Titlebook: Generalized Principal Component Analysis; René Vidal,Yi Ma,S.S. Sastry Textbook 2016 Springer-Verlag New York 2016 Principal component ana

NEEDY

Nonlinear and Nonparametric Extensionsl circle embedded in a high-dimensional space, whose structure is not well captured by a one-dimensional line. More generally, a collection of face images observed from different viewpoints is not well approximated by a single linear or affine subspace, as illustrated in the following example.

Grasping

Acupressure

Statistical Methodse in the data, they do not make explicit assumptions about the distribution of the noise or the data inside the subspaces. Therefore, the estimated subspaces need not be optimal from a statistical perspective, e.g., in a maximum likelihood (ML) sense.

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Motion Segmentationpaces to represent and segment time series, e.g., video and motion capture data. In particular, we will use different subspaces to account for multiple characteristics of the dynamics of a time series, such as multiple moving objects or multiple temporal events.

Spartan

领巾

衍生

Optical Physics and EngineeringPrincipal component analysis (PCA) is the problem of fitting a low-dimensional affine subspace to a set of data points in a high-dimensional space. PCA is, by now, well established in the literature, and has become one of the most useful tools for data modeling, compression, and visualization.

Hectic

https://doi.org/10.1007/978-3-319-28100-1In the previous chapter, we considered the PCA problem under the assumption that all the sample points are drawn from the same statistical or geometric model: a low-dimensional subspace.

伪造

Michael Mix MD,Anurag K. Singh MDIn this chapter, we consider a generalization of PCA in which the given sample points are drawn from an unknown arrangement of subspaces of unknown and possibly different dimensions.

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Mediation and the Ending of ConflictsIn this and the following chapters, we demonstrate why multiple subspaces can be a very useful class of models for image processing and how the subspace clustering techniques may facilitate many important image processing tasks, such as image representation, compression, image segmentation, and video segmentation.