Time-evolving data mining

The thesis will focus on the use of various tensor factorization models (multi-way data analysis) to capture the underlying patterns as well as evolution of those patterns in multi-way data. The primary application of interest will be a neuroscience application.
Master

Time-evolving data can often be represented as higher-order tensors, with one of the modes being the time mode. Tensor factorizations [1, 2], i.e., extensions of matrix factorizations to higher-order tensors, have proved useful in terms of capturing the underlying patterns in higher-order data sets. There are several approaches to incorporate the special structure of the temporal mode such as using temporal patterns in a subsequent time series analysis to make future predictions [3], and incorporating regularizers that takes into account temporal correlations [4]. However, the common assumption is that underlying patterns do not evolve in time.

Goal

In this project, we will use various tensor factorization methods that take into account the evolution of underlying patterns to analyze neuroimaging signals from patients with various disorders and healthy controls during different tasks. Available tensor methods as well as their modifications incorporating various constraints to improve interpretability and uniqueness of the models will be assessed on both simulated and real data sets.

Learning outcome

The project will develop both algorithmic and data analysis skills. Students will also gain experience in interdisciplinary research.

Qualifications

Linear algebra and programming skills (BS in Computer Science/Applied Math/Statistics, excellent oral and written English skills).

Supervisors

Evrim Acar Ataman

Collaboration partners

University of Maryland, Baltimore, MD

References

  1. E. Acar, B. Yener. Unsupervised Multiway Data Analysis: A Literature Survey, IEEE Transactions on Knowledge and Data Engineering, 21(1): 6-20, 2009
  2. T. G. Kolda, B. W. Bader. Tensor Decompositions and Applications, SIAM Review, 51(3): 455-500, 2009
  3. D. M. Dunlavy, T. G. Kolda, E. Acar, Temporal link prediction using matrix and tensor factorizations, ACM Transactions on Knowledge and Data Engineering, 5(2):10: 2011
  4. K. Takeuchi, H. Kashima, and N. Ueda, Autoregressive tensor factorization for spatio-temporal predictions, Proceedings of the IEEE International Conference on Data Mining (ICDM), pp. 1105–1110, 2017

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