In Patch Alignment for Dimensionality Reduction (TKDE 2009), orthogonal constrain is defined in Eq. (7) and (8). Tianyi said that,正交約束有兩個作用，
(1)希望U的各個列盡可能線性無關(線性代數上，兩個向量正交一定是線性無關的。注意與概率論與數理統計上相關系數區別，分別看兩者定義)；（2）防止U為0。這二個作用對分類可能意義不大。他的Manifold elastic net因為投影矩陣不會為零，故沒有加正交約束
Sparsity preserving projections with applications to face recognition的公式19下面，為什么引入約束，就這么一句：
To avoid degenerate solutions, we constrain (w^T)X(X^T)w = 1.
Manifold Regularized Discriminative Nonnegative的公式10; Unsupervised Feature Selection Using Nonnegative Spectral Analysis的公式9到10 的轉換,將正交約束進行轉換