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Estimation of Rank Deficient Matrices from Partial Observations

Summary: Estimation of Rank Deficient Matrices
from Partial Observations:
Two-Step Iterative Algorithms
Rui F. C. Guerreiro and Pedro M. Q. Aguiar
Institute for Systems and Robotics / IST, Lisboa, Portugal
WWW home page: http://www.isr.ist.utl.pt/~{rfcg,aguiar}
Abstract. Several computer vision applications require estimating a
rank deficient matrix from noisy observations of its entries. When the
observation matrix has no missing data, the LS solution of such problem
is known to be given by the SVD. However, in practice, when several
entries of the matrix are not observed, the problem has no closed form
solution. In this paper, we study two iterative algorithms for minimizing
the non-linear LS cost function obtained when estimating rank deficient
matrices from partial observations. In the first algorithm, the iterations
are the well known Expectation and Maximization (EM) steps that have
succeeded in several estimation problems with missing data. The sec-
ond algorithm, which we call Row-Column (RC), estimates, in alternate
steps, the row and column spaces of the solution matrix. Our conclusions
are that RC performs better than EM in what respects to the robustness


Source: Aguiar, Pedro M. Q. - Institute for Systems and Robotics (Lisbon)


Collections: Engineering