Tensor Decompositions for Analyzing Multi-link Graphs

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SIAM Data: Journal PredictionGraph of confusion matrix• Layout via Barnes-Hut• Node color = cluster• Node size = % correct (0-66)
Tensors and HPC• Sparse tensors– Data partitioning and load balancing issues– Partially sorted coordinate format• Optimize unfolding for single mode• Scalable decomposition algorithms– CP, Tucker, PARAFAC2, DEDICOM, INDSCAL, …• Different operations, data partitioning issues• Applications– Network analysis, web analysis, multi-way clustering,data fusion, cross-language IR, feature vector generation• Different operations, data partitioning issues• Leverage Sandia’s Trilinos packages– Data structures, load balancing, SVD, Eigen.
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 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: SIAM Data: Journal Prediction• CP
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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