Tensor Decompositions for Analyzing Multi-link Graphs

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CANDECOMP/PARAFAC (CP) DecompositionCI x J x KI x RK x RJ x R≈B=+…+AR x R x R• CANDECOMP = Canonical Decomposition [Carroll & Chang, 1970]• PARAFAC = Parallel Factors [Harshman, 1970]• Core is diagonal (specified by the vector λ)• Columns of A, B, and C are not orthonormal
CP Alternating Least Squares (CP-ALS)= + + …Khatri-Rao PseudoinverseI x J x KFind all the vectors in onedirection simultaneously• Fix A, B, and Λ, solve <strong>for</strong> C:• Optimal C is the least squares solution:[Smilde et al., 2004]• Successively solve <strong>for</strong> each component (C,B,A)
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 and 10: Specially Structured TensorsTucker
Page 11: Tucker DecompositionThree-mode fact
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•
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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

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