In Patch Alignment for Dimensionality Reduction (TKDE 2009), orthogonal constrain is defined in Eq. (7) and (8). Tianyi said that,正交约束有两个作用，
(1)希望U的各个列尽可能线性无关(线性代数上，两个向量正交一定是线性无关的。注意与概率论与数理统计上相关系数区别，分别看两者定义)；（2）防止U为0。这二个作用对分类可能意义不大。他的Manifold elastic net因为投影矩阵不会为零，故没有加正交约束
Sparsity preserving projections with applications to face recognition的公式19下面，为什么引入约束，就这么一句：
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 的转换,将正交约束进行转换