Intelligent Database Systems Lab

Presenter : Wei-Hao Huang

Authors : Miguel ´ A. Carreira-Perpi˜n´an

ICML, 2010

The Elastic Embedding Algorithm for Dimensionality Reduction

Intelligent Database Systems Lab

OutlinesMotivationObjectivesMethodologyExperimentsConclusionsComments

Intelligent Database Systems Lab

Motivation• The disadvantage of dimensionality reduction

– Difficult to understand their objective function.

– Optimisation is costly and prone to local optima.

Intelligent Database Systems Lab

Objectives• To propose a new dimensionality reduction

More efficient and robust

Further our understanding algorithms

Intelligent Database Systems Lab

Methodology - Framework

Elastic Embedding High dimension dataset

Low dimension data

Laplacian eigenmaps SNE+

Objective function

Intelligent Database Systems Lab

Methodology – Elastic Embedding

• Object function

• Gradient of E

Intelligent Database Systems Lab

Methodology - Study of λ

• N=2

• N>2

Intelligent Database Systems Lab

Methodology – Out of sample

• Objective function

• Mapping and reconstruction mappings

Intelligent Database Systems Lab

Experiments – 2D spiral

Intelligent Database Systems Lab

Experiments – Swiss roll

Intelligent Database Systems Lab

Experiments – COIL-20 dataset

Intelligent Database Systems Lab

Conclusions• EE dimensionality reduction improves over SNE

methods.

• EE produces better quality more quickly and robustly.

• All of ideas can be directly applied to SNE, t-SNE and

earlier algorithms.

Intelligent Database Systems Lab

Comments• Advantages– EE improves disadvantage of SNE on different

versions• Applications– Dimensionality Reduction