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* [[Tucker decomposition]];
* [[matrix product state]]s, and operators or tensor trains;
* [[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 web |last1=Lathauwer |first1=Lieven De |title=Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness |url=https://epubs.siam.org/doi/abs/10.1137/070690729|doi=10.1137/070690729}}</ref><ref>{{cite web |last1=Gujral |first1=Ekta |title=Beyond rank-1: Discovering rich community structure in multi-aspect graphs |url=https://dl.acm.org/doi/abs/10.1145/3366423.3380129|doi=10.1145/3366423.3380129}}</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
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