A generalized least-squares approach regularized with graph embedding for dimensionality reduction.

•It seeks a generalized orthogonality constraint based on the PCA idea of minimizing least-squares reconstruction errors, which restrains orthogonality on data while inducing a penalty factor to scale the influence of each data point.•The proposed generalized least-squares approach shares both advantages of Dimensionality Reduction (DR) and least-squares reconstruction error. Our proposed method can achieve a balance between keeping global structure by data reconstruction technique and local structure by graph embedding technique.•Our proposed framework can easily be extended to supervised and semi-supervised scenarios on the existing DR frameworks.