# Flexible Manifold Embedding: A Framework for Semi-Supervised and Unsupervised Dimension Reduction

@article{Nie2010FlexibleME, title={Flexible Manifold Embedding: A Framework for Semi-Supervised and Unsupervised Dimension Reduction}, author={Feiping Nie and Dong Xu and Ivor Wai-Hung Tsang and Changshui Zhang}, journal={IEEE Transactions on Image Processing}, year={2010}, volume={19}, pages={1921-1932} }

We propose a unified manifold learning framework for semi-supervised and unsupervised dimension reduction by employing a simple but effective linear regression function to map the new data points. For semi-supervised dimension reduction, we aim to find the optimal prediction labels F for all the training samples X, the linear regression function h(X) and the regression residue F0 = F - h(X) simultaneously. Our new objective function integrates two terms related to label fitness and manifold…

## 391 Citations

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A graph-based semi-supervised embedding method as well as its kernelized version for generic classification and recognition tasks and has an obvious advantage that the learnt subspace has a direct out-of-sample extension to novel samples, and are thus easily generalized to the entire high-dimensional input space.

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