Tensors are multi-way arrays that generalize matrices and vectors. For example, a Rubik's cube filled with numbers can be thought of as a 3x3x3 tensor. Often it is natural and beneficial to store and analyze data in higher dimensional tensors instead of matrices. Especially the investigation of rank decompositions of data tensors has been powerful in many applications. The aim of this seminar is to study how tensors have been useful in different applications, eg medicine, neuroscience, signal processing, chemometrics etc.
In the first seminar, I will give an introductory lecture about tensors, tensor rank and tensor decompositions. In the rest of the seminars, seminar participants will present articles that can be chosen from the literature list below or according to one's interests and specialization (please confirm the presentation topic with me). The target audience are Masters and PhD students from all departments at Aalto.
Grading: pass/fail. Making a presentation and attending five out of six seminars are required for passing the course. Presentations can be made alone or in small groups.
When and where: During IV period, Wednesdays 10:15-12:00 in M2 (Otakaari 1). First seminar is on 22.02.2017.
Please contact me by e-mail (email@example.com) if you think about attending the seminar, would like to choose a topic or have other questions.
General background on tensors:
- Comon, Pierre. "Tensors: a brief introduction." IEEE Signal Processing Magazine 31.3 (2014): 44-53. https://hal.archives-ouvertes.fr/hal-00923279v4/document
- Kolda, Tamara G., and Brett W. Bader. "Tensor decompositions and applications." SIAM review 51.3 (2009): 455-500. http://epubs.siam.org/doi/pdf/10.1137/07070111X
- Sun, Shiliang. "A survey of multi-view machine learning." Neural Computing and Applications 23.7-8 (2013): 2031-2038. http://link.springer.com/article/10.1007/s00521-013-1362-6
Possible articles to present:
- Acar, Evrim, et al. "Multiway analysis of epilepsy tensors." Bioinformatics 23.13 (2007): i10-i18. https://academic.oup.com/bioinformatics/article/23/13/i10/234097/Multiway-analysis-of-epilepsy-tensors
- Andersen, Charlotte Møller, and R. Bro. "Practical aspects of PARAFAC modeling of fluorescence excitation‐emission data." Journal of Chemometrics 17.4 (2003): 200-215.http://onlinelibrary.wiley.com/doi/10.1002/cem.790/epdf
- Carroll, J. Douglas, and Jih-Jie Chang. "Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition." Psychometrika 35.3 (1970): 283-319.
- Hore, Victoria, et al. "Tensor decomposition for multiple-tissue gene expression experiments." Nature Genetics 48.9 (2016): 1094-1100. http://www.nature.com/ng/journal/v48/n9/pdf/ng.3624.pdf
- Lim, Lek-Heng, and Pierre Comon. "Blind multilinear identification." IEEE Transactions on Information Theory 60.2 (2014): 1260-1280. https://www.stat.uchicago.edu/~lekheng/work/inform.pdf
- Sankaranarayanan, Preethi, et al. "Tensor GSVD of patient-and platform-matched tumor and normal DNA copy-number profiles uncovers chromosome arm-wide patterns of tumor-exclusive platform-consistent alterations encoding for cell transformation and predicting ovarian cancer survival." PloS one 10.4 (2015): e0121396. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0121396
- Seigal, Anna, et al. "Tensors and algebra give interpretable groups for crosstalk mechanisms in breast cancer." arXiv preprint arXiv:1612.08116 (2016). https://arxiv.org/pdf/1612.08116v1.pdf
22.2 Kaie: Introduction to tensors, tensor rank and tensor decompositions
15.3 Mateo: Blind multilinear identification
22.3 Matti: Matrix multiplication tensor
Petteri: Arithmetic circuits for multilinear tasks
Piermarco: Revisit Joint Channel and Source Estimation example