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(gè)作用，
(1)希望U的各個(gè)列盡可能線性無關(guān)(線性代數(shù)上，兩個(gè)向量正交一定是線性無關(guān)的。注意與概率論與數(shù)理統(tǒng)計(jì)上相關(guān)系數(shù)區(qū)別，分別看兩者定義)；（2）防止U為0。這二個(gè)作用對分類可能意義不大。他的Manifold elastic net因?yàn)橥队熬仃嚥粫?huì)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(zhuǎn)換,將正交約束進(jìn)行轉(zhuǎn)換