 
Summary: Interest Zone Matrix Approximation
Gil Shabat and Amir Averbuch
December 19, 2011
Abstract
We describe an algorithm for matrix approximation when only some its entries are taken into
consideration. The approximation constrain can be any whose approximated solution is known
for the full matrix. For low rank approximations, this type of algorithms appears recently in the
literature under different names, where it usually uses the EM algorithm that maximizes the
likelihood for the missing entries without any relation for mean square error minimization. In
this paper, we show that the algorithm can be extended to different cases other than low rank
approximations under Frobenius norm such as minimizing the Frobenius norm under nuclear
norm contrain, spectral norm constrain, orthogonality constrain and more. We also discuss the
geometric interpretation of the proposed approximation process. Its applications to physics,
electrical engineering and data interpolation problems are described.
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 and computer vision/image
processing [4], to name some. Rank reduction by matrix approximation is important for example
in compression where low rank indicates the existence of redundant information. Therefore, low
rank matrices are better compressed. In statistics, matrix completion can be used for survey
