Semi-Supervised Nonlinear Dimensionality Reduction

Prior information canbe obtained from experts on the subject of inter-est and/or by performing experiments. For exam-ple, in moving object tracking, the coordinates of theobject in certain frames can be determined manu-ally, and can be used as prior information. We con-sider prior information in the form of on-manifoldcoordinates of certain data samples. We considerboth exact and inexact prior information. We callthe new algorithms Semi-Supervised LLE (SS-LLE),Semi-Supervised ISOMAP (SS-ISOMAP), and Semi-Supervised LTSA (SS-LTSA). Assuming the prior in-formation has a physical meaning, then our semi-supervised algorithms yield global low dimensional co-ordinates that bear the same physical meaning.

Xin Yang et al in a paper consider both exact and inexact prior information. They call the new algorithms Semi-Supervised LLE (SS-LLE),Semi-Supervised ISOMAP (SS-ISOMAP), and Semi-Supervised LTSA (SS-LTSA). Assuming the prior in-formation has a physical meaning, then the semi-supervised algorithms yield global low dimensional coordinates that bear the same physical meaning.