Factor Analysis of Incidence Data via Novel Decomposition of Matrices

Matrix decomposition methods provide representations of an object-variable data matrix by a product of two different matrices, one describing relationship between objects and hidden variables or factors, and the other describing relationship between the factors and the original variables. We present a novel approach to decomposition and factor analysis of matrices with incidence data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red or a person performs well in a test. We assume that the grades belong to a scale bounded by 0 and 1 which is equipped with certain aggregation operators and forms a complete residuated lattice. We present an approximation algorithm for the problem of decomposition of such matrices with grades into products of two matrices with grades with the number of factors as small as possible. Decomposition of binary matrices into Boolean products of binary matrices is a ...

• Type: Conference
• Year: 2009
• Where: ICFCA
• Authors: Radim Belohlávek, Vilém Vychodil
• Keywords: Binary Matrices, Decomposition, Formal Languages, ICFCA 2009, Matrix Decomposition Methods