Decompositions of a Higher-Order Tensor in Block Terms - Part II: Definitions and Uniqueness

By Lieven De Lathauwer. SIAM Journal on Matrix Analysis and Applications, 2008

519 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/abf8552208d52de45fdaa551b3b8fe69bea5cea8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jianfeng Gao
2. Xiaodong He
3. Derya Soydaner
4. Li Deng
5. Mohit Bansal
6. Nan Duan
7. M. Zhou
8. Zhe Gan

In Computational Mathematics

1. Derya Soydaner
2. Pierre-Antoine Absil
3. Mariya Ishteva
4. S. Van Huffel
5. Deren Han
6. Xiaodong He
7. Yusuke Ijima
8. Hiroki Kanagawa

In Computer Networks and Communications

1. Derya Soydaner
2. Mariya Ishteva
3. S. Van Huffel
4. Pierre-Antoine Absil
5. Xiaodong He
6. Li Deng
7. Chao Zhang
8. Zichao Yang

Citations in the corpus

• New ALS Methods With Extrapolating Search Directions and Optimal Step Size for Complex-Valued Tensor Decompositions (2011, background): “[8], [9] and by De Lathauwer [12], [13], [22], [25].”
• Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects (2015, background): “Tensor decompositions that can be reformulated as M ( m ) ( ( z )) include rank-1 decompositions (CPD, PARAFAC), decompositions into rank 1 terms, Tucker, BTD, PARAFAC2 [70], and many others.”
• Lightweight LPCNet-Based Neural Vocoder with Tensor Decomposition (2020, background): “To further enhance the speed, we will explore the block-term decomposition [20] in the future that can avoid this operation and has fewer parameters [21].”
• A Tensorized Transformer for Language Modeling (2019, methodology): “Recently, Block-Term Tensor Decomposition(BTD) [9] is used to compress recurrent neural networks (RNNs) [38].”
• On the best low multilinear rank approximation of higher-order tensors (2010, methodology): “A unifying framework for Tucker/HOSVD and CANDE-COMP/PARAFAC is given by the block term decompositions [18, 19 , 26].”
• Multimodal Intelligence: Representation Learning, Information Fusion, and Applications (2019, methodology): “block-based super-diagonal fusion framework, was proposed to perform block-term decomposition [178] to compute bilinear pooling [179].”
• Attention mechanism in neural networks: where it comes and where it goes (2022, methodology): “To this end, it uses a novel selfattention model multi-linear attention with Block-Term Tensor Decomposition (BTD) [137].”
• Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors (2008, background): “Recently, block term decompositions have been proposed as a hybrid between Tucker/HOSVD and CANDECOMP/PARAFAC [11, 12, 18].”
• Tensor Algebra and Multidimensional Harmonic Retrieval in Signal Processing for MIMO Radar (2010, unknown): “In this situation, the number of targets can still be estimated by the core consistency diagnostic (CORCONDIA) procedure [50].”
• TensoRF: Tensorial Radiance Fields (2022, methodology): “By combining CP and Tucker decomposition, block term decomposition (BTD) has been proposed with its many variants [9] and used in many vision and learning tasks [45,1,44].”