Sketches by MoSSaRT: Representative selection from manifolds with gross sparse corruptions
Sketches by MoSSaRT: Representative selection from manifolds with gross sparse corruptions
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DOI：
10.1016/j.patcog.2021.108454
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
M. Sedghi;M. Georgiopoulos;George K. Atia
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文献类型：
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作者：
M. Sedghi;M. Georgiopoulos;George K. Atia
传统的采样技术无法选择编码非线性流形底层构象的代表。如果数据受到严重稀疏损坏的污染，问题就会加剧。在本文中，我们提出了一种数据选择方法，称为MoSSaRT，它绘制了严重损坏的流形结构的鲁棒性和描述性草图。基于明确的随机转换，我们获得了数据关系的明智设计表示，这有助于多种选择方法同时考虑对所选代表的总体腐败，描述性和新颖性的鲁棒性。我们的模型适合于一个具有高效并行算法的凸公式，它与我们的随机矩阵结构相结合，产生了一个高度可扩展的实现。理论分析保证了近似函数对期望目标函数的概率收敛，并揭示了所选代表的深刻的几何特征。最后，在真实数据和合成数据上进行的实验证明，MoSSaRT的性能大大优于最先进的算法。
Conventional sampling techniques fall short of selecting representatives that encode the underlying conformation of non-linear manifolds. The problem is exacerbated if the data is contaminated with gross sparse corruptions. In this paper, we present a data selection approach, dubbed MoSSaRT, which draws robust and descriptive sketches of grossly corrupted manifold structures. Built upon an explicit randomized transformation, we obtain a judiciously designed representation of the data relations, which facilitates a versatile selection approach accounting for robustness to gross corruption, descriptiveness and novelty of the chosen representatives, simultaneously. Our model lends itself to a convex formulation with an efficient parallelizable algorithm, which coupled with our randomized matrix structures gives rise to a highly scalable implementation. Theoretical analysis guarantees probabilistic convergence of the approximate function to the desired objective function and reveals insightful geometrical characterization of the chosen representatives. Finally, MoSSaRT substantially outperforms the state-of-the-art algorithms as demonstrated by experiments conducted on both real and synthetic data.