Optimization of symmetric tensor computations

Abstract

For applications that deal with large amounts of high dimensional multi-aspect data, it is natural to represent such data as tensors or multi-way arrays. Tensor computations, such as tensor decompositions, are increasingly being used to extract and explain properties of such data. An important class of tensors is the symmetric tensor, which shows up in real-world applications such as signal processing, biomedical engineering, and data analysis. In this work, we describe novel optimizations that exploit the symmetry in tensors in order to reduce redundancy in computations and storage and effectively parallelize operations involving symmetric tensors. Specifically, we apply our optimizations on the matricized tensor times Khatri Rao product (mttkrp) operation, a key operation in tensor decomposition algorithms such as INDSCAL (individual differences in scaling) for symmetric tensors. We demonstrate improved performance for both sequential and parallel execution using our techniques on various synthetic and real data sets.