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A Self-Consistent-Field Iteration for Orthogonal Canonical Correlation Analysis.
- Source :
-
IEEE Transactions on Pattern Analysis & Machine Intelligence . Feb2022, Vol. 44 Issue 2, p890-904. 15p. - Publication Year :
- 2022
-
Abstract
- We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for visualization, pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerically unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods. In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonality constraint. A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised. It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges. We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA and propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the SCF iteration. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods, including real-world applications of multi-label classification and multi-view feature extraction. Experimental results show that our methods not only perform competitively to or better than the existing methods but also are more efficient. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01628828
- Volume :
- 44
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Pattern Analysis & Machine Intelligence
- Publication Type :
- Academic Journal
- Accession number :
- 154763590
- Full Text :
- https://doi.org/10.1109/TPAMI.2020.3012541