Tensor decomposition: Difference between revisions

Revision as of 19:39, 12 March 2023

Revision as of 19:41, 12 March 2023

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* [[Online Tensor Decompositions]]<ref>{{cite journal |last1=Gujral |first1=Ekta |last2=Pasricha |first2=Ravdeep |last3=Papalexakis |first3=Evangelos E. |title=SamBaTen: Sampling-based Batch Incremental Tensor Decomposition|journal=Proceedings of the 2018 SIAM International Conference on Data Mining |date=7 May 2018 |doi=10.1137/1.9781611975321}}</ref><ref>{{cite journal |last1=Gujral |first1=Ekta |last2=Papalexakis |first2=Evangelos E. |title=OnlineBTD: Streaming Algorithms to Track the Block Term Decomposition of Large Tensors |journal=2020 IEEE 7th International Conference on Data Science and Advanced Analytics (DSAA) |date=9 October 2020 |doi=10.1109/DSAA49011.2020.00029}}</ref><ref name="ektagujral">{{Cite journal |last=Gujral |first=Ekta |date=2022 |title=Modeling and Mining Multi-Aspect Graphs With Scalable Streaming Tensor Decomposition |url=https://arxiv.org/abs/2210.04404 |doi=10.48550/ARXIV.2210.04404}}</ref>

* [[hierarchical Tucker decomposition]]; and

* [[block term decomposition]]<ref>{{Cite journal |last=De Lathauwer |first=Lieven |date=2008-01 |title=Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness |url=http://epubs.siam.org/doi/10.1137/070690729 |journal=SIAM Journal on Matrix Analysis and Applications |language=en |volume=30 |issue=3 |pages=1033–1066 |doi=10.1137/070690729 |issn=0895-4798}}</ref><ref>{{Cite journal |last=Gujral |first=Ekta |last2=Pasricha |first2=Ravdeep |last3=Papalexakis |first3=Evangelos |date=2020-04-20 |title=Beyond Rank-1: Discovering Rich Community Structure in Multi-Aspect Graphs |url=https://dl.acm.org/doi/10.1145/3366423.3380129 |journal=Proceedings of The Web Conference 2020 |language=en |___location=Taipei Taiwan |publisher=ACM |pages=452–462 |doi=10.1145/3366423.3380129 |isbn=978-1-4503-7023-3}}</ref>

==Preliminary Definitions and Notation==

This section introduces basic notations and operations that are widely used in the field. A summary of symbols that we use through the whole thesis can be found in the table.