Min-plus algebraic low rank matrix approximation: a new method for revealing structure in networks

I n this paper we introduce min-plus low rank matrix approximation. By using min and plus rather than plus and times as the basic operations in the matrix multiplication; min-plus low rank matrix approximation is able to detect characteristically different structures than classical low rank approximation techniques such as Principal Component Analysis (PCA). We also show howminplus matrix algebra can be interpreted in terms of shortest paths through graphs, and consequently how min-plus low rank matrix approximation is able to find and express the predominant structure of a network.