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

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Authors Feiping Nie, Dong Xu, Ivor W. Tsang, Changshui Zhang
Journal/Conference Name IEEE Transactions on Image Processing (TIP)
Paper Category
Paper Abstract 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 smoothness as well as a flexible penalty term defined on the residue F0. 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 h(X) and F, we show that FME relaxes the hard linear constraint F = h(X) in manifold regularization (MR), making it better cope with the data sampled from a nonlinear manifold. In addition, we propose a simplified version (referred to as FME/U) for unsupervised dimension reduction. We also show that our proposed framework provides a unified view to explain and understand many semi-supervised, supervised and unsupervised dimension reduction techniques. Comprehensive experiments on several benchmark databases demonstrate the significant improvement over existing dimension reduction algorithms.
Date of publication 2010
Code Programming Language MATLAB

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