Gemoetrically local embedding in manifolds for dimension reduction

Gemoetrically local embedding in manifolds for dimension reduction Presenter : Kung, Chien-HaoAuthors : Shuzhi Sam Ge, Hongsheng He, ChengyaoShen2012,PR

Outlines • Motivation • Objectives • Methodology • Experiments • Conclusions • Comments

Motivation • LLE is a dimension reduction technique which preserve neighborhood relationships amongst data. • However, Euclidean distance is limited as only the pairwise distance to the target data is considered.

Objectives • This paper uses geometry distance which emphasized the local geometrical structure of the manifold spanned instead of computing the pairwise metric between data.

Methodology-Framework Geometrical distance construction Optimal reconstruction Outlier-suppressingembedding

Methodology Neighbor selection using geometry distances Tikhonov regularization

Methodology Alternative neighbor selection

Methodology Linear embedding

Methodology Outlier data filtering

Experiment

Conclusions • The GLE algorithm performs well in extracting inner structures of input linear manifold with outliers. • The GLE behaves as a clustering and classification method by projecting the feature data into low-dimensional separable regions. • The major drawback of GLE is the slow computation speed compared with other algorithms when the input data is small.

Comments • Advantages • This paper supplies the completely formula information. But this paper is hard to understand when the reader is a lack of prior knowledge. • Applications • Dimension reduction.

Gemoetrically local embedding in manifolds for dimension reduction