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Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear, ``branched, ``disconnected, ``bended, ``curved, ``heterogeneous, or, more general, ``complex. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localiz
This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are optimal for ex
The volume of data that will be produced by the next generation of astrophysical instruments represents a significant opportunity for making unplanned and unexpected discoveries. Conversely, finding unexpected objects or phenomena within such large v
We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen--Lo`eve expansion of the unobserved derivatives and leads t
The U.S. Virtual Astronomical Observatory was a software infrastructure and development project designed both to begin the establishment of an operational Virtual Observatory (VO) and to provide the U.S. coordination with the international VO effort.
Principal manifolds are defined as lines or surfaces passing through ``the middle of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Rec