dimensionality reduction mappings

Intelligent Database Systems Lab

國立雲林科技大學National Yunlin University of Science and Technology

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Dimensionality Reduction Mappings

Presenter : Wei-Hao Huang 　Authors : Kerstin Bunte, Michael Biehl, Barbara Hammer

CIDM, 2011

Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.

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Outlines Motivation Objectives Methodology Experiments Conclusions Comments

Intelligent Database Systems Lab

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Motivation· Providing a mapping of a priorly given finite set

of points only, requiring additional steps for out-of-sample extensions.

Dimensionality Reduction(tSNE, MDS, Isomap)Old data

New data

Map

Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.Objectives

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• To propose general view on dimensionality reduction based on the concept of cost functions, and based on this general principle

Dimensionality ReductionPrior (tSNE, MDS, Isomap)Old data

New data

Map

Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.Methodology· General View

· General Principle

· Generalization Ability

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Intelligent Database Systems Lab

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Methodology

Data

Characteristics of data(Euclidean distance)

Characteristics of projections(Euclidean distance)

Error measure(Cost function)

Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.Methodology

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Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.Methodology· General Principle

· Apply on tSNE─ Global linear mapping

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Intelligent Database Systems Lab

N.Y.U.S.T.

I. M.Methodology· Apply on tSNE

─ Local linear mappings

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Intelligent Database Systems Lab

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I. M.Methodology· Generalization Ability

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Intelligent Database Systems Lab

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I. M.Experiments· Unsupervised clustering

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Intelligent Database Systems Lab

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I. M.Experiments

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Intelligent Database Systems Lab

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I. M.Conclusions· The paper opens a way towards a theory of

data visualization taking the perspective of its generalization ability to new data points.

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Intelligent Database Systems Lab

N.Y.U.S.T.

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Comments· Advantages

─ This paper opens a way towards a theory of data visualization

· Applications─ Dimensionality reduction