Tensor Decompositions for Analyzing Multi-link Graphs

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SIAM Data: CP Applications• Community Identification– Communities of papers connected by different link types• Latent Document Similarity– Using tensor decompositions for LSA-like analysis• Analysis of a Body of Work via Centroids– Body of work defined by query terms– Body of work defined by authorship• Author Disambiguation– List of most prolific authors in collection changes– Multiple author disambiguation• Journal Prediction– Co-reference information to define journal characteristics
SIAM Data: Document SimilarityLink Analysis: Hubs and Authorities on the World Wide Web,C.H.Q. Ding, H. Zha, X. He, P. Husbands, and H.D. Simon, SIREV, 2004.• CP decomposition, R = 10:• Similarity scores:Interior Point Methods (Not related)Sparse approximate inverses (Arguably distantly related)Graph Partitioning(Related)
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: SIAM Data: Tensor Construction• w
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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