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- Sungkyu Jung, J S Marron
- 2008

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows (i.e. High Dimension, Low Sample Size (HDLSS)) are becoming increasingly relevant. We investigate the asymptotic behavior of the… (More)

In High Dimension, Low Sample Size (HDLSS) data situations, where the dimension d is much larger than the sample size n, principal component analysis (PCA) plays an important role in statistical analysis. Under which conditions does the sample PCA well reflect the population covariance struc-ture? We answer this question in a relevant asymptotic context… (More)

A novel backwards viewpoint of Principal Component Analysis is proposed. In a wide variety of cases, that fall into the area of Object Oriented Data Analysis, this viewpoint is seen to provide much more natural and accessable analogs of PCA than the standard forward viewpoint. Examples considered here include principal curves, landmark based shape analysis,… (More)

We seek a form of object model that exactly and completely captures the interior of most non-branching anatomic objects and simultaneously is well suited for probabilistic analysis on populations of such objects. We show that certain nearly medial, skeletal models satisfy these requirements. These models are first mathematically defined in continuous… (More)

- Sungkyu Jung
- 2011

We consider dimension reduction of multivariate data under the existence of various types of auxiliary information. We propose a criterion that provides a series of orthogonal directional vectors, that form a basis for dimension reduction. The proposed method can be thought of as an extension from the continuum regression, and the resulting basis is called… (More)