IEEE Trans Image Process - Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction.

Tópicos

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{ problem(2511) optim(1539) algorithm(950) }
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Resumo

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 F(0) = 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 F(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 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.

Resumo Limpo

propos unifi manifold learn framework semisupervis unsupervis dimens reduct employ simpl effect linear regress function map new data point semisupervis dimens reduct aim find optim predict label f train sampl x linear regress function hx regress residu f f hx simultan new object function integr two term relat label fit manifold smooth well flexibl penalti term defin residu f semisupervis learn framework refer flexibl manifold embed fme can effect util label inform label data well manifold structur label unlabel data model mismatch hx f show fme relax hard linear constraint f hx manifold regular mr make better cope data sampl nonlinear manifold addit propos simplifi version refer fmeu unsupervis dimens reduct also show propos framework provid unifi view explain understand mani semisupervis supervis unsupervis dimens reduct techniqu comprehens experi sever benchmark databas demonstr signific improv exist dimens reduct algorithm

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