Energy Landscape for large average submatrix detection problems in Gaussian random matrices

Understand

The problem of finding large average submatrices of a real-valued matrix arises in the exploratory analysis of data from a variety of disciplines, ranging from genomics to social sciences.

• In this paper we provide a detailed asymptotic analysis of large average submatrices of an $n \times n$ Gaussian random matrix.
• The first part of the paper addresses global maxima.
• For fixed $k$ we identify the average and the joint distribution of the $k \times k$ submatrix having largest average value.