Guest editorial: special issue on data mining with matrices, graphs and tensors

Abstract

The field of data mining increasingly adapts methods and algorithms from advanced matrix computations, graph theory and optimization. In these methods, the data is described using matrix representations (graphs are represented by their adjacency matrices) and the data mining problem is formulated as an optimization problem with matrix variables. With these, the data mining task becomes a process of minimizing or maximizing a desired objective function of matrix variables. Prominent examples include spectral clustering, non-negative matrix factorization, Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) related clustering and dimension reduction, tensor analysis and L-1 regularization. These matrix-formulated optimization-centric methodologies are rapidly becoming a significant part of data mining, and have evolved into a popular and rapidlyexpanding research area for solving challenging data mining problems. First, they are amenable to vigorous analysis and benefit from the well-established knowledge in linear algebra, graph theory and optimization accumulated through centuries. Second, they can be efficiently computed thanks to the mature software tools developed by scientific computing communities. Third, they are simple to implement and easy to