Survey:

- Tamara Kolda et al. [Tensor Decompositions and Applications], SIAM Rev., 2009
- (two other new surveys)
- (Anima’s)

**Tensor Formats:**

- Dense tensor
- Traditional linear storage with a specified leading dimension
- (an old one)
- Morton ordering

- Sparse tensor
- COO
- CSF (Compressed Sparse Fiber): S. Smith et al. [Tensor-matrix products with a compressed sparse tensor], SC IA^3, 2015
- F-COO (Flagged-COOrdinate): “A Unified Optimization Approach for Sparse Tensor Operations on GPUs” — Bangtian Liu et al. 2017, ArXiv
- Block-wise

- Semi-sparse tensor
- “mode-specific”
- or sCOO: J. Li et al. [Optimizing sparse tensor times matrix on multi-core and many-core architectures], SC IA^3, 2016
- vCSF

**Sparse Tensor Parallelization:**

- Shared memory systems
- SpTTM:
- J. Li et al. [Optimizing sparse tensor times matrix on multi-core and many-core architectures], SC IA^3, 2016

- CP Decomp:
- S. Smith, et al. [SPLATTt:Efficient and parallel sparse tensor-matrix multiplication]

- Tucker Decomp:

- SpTTM:
- Distributed systems with MapReduce
- CP Decomp:
- GigaTensor: U Kang et al. [GigaTensor: scaling tensor analysis up by 100 times-algorithms and discoveries], SIGKDD, 2012
- HaTen2: I. Jeon et al. [HaTen2: Billion-scale tensor decompositions], ICDM, 2015

- Tucker Decomp
- HaTen2: I. Jeon et al. [HaTen2: Billion-scale tensor decompositions], ICDM, 2015

- CP Decomp:
- Distributed systems with MPI
- CP Decomp:
- DFacTo: [DFacTo: Distributed Factorization of Tensors], NIPS, 2014
- O. Kaya and B. Ucar, [Scalable sparse tensor decompositions in distributed memory systems], SC, 2015

- Tucker Decomp:
- O. Kaya and B. Ucar, [High performance parallel algorithms for the tucker decomposition of sparse tensors], ICPP, 2016

- CP Decomp:
- Accelerators — Intel Xeon Phi
- CP Decomp:

- Accelerators — GPUs
- SpTTM:
- J. Li et al. [Optimizing sparse tensor times matrix on multi-core and many-core architectures], SC IA^3, 2016

- SpTTM:

**Current Development:**

- Fundamental tensor operations
- TTM
- MTTKRP
- Tensor contraction

- Tensor Decompositions
- CP decomposition
- Tucker decomposition
- (Anima’s )
- Tensor Train decomposition
- Hierarchical Tucker decomposition

**Applications:**

- Healthcare
- Deep Learning
- Traditional Machine Learning
- Social Networks

**Software:**

- Matlab
- Tensor Toolbox
- N-way Toolbox

- C++
- CTF (Cyclops Tensor Framework)
- SPLATT
- ParTI