By René Vidal, Yi Ma, Shankar Sastry
This ebook offers a entire creation to the newest advances within the mathematical thought and computational instruments for modeling high-dimensional information drawn from one or a number of low-dimensional subspaces (or manifolds) and most likely corrupted by way of noise, gross blunders, or outliers. This not easy job calls for the advance of latest algebraic, geometric, statistical, and computational equipment for effective and strong estimation and segmentation of 1 or a number of subspaces. The booklet additionally offers attention-grabbing real-world purposes of those new tools in photo processing, photograph and video segmentation, face attractiveness and clustering, and hybrid procedure identity and so on.
This ebook is meant to function a textbook for graduate scholars and starting researchers in info technological know-how, laptop studying, machine imaginative and prescient, picture and sign processing, and platforms conception. It comprises plentiful illustrations, examples, and routines and is made principally self-contained with 3 Appendices which survey uncomplicated ideas and rules from statistics, optimization, and algebraic-geometry utilized in this book.
René Vidal is a Professor of Biomedical Engineering and Director of the imaginative and prescient Dynamics and studying Lab on the Johns Hopkins college.
Yi Ma is govt Dean and Professor on the college of knowledge technology and expertise at ShanghaiTech college. S. Shankar Sastry is Dean of the varsity of Engineering, Professor of electric Engineering and desktop technology and Professor of Bioengineering on the collage of California, Berkeley.
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Extra resources for Generalized Principal Component Analysis
A typical video sequence contains multiple activities or events separated in time. 6(a) shows a news sequence in which the host is interviewing a guest and the camera is switching between the frames containing the host, the guest, or both the host and the guest. The problem is to separate the video sequence into subsequences, so that each subsequence corresponds to one of the three events. For this purpose, we assume that all the frames associated with the same event live in a low-dimensional subspace of the space spanned by all the images in the video, and that different events correspond to different subspaces.
Precisely in this sense, we call the data set X mixed (with respect to the chosen model class M) and call the collection of primitive models fMi gniD1 a mixture model for X . 2. 2 Modeling Mixed Data with a Mixture Model 7 R3 P L1 L2 Fig. 2 A set of sample points in R3 are well fit by a mixture model with two straight lines and a plane. line, plane, or smooth surface in R3 ; however, once they are grouped into three subsets, each subset can be fit well by a line or a plane. Note that in this example, the topology of the data is “hybrid”: two of the subspaces are of dimension one, and the other is of dimension two.
4. 5. 6. 7. Set theory and logic symbols Sets and linear spaces Transformation groups Vector and matrix operations Geometric primitives in space Probability and statistics Graph theory Image formation Throughout the book, every vector is a column vector unless stated otherwise! 0. s/ is true 2 s 2 S means s is an element of set S jSj The number of elements in set S n S1 n S2 is the difference of set S1 minus set S2 S1 S2 means S1 is a proper subset of S2 fsg A set consists of elements like s ! f W D !
Generalized Principal Component Analysis by René Vidal, Yi Ma, Shankar Sastry