Gemoetrically local embedding in manifolds for dimension reduction

Intelligent Database Systems Lab

Presenter : Kung, Chien-Hao

Authors : Shuzhi Sam Ge, Hongsheng He, Chengyao Shen

2012,PR

Outlines

MotivationObjectivesMethodologyExperimentsConclusionsComments

Motivation• LLE is a dimension reduction

technique which preserve

neighborhood relationships amongst

• 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-FrameworkGeometrical distance

construction

Optimal reconstruction

Outlier-suppressingembedding

MethodologyNeighbor selection using geometry distances

Tikhonov regularization

MethodologyAlternative neighbor selection

MethodologyLinear embedding

MethodologyOutlier 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

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