Abstract
Low-rank matrix factorization can reveal fundamental structure in data. For example, joint-PCA on multi-datasets can find a joint, lower-dimensional representation of the data. Recently other similar matrix factorization methods have been introduced for multi-dataset analysis, e.g., the shared response model (SRM) and hyperalignment (HA). We provide a comparison of these methods with joint-PCA that highlights similarities and differences. Necessary and sufficient conditions under which the solution set to SRM and HA can be derived from the joint-PCA are identified. In particular, if there exists a common template and a set of generalized rotation matrices through which datasets can be exactly aligned to the template, then for any number of features, SRM and HA solutions can be readily derived from the joint-PCA of datasets. Not surprisingly, this assumption fails to hold for complex multi-datasets, e.g., multi-subject fMRI datasets. We show that if the desired conditions are not satisfied, joint-PCA can easily over-fit to the training data when the dimension of the projected space is high (∼> 50). We also examine how well low-dimensional matrix factorization can be computed using gradient descent-type algorithms using Google's TensorFlow library.
| Original language | English (US) |
|---|---|
| Title of host publication | 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| ISBN (Electronic) | 9781728111513 |
| DOIs | |
| State | Published - Apr 16 2019 |
| Event | 53rd Annual Conference on Information Sciences and Systems, CISS 2019 - Baltimore, United States Duration: Mar 20 2019 → Mar 22 2019 |
Publication series
| Name | 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |
|---|
Conference
| Conference | 53rd Annual Conference on Information Sciences and Systems, CISS 2019 |
|---|---|
| Country | United States |
| City | Baltimore |
| Period | 3/20/19 → 3/22/19 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Information Systems
Cite this
}
Multi-dataset Low-rank Matrix Factorization. / Valavi, Hossein; Ramadge, Peter Jeffrey.
2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8692932 (2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
TY - GEN
T1 - Multi-dataset Low-rank Matrix Factorization
AU - Valavi, Hossein
AU - Ramadge, Peter Jeffrey
PY - 2019/4/16
Y1 - 2019/4/16
N2 - Low-rank matrix factorization can reveal fundamental structure in data. For example, joint-PCA on multi-datasets can find a joint, lower-dimensional representation of the data. Recently other similar matrix factorization methods have been introduced for multi-dataset analysis, e.g., the shared response model (SRM) and hyperalignment (HA). We provide a comparison of these methods with joint-PCA that highlights similarities and differences. Necessary and sufficient conditions under which the solution set to SRM and HA can be derived from the joint-PCA are identified. In particular, if there exists a common template and a set of generalized rotation matrices through which datasets can be exactly aligned to the template, then for any number of features, SRM and HA solutions can be readily derived from the joint-PCA of datasets. Not surprisingly, this assumption fails to hold for complex multi-datasets, e.g., multi-subject fMRI datasets. We show that if the desired conditions are not satisfied, joint-PCA can easily over-fit to the training data when the dimension of the projected space is high (∼> 50). We also examine how well low-dimensional matrix factorization can be computed using gradient descent-type algorithms using Google's TensorFlow library.
AB - Low-rank matrix factorization can reveal fundamental structure in data. For example, joint-PCA on multi-datasets can find a joint, lower-dimensional representation of the data. Recently other similar matrix factorization methods have been introduced for multi-dataset analysis, e.g., the shared response model (SRM) and hyperalignment (HA). We provide a comparison of these methods with joint-PCA that highlights similarities and differences. Necessary and sufficient conditions under which the solution set to SRM and HA can be derived from the joint-PCA are identified. In particular, if there exists a common template and a set of generalized rotation matrices through which datasets can be exactly aligned to the template, then for any number of features, SRM and HA solutions can be readily derived from the joint-PCA of datasets. Not surprisingly, this assumption fails to hold for complex multi-datasets, e.g., multi-subject fMRI datasets. We show that if the desired conditions are not satisfied, joint-PCA can easily over-fit to the training data when the dimension of the projected space is high (∼> 50). We also examine how well low-dimensional matrix factorization can be computed using gradient descent-type algorithms using Google's TensorFlow library.
UR - http://www.scopus.com/inward/record.url?scp=85065180310&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065180310&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/CISS.2019.8692932
DO - https://doi.org/10.1109/CISS.2019.8692932
M3 - Conference contribution
T3 - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019
BT - 2019 53rd Annual Conference on Information Sciences and Systems, CISS 2019
PB - Institute of Electrical and Electronics Engineers Inc.
ER -