GPCA with denoising: A moments-based convex approach
GPCA with denoising: A moments-based convex approach
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带降噪的 GPCA：基于矩的凸方法
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
O. Camps
中科院分区：
文献类型：
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作者：
N. Ozay;M. Sznaier;C. Lagoa;O. Camps
本文讨论的问题分割的线性子空间和二次曲面的组合样本数据点损坏（不一定很小）噪声。我们的主要结果表明，这个问题可以减少到最小化的矩阵，其条目是仿射的优化变量的秩，受到凸约束施加这些变量是（未知）的概率分布函数的时刻与有限的支持。利用基于线性矩阵不等式的矩问题的特征，并呼吁众所周知的凸松弛的秩导致一个整体的半定优化问题。我们应用我们的方法，如同时从两个角度来看，二维运动分割和运动分割的问题，并说明我们的配方大大降低了现有方法的噪声敏感性。
This paper addresses the problem of segmenting a combination of linear subspaces and quadratic surfaces from sample data points corrupted by (not necessarily small) noise. Our main result shows that this problem can be reduced to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) probability distribution function with finite support. Exploiting the linear matrix inequality based characterization of the moments problem and appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem. We apply our method to problems such as simultaneous 2D motion segmentation and motion segmentation from two perspective views and illustrate that our formulation substantially reduces the noise sensitivity of existing approaches.