Date:
- 2020-07-02
- Subjects:
- Classification -- Covering ellipse balls -- Manifold -- SVM -- Vector field
Statistics -- Periodicals
Statistics -- Periodicals
Statistiques -- Périodiques
États-Unis -- Statistiques -- Périodiques
519.5 - Journal URLs:
- http://www.jstor.org/journals/01621459.html ↗
http://www.ingentaconnect.com/content/asa/jasa ↗
http://www.tandfonline.com/loi/uasa20 ↗
http://www.tandfonline.com/ ↗ - DOI:
- 10.1080/01621459.2019.1610660 ↗
- Languages:
- English
- ISSNs:
- 0162-1459
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 4694.000000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 14041.xml