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Visualization of High dimensional Datasets

Visualization of High dimensional Datasets. Jahangheer Shaik. Why do we need Visualization?. Data visualization techniques are often required to obtain meaningful insights by reducing the cognitive load to effectively convert the data into information and knowledge for subsequent applications. .

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Visualization of High dimensional Datasets

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  1. Visualization of High dimensional Datasets Jahangheer Shaik

  2. Why do we need Visualization? Data visualization techniques are often required to obtain meaningful insights by reducing the cognitive load to effectively convert the data into information and knowledge for subsequent applications. • Noise? • Distribution? • Classes? • Structure?

  3. Line Graphs • Line graphs are used for displaying single valued or piecewise continuous functions of one variable

  4. Problems • Different types of lines (colored, dashed) have to be used to distinguish between the labeled classes • Each of the dimensions may have different scale

  5. Bar Charts, Histograms • Histograms visualize discrete probability density functions

  6. Hierarchical Clustering

  7. Scatter Plot • Most popular tool • Helps find clusters, outliers, trends, correlations etc • Glyphs, icons, colors etc may be used for better understanding • Not very intuitive when dimensions increase

  8. Scatter Plot Matrix

  9. Eigen values and Eigen vectors

  10. Eigen vectors(contd..) • A transformation matrix transforms a vector from its original position to another position • If the transform results in the vector itself then the vector and all multiples of it would be eigen vector of transformation matrix

  11. Properties of eigen vectors • Eigen vectors can be found for only square matrices • Given a n x n matrix, there are ‘n’ eigen vectors • It’s the direction that matters not scale • Eigen vectors are orthogonal to each other

  12. Linear Discriminant Analysis • Maximizes the ratio of between class variance to within class variance

  13. PCA-LDA

  14. Dimensions: Orthogonality • Dimensions are organized such that they are orthogonal to each other • Inselberg points out that orthogonality uses up the space rapidly

  15. Parallel Coordinates

  16. Circular Parallel co-ordinates

  17. Star coordinate projection

  18. Star Coordinate Projection J. Shaik and M. Yeasin, "Visualization of High Dimensional Data using an Automated 3D Star Co-ordinate System," Proceedings of IEEE IJCNN'06, Vancouver, Canada., pp. 1339-1346, 2006

  19. Mathematical Representation

  20. 2D vs 3D

  21. 3D star coordinate system

  22. Results

  23. Results

  24. Results

  25. Results

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