Gemoetrically local embedding in manifolds for dimension reduction
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Transcript of Gemoetrically local embedding in manifolds for dimension reduction
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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
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Intelligent Database Systems Lab
Outlines
MotivationObjectivesMethodologyExperimentsConclusionsComments
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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.
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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.
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Intelligent Database Systems Lab
Methodology-FrameworkGeometrical distance
construction
Optimal reconstruction
Outlier-suppressingembedding
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Intelligent Database Systems Lab
MethodologyNeighbor selection using geometry distances
Tikhonov regularization
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Intelligent Database Systems Lab
MethodologyAlternative neighbor selection
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Intelligent Database Systems Lab
MethodologyLinear embedding
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Intelligent Database Systems Lab
MethodologyOutlier data filtering
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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Intelligent Database Systems Lab
Experiment
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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.
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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.