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Dimensionality Reduction with Linear Transformations project update

Dimensionality Reduction with Linear Transformations project update. by Mingyue Tan March 17, 2004. Questions to answer - What’s the shape of the clusters? - Which clusters are dense/heterogeneous? - Which data coordinates

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Dimensionality Reduction with Linear Transformations project update

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  1. Dimensionality Reduction with Linear Transformationsproject update by Mingyue Tan March 17, 2004

  2. Questions to answer - What’s the shape of the clusters? - Which clusters are dense/heterogeneous? - Which data coordinates account for the decomposition to clusters? - Which data points are outliers? Domain and Task Data are labeled

  3. Solution - Dimension Reduction 1. Project the high-dimensional points in a low dimensional space while preserving the “essence” of the data - i.e. distances are preserved as well as possible 2. Solve the problems in low dimensions Dimensionality reduction

  4. Principal Component Analysis • Intuition: find the axis that shows the greatest variation, and project all points into this axis f2 e1 e2 f1

  5. Problem with PCA • Not robust - sensitive to outliers • Usually does not show clustering structure

  6. PCA - seeks a projection that maximizes the sum Weighted PCA - seeks a projection that maximizes the weighted sum - flexibility New Approach Bigger wij -> More important to put them apart

  7. Weighted PCA Varying wijgives: • Weights specified by user • Normalized PCA – robust towards outliers • Supervised PCA – shows cluster structures - Ifiandjbelong to the same cluster  setwij=0 - Maximize inter-cluster scatter

  8. Comparison – with outliers - PCA: Outliers typically govern the projection direction

  9. Comparison – cluster structure - Projections that maximize scatter ≠ Projections that separate clusters

  10. Summary

  11. Interface

  12. Interface - File

  13. Interface - task

  14. Interface - method

  15. Interface

  16. Milestones • Dataset Assembled - same dataset used in the paper • Get familiar with NetBeans - implemented preliminary interface (no functionality) • Rewrite PCA in Java (from an existing Matlab implementation) – partially done • Implement four new methods

  17. Reference • [1] Y. Koren and L. Carmel, “Visualization of Labeled Data Using Linear Transformations", Proc. IEEE Information Visualization (InfoVis?3), IEEE, pp.121-128, 2003.

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