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

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 for all the training samples , the linear regression function ( ) and the regression residue 0 = ( ) simultaneously. Our new objective function integrates two terms related to label fitness and manifold smoothness as well as a flexible penalty term defined on the residue 0. Our Semi-Supervised learning framework, referred to as flexible manifold embedding (FME), can effectively utilize label information from labeled data as well as a manifold structure from both labeled and unlabeled data. By modeling the mismatch between ( ) and , we show that FME relaxes the hard linear constraint = ( ) in manifold regularization (MR), making it better cope with the data sampled from a nonlinear manifold. In addition, we p...

• Type: Journal
• Year: 2010
• Where: TIP
• Authors: Feiping Nie, Dong Xu, Ivor Wai-Hung Tsang, Changshui Zhang
• Keywords: Dimension Reduction, Education, Manifold, TIP 2010, Unsupervised Dimension Reduction