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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)

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)

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)

This paper discusses a novel framework to analyze rotational deformations of real 3D objects. The rotational deformations such as twisting or bending have been observed as the major variation in some medical applications, where the features of the deformed 3D objects are directional data. We propose modeling and estimation of the global deformations in… (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)

- Stephen M. Pizer, Junpyo Hong, Sungkyu Jung, J. S. Marron, Jörn Schulz, Jared Vicory
- 2014

Aims: The single-figure discrete quasi-medial skeletal representation of anatomic objects called the s-rep (Fig.), capturing position (via skeletal samples), orientation (of the quasi-boundary-normals forming the s-rep spokes), and width properties (spoke lengths), has been used for a variety of goals of or using shape statistics. We summarize the… (More)

- Sungkyu Jung
- 2009

This short note describes the procedure for generating random unit vectors following the von Mises-Fisher distribution on the sphere S m−1 for m = 3. We use the fact (from [2], [1] and [3]) that the unit 3-vector X has von Mises-Fisher distribution with modal direction (0, 0, 1) and the concentration parameter κ if and only if X = ((1 − W 2) 1 2 V, W) , (1)… (More)