子空间识别从部分数据的算法局部收敛性
Local Convergence of an Algorithm for Subspace Identification from Partial Data
AI总结：
本文研究了GROUSE算法在部分数据下的局部收敛性，基于随机向量和子空间与坐标方向的不相干性，证明了线性收敛率。
摘要：
GROUSE（Grassmannian Rank-One Update Subspace Estimation）是一种迭代算法，用于从随机向量的部分观测数据中识别R^n中的线性子空间。本文在随机向量、每次迭代中观测子集的随机性和子空间与坐标方向的不相干性假设下，研究了GROUSE的局部收敛性。在某些假设下，证明了期望线性收敛率。每次迭代中揭示完整随机向量的情况允许更简单的分析，并被描述。GROUSE与增量SVD方法和优化中的梯度投影算法有关。
英文摘要：
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of R^n from data consisting of partial observations of random vectors from that subspace. This paper examines local convergence properties of GROUSE, under assumptions on the randomness of the observed vectors, the randomness of the subset of elements observed at each iteration, and incoherence of the subspace with the coordinate directions. Convergence at an expected linear rate is demonstrated under certain assumptions. The case in which the full random vector is revealed at each iteration allows for much simpler analysis, and is also described. GROUSE is related to incremental SVD methods and to gradient projection algorithms in optimization.
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