@article {609355,
	title = {Subspace Estimation from Incomplete Observations: A High-Dimensional Analysis},
	journal = {IEEE Journal of Selected Topics in Signal Processing},
	volume = {12},
	number = {6},
	year = {2018},
	abstract = {We present a high-dimensional analysis of three popular\&nbsp;algorithms, namely, Oja{\textquoteright}s method, GROUSE and PETRELS, for subspace estimation from streaming and highly incomplete observations. \&nbsp;We show that, with proper time scaling, the time-varying\&nbsp;principal angles between the true subspace and its estimates given by the algorithms\&nbsp;converge weakly to deterministic processes when the ambient dimension\&nbsp;\(n\) tends to infinity. Moreover, the limiting processes can be exactly characterized as the unique solutions of certain ordinary differential equations (ODEs). A finite sample bound is also given, showing that the rate of convergence towards such limits is\&nbsp;\(\mathcal{O}(1/\sqrt{n})\). In addition to providing asymptotically exact predictions of the dynamic performance of the algorithms, our high-dimensional analysis yields several insights, including an asymptotic equivalence between Oja{\textquoteright}s method and GROUSE, and a precise scaling relationship linking the amount of missing data to the signal-to-noise ratio. By analyzing the solutions of the limiting ODEs, we also establish phase transition phenomena associated with the steady-state performance of these techniques.},
	url = {https://arxiv.org/abs/1805.06834},
	author = {Chuang Wang and Yonina C. Eldar and Yue M. Lu}
}
