Vector Representation of Arbitrary-sized Matrices

In the thesis, we aim to compare matrices that can vary in size or shape, and their columns/rows are permutation invariant. We propose a general solution to such problem by using the vector representation to represent a matrix. Several feature representations are invented and investigated in the thesis, based on histogram, statistics, eigenvalues/singular values and multiple instance representation. They are used to identify structural patterns in an organization management problem based on questionnaire-like data. We further extend the work to other matrix-like data (e.g. graph data) to verify the efficacy of our proposed method.