Tensor Analysis for Networks and Sparse Data

Tensor Analysis for Networks and Sparse Data: Tensors are higher-order or n-way arrays. They have proven useful in a wide variety of data analysis tasks in applications ranging from chemometrics to sociology to neuroscience, and much more. We consider the utility of canonical polyadic (aka CANDECOMP or PARAFAC) tensor decompositions and briefly survey. Tensors are useful for analyzing large-scale networks with attributed connections. For instance, a time-evolving network can be naturally expressed as a third-order tensor. We explore the applicability of tensor analysis, its connection to matrix-based methods, different statistical assumptions and corresponding optimization objective functions, and how to efficiently handle spares data. We illustrate the utility of tensor decompositions with several examples.