Tensor Decompositions for Analyzing Multi-link Graphs

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Specially Structured Tensors• Tucker Tucker Tensor• Tucker Kruskal Tensor TensorIn matrix form:In matrix form:
Tucker DecompositionThree-mode factor analysis [Tucker, 1966]Three-mode PCA [Kroonenberg, et al. 1980]N-mode PCA [Kapteyn et al., 1986]Higher-order SVD (HO-SVD) [De Lathauwer et al., 2000]K x TCI x J x KI x RJ x S≈AR x S x TBGiven A, B, C, the optimal core is:• A, B, and C may be orthonormal (generally, full column rank)• is not diagonal• Decomposition is not unique
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 and 8: Tensor n-Mode MultiplicationTensor
Page 9: Specially Structured TensorsTucker
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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