Tensor Decompositions for Analyzing Multi-link Graphs

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Outer, Kronecker, & Khatri-Rao Products3-Way Outer ProductMatrix Kronecker ProductM x NP x QMP x NQ=Matrix Khatri-Rao ProductRank-1 TensorM x R N x R MN x RObserve: For two vectors a and b, a ◦ b and a ⊗ b have the same elements,but one is shaped into a matrix and the other into a vector.
Specially Structured TensorsTucker Tensor• Tucker TensorKruskal Tensor• Tucker TensorOurNotationOurNotationK x TK x RWWI x J x KI x RJ x SI x J x KI x Rw 1w RJ x R=UR x S x TV==Uu 1v 1+…+R x R x RVu Rv R
Page 1 and 2: Tensor Decompositionsfor AnalyzingM
Page 3 and 4: Multi-Link GraphsTermsDocuments•
Page 5 and 6: TensorsAn I × J × K tensorKColumn
Page 7: Tensor n-Mode MultiplicationTensor
Page 11 and 12: Tucker DecompositionThree-mode fact
Page 13 and 14: CP Alternating Least Squares (CP-AL
Page 15 and 16: Analyzing SIAM Publication Data1999
Page 17 and 18: SIAM Data: Tensor Construction• w
Page 19 and 20: SIAM Data: Document SimilarityLink
Page 21 and 22: SIAM Data: Author Disambiguation•
Page 23 and 24: SIAM Data: Author DisambiguationDis
Page 25 and 26: SIAM Data: Journal Prediction• CP
Page 27 and 28: Tensors and HPC• Sparse tensors-
Page 29 and 30: Thank YouTensor Decompositionsfor A
Page 31 and 32: High-Order Analogue of the Matrix S

Tensor Decompositions for Analyzing Multi-link Graphs

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