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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)
A series of trans-stilbene derivatives containing a 3,5-dimethoxyphenyl moiety were prepared through a new efficient solution phase synthetic pathway, and their inhibitory activities were evaluated on human cytochrome P450s (CYP) 1A1, 1A2, and 1B1 to find a potent and selective CYP1B1 inhibitor. We found that a substituent at the 2-position of the stilbene(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)
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)
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)
Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with N sets of observations, where each set is labeled with class information, and the prediction of a class label is performed also with a set of observations. Data sets(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)