Gemoetrically local embedding in manifolds for dimension reduction
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Transcript of 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
Gemoetrically local embedding in manifolds for dimension reduction
Intelligent Database Systems Lab
Outlines
MotivationObjectivesMethodologyExperimentsConclusionsComments
Intelligent Database Systems Lab
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.
Intelligent Database Systems Lab
Objectives• This paper uses geometry distance which emphasized
the local geometrical structure of the manifold
spanned instead of computing the pairwise metric
between data.
Intelligent Database Systems Lab
Methodology-FrameworkGeometrical distance
construction
Optimal reconstruction
Outlier-suppressingembedding
Intelligent Database Systems Lab
MethodologyNeighbor selection using geometry distances
Tikhonov regularization
Intelligent Database Systems Lab
MethodologyAlternative neighbor selection
Intelligent Database Systems Lab
MethodologyLinear embedding
Intelligent Database Systems Lab
MethodologyOutlier data filtering
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
Experiment
Intelligent Database Systems Lab
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.
Intelligent Database Systems Lab
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.