SYMMETRIC GENERALIZED CP TENSOR DECOMPOSITION

Abstract

Canonical Polyadic (CP) tensor decomposition is an emerging workhorse algo rithm in data science for fnding underlying low-dimensional structure in tensor data (i.e., N-way arrays). Generalized CP (GCP) decompositions generalize conventional CP by allowing general loss functions that can be more appropriate for data such as bi nary and count data, or that can allow desired statistical properties such as robustness to outliers. In this thesis, we develop a new Symmetric GCP (SymGCP) decomposition for data tensors that exhibit symmetry across some of their dimensions, which arises in applications such as dynamic social networks and higher-order statistical moments. SymGCP accounts for the symmetry in the data by producing a decomposition with matching symmetry, which involves developing a new corresponding optimization algo rithm. To enable SymGCP to scale to large tensors, we develop an effcient stochastic approach for computing SymGCP decompositions. Finally, we demonstrate the utility of SymGCP on a variety of experiments with real and synthetic data.