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Supervised Dimensionality Reduction Methods via Recursive Regression
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DOI：10.1109/TNNLS.2019.2940088.png)
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Abstract
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In this article, the recursive problems of both orthogonal linear discriminant analysis (OLDA) and orthogonal least squares regression (OLSR) are investigated. Different from other works, the associated recursive problems are addressed via a novel recursive regression method, which achieves the dimensionality reduction in the orthogonal complement space heuristically. As for the OLDA, an efficient method is developed to obtain the associated optimal subspace, which is closely related to the orthonormal basis of the optimal solution to the ridge regression. As for the OLSR, the scalable subspace is introduced to build up an original OLSR with optimal scaling (OS). Through further relaxing the proposed problem into a convex parameterized orthogonal quadratic problem, an effective approach is derived, such that not only the optimal subspace can be achieved but also the OS could be obtained automatically. Accordingly, two supervised dimensionality reduction methods are proposed via obtaining the heuristic solutions to the recursive problems of the OLDA and the OLSR.
Keywords:
Dimensionality reduction
Linear discriminant analysis
Eigenvalues and eigenfunctions
Learning systems
Computer science
Optical imaging
Optics
Optimal scaling (OS)
orthogonal least squares regression (OLSR)
orthogonal linear discriminant analysis (OLDA)
recursive regression
supervised dimensionality reduction
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