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Algorithms such as Latent Dirichlet Allocation (LDA) have achieved significant progress in modeling word document relationships. These algorithms assume each word in the document was generated by a hidden topic and explicitly model the word distribution of each topic as well as the prior distribution over topics in the document. Given these parameters, the(More)
Multibody factorization algorithms give an elegant and simple solution to the problem of structure from motion even for scenes containing multiple independent motions. Despite this elegance, it is still quite difficult to apply these algorithms to arbitrary scenes. First, their performance deteriorates rapidly with increasing noise. Second, they cannot be(More)
We address the problem of segmenting an image sequence into rigidly moving 3D objects. An elegant solution to this problem is the multibody factorization approach in which the measurement matrix is factored into lower rank matrices. Despite progress in factorization algorithms, the performance is still far from satisfactory and in scenes with missing data(More)
We extend the l<inf>o</inf>-norm &#x201C;subspectral&#x201D; algorithms developed for sparse-LDA [5] and sparse-PCA [6] to more general quadratic costs such as MSE in linear (or kernel) regression. The resulting &#x201C;Sparse Least Squares&#x201D; (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem. Specifically,(More)
The problem of “Structure From Motion” is a central problem in vision: given the 2D locations of certain points we wish to recover the camera motion and the 3D coordinates of the points. Under simplified camera models, the problem reduces to factorizing a measurement matrix into the product of two low rank matrices. Each element of the measurement matrix(More)
Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. In this work we focus on the problem of ”structure from motion” in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When(More)
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