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In this work, sub-manifold projections based semi-supervised dimensionality reduction (DR) problem learning from partial constrained data is discussed. Two semi-supervised DR algorithms termed Marginal Semi-Supervised Sub-Manifold Projections (MS3MP) and orthogonal MS3MP (OMS3MP) are proposed. MS3MP in the singular case is also discussed. We also present the weighted least squares view of MS3MP. Based...
Supervised Fisher Linear Discriminant Analysis (LDA) is a classical dimensionality reduction approach. LDA assumes each class has a Gaussian density and may suffer from the singularity problem when handling high-dimensional data. We in this work consider more general class densities and show that optimizing LDA criterion cannot always achieve maximum class discrimination with the geometrical interpretation...
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