Tensor completion is a problem of filling the missing or unobserved entries of partially
observed tensors. Due to the multidimensional character of tensors in describing complex …

Sparse linear algebra includes the fundamental and important operations in various large-
scale scientific computing and real-world applications. There exists performance bottleneck …

This paper proposes a new storage format for sparse tensors, called Hierarchical
COOrdinate (HiCOO; pronounced:“haiku”). It derives from coordinate (COO) format, arguably …

Low-rank Tucker and CP tensor decompositions are powerful tools in data analytics. The
widely used alternating least squares (ALS) method, which solves a sequence of over …

The Tucker decomposition is a higher-order analogue of the singular value decomposition
and is a popular method of performing analysis on multi-way data (tensors). Computing the …

Sparse matricized tensor times Khatri-Rao product (MTTKRP) is one of the most
computationally expensive kernels in sparse tensor computations. This work focuses on …

In this paper, we develop software for decomposing sparse tensors that is portable to and
performant on a variety of multicore, manycore, and GPU computing architectures. The result …

Given an input tensor, its CANDECOMP/PARAFAC decomposition (or CPD) is a low-rank
representation. CPDs are of particular interest in data analysis and mining, especially when …

Sparse tensor contractions appear commonly in many applications. Efficiently computing a
two sparse tensor product is challenging: It not only inherits the challenges from common …

Multi-dimensional, large-scale, and sparse data, which can be neatly represented by sparse
tensors, are increasingly used in various applications such as data analysis and machine …