 
Summary: Interest Zone Matrix Approximation
Gil Shabat and Amir Averbuch
February 19, 2011
Abstract
We present an algorithm for low rank approximation of matrices where only some
of the entries in the matrix are taken into consideration. This algorithm appears in
recent literature under different names, where it is described as an EM based algorithm
that maximizes the likelihood for the missing entries without any relation for the mean
square error minimization. When the algorithm is minimized from a meansquareerror
point of view, we prove that the error produced by the algorithm is monotonically
decreasing. It guarantees to converge to a local MSE minimum. We also show that
an extension of the EM based algorithm for weighted low rank approximation, which
appeared in recent literature, claiming that it converges to a local minimum of the
MSE is wrong. Finally, we show the use of the algorithm in different applications for
physics, electrical engineering and data interpolation.
Keywords: Singular Value Decomposition, matrix completion, matrix approximation
1 Introduction
Matrix completion and matrix approximation are important problems in a variety of fields
such as statistics [1], biology [2], statistical machine learning [3], signal processing and com
puter vision/image processing [4]. Rank reduction by matrix approximation is important for
