Ph. D. Project
Title:
Uniqueness of coupled tensor models with shared and distinct factors
Dates:
2024/11/04 - 2027/11/17
Student:
Supervisor(s):
Other supervisor(s):
Prof. Adali Tülay (adali@umbc.edu)
Description:
Data fusion has become increasingly important in many applications [1]. A fundamental problem is to merge heterogeneous datasets containing dataset-specific information [4]. Furthermore, in many applications, data have three or more dimensions, which is a challenge for conventional processing methods.
Challenges : The study of flexible tensor/matrix factorizations is still in its infancy. The uniqueness of coupled tensor decompositions has recently been the subject of a number of studies [3]. More flexible decompositions have been proposed [5], but current uniqueness results for this type of decomposition remain limited [2]. Current methods have limited ability to simultaneously integrate information common to and distinct to different subgroups of matrix/tensor sets. Overcoming these challenges is of crucial importance for many engineering applications.
Research program: The PhD candidate will develop flexible matrix/tensor decomposition methods to recover common and distinct information across
different multidimensional datasets, enabling the discovery of subsets sharing common factors. An essential aspect of the methods developed will be their theoretical guarantees, for which the use of tensor decompositions provides a suitable mathematical framework [3]. This will involve measuring the similarity between tensor data sets (distances on Riemannian manifolds, for example) and the solution of large-scale optimization problems.
References :
[1] D. Lahat et al., ``Multimodal data fusion: an overview of methods, challenges, and prospects,'' Proceedings of the IEEE, vol. 103, no. 9, pp. 1449⬓1477, 2015.
[2] R. A. Borsoi et al., ``Coupled tensor decomposition for hyperspectral and multispectral image fusion with inter-image variability,'' IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 3, pp. 702-717, 2021.
[3] M. Sørensen and L. D. De Lathauwer, ``Coupled canonical polyadic decompositions and (coupled) decompositions in multilinear rank-
(L_{r,n},L_{r,n},1) terms-part I: Uniqueness,'' SIAM Journal on Matrix Analysis and Applications, vol. 36, no. 2, pp. 496-522, 2015.
[4] A. K. Smilde et al., ``Common and distinct components in data fusion,'' Journal of Chemometrics, vol. 31, no. 7, p. e2900, 2017.
[5] E. Acar et al., ``Structure-revealing data fusion,'' BMC Bioinformatics, vol. 15, no. 1, pp. 1-17, 2014.
Challenges : The study of flexible tensor/matrix factorizations is still in its infancy. The uniqueness of coupled tensor decompositions has recently been the subject of a number of studies [3]. More flexible decompositions have been proposed [5], but current uniqueness results for this type of decomposition remain limited [2]. Current methods have limited ability to simultaneously integrate information common to and distinct to different subgroups of matrix/tensor sets. Overcoming these challenges is of crucial importance for many engineering applications.
Research program: The PhD candidate will develop flexible matrix/tensor decomposition methods to recover common and distinct information across
different multidimensional datasets, enabling the discovery of subsets sharing common factors. An essential aspect of the methods developed will be their theoretical guarantees, for which the use of tensor decompositions provides a suitable mathematical framework [3]. This will involve measuring the similarity between tensor data sets (distances on Riemannian manifolds, for example) and the solution of large-scale optimization problems.
References :
[1] D. Lahat et al., ``Multimodal data fusion: an overview of methods, challenges, and prospects,'' Proceedings of the IEEE, vol. 103, no. 9, pp. 1449⬓1477, 2015.
[2] R. A. Borsoi et al., ``Coupled tensor decomposition for hyperspectral and multispectral image fusion with inter-image variability,'' IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 3, pp. 702-717, 2021.
[3] M. Sørensen and L. D. De Lathauwer, ``Coupled canonical polyadic decompositions and (coupled) decompositions in multilinear rank-
(L_{r,n},L_{r,n},1) terms-part I: Uniqueness,'' SIAM Journal on Matrix Analysis and Applications, vol. 36, no. 2, pp. 496-522, 2015.
[4] A. K. Smilde et al., ``Common and distinct components in data fusion,'' Journal of Chemometrics, vol. 31, no. 7, p. e2900, 2017.
[5] E. Acar et al., ``Structure-revealing data fusion,'' BMC Bioinformatics, vol. 15, no. 1, pp. 1-17, 2014.
Keywords:
Uniqueness, statistical models, tensor decompositions, multidimensional data
Department(s):
| Biology, Signals and Systems in Cancer and Neuroscience |