1. Dimensionality Reduction Mappings Presenter : Wei-Hao Huang Authors : Kerstin Bunte, Michael Biehl, Barbara Hammer CIDM, 2011

2. Outlines • Motivation • Objectives • Methodology • Experiments • Conclusions • Comments

3. 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 Map New data

4. Objectives • To propose general view on dimensionality reduction based on the concept of cost functions, and based on this general principle Dimensionality Reduction Prior(tSNE, MDS, Isomap) Old data Map New data

5. Methodology General View General Principle Generalization Ability

6. Methodology Data Characteristics of data (Euclidean distance) Characteristics of projections (Euclidean distance) Error measure (Cost function)

7. Methodology

8. Methodology • General Principle • Apply on tSNE • Global linear mapping

9. Methodology • Apply on tSNE • Local linear mappings

10. Methodology • Generalization Ability

11. Experiments Unsupervised clustering

12. Experiments

13. Conclusions The paper opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points.

14. Comments • Advantages • This paper opens a way towards a theory of data visualization • Applications • Dimensionality reduction