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NMF Computer Demonstration Overview: Faces, Shapes, and Cars

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This overview presents a demonstration of Non-negative Matrix Factorization (NMF) applied to various datasets, including facial images, random shapes, and car images. The training sets consist of 2429 examples, with specific focus on images like 19x19 centered faces, geometric shapes (squares, rectangles, circles), and cars captured at various orientations. Key parameters include rank, iterations, and output analysis for basis images. This demonstration highlights the practical applications of NMF in analyzing and reconstructing image data while addressing issues and choices in the methodology.

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NMF Computer Demonstration Overview: Faces, Shapes, and Cars

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Presentation Transcript

  1. NMF Demo: Lee, Seung Bryan Russell 6.899 Computer Demonstration

  2. Overview • Training sets • Faces • Random noise • “Block world” • Cars • Issues/Choices • Rank • Number of iterations • Dataset

  3. NMF: Equations • Objective Function:

  4. NMF: Equations • Update equations:

  5. Faces • Training set: 2429 examples • First 25 examples shown at right • Set consists of 19x19 centered face images

  6. Faces • Basis Images: • Rank: 49 • Iterations: 50

  7. Faces Original = x

  8. Faces • Basis Images • Rank: 49 • Iterations: 500

  9. Faces Original = x

  10. Random • Training set: 2429 examples • First 25 examples listed to the right • Gray-level values generated randomly

  11. Random • Basis Images • Rank: 49 • Iterations: 50

  12. Random Original = x

  13. Random • Basis Images • Rank: 49 • Iterations: 500

  14. Random Original Output

  15. Random Originals (1-25) Output (1-25)

  16. “Blocks” • Training set: 2429 examples • First 25 examples listed to the right • Three “shapes”: squares, rectangles, and circles • Shapes centered at two points in image

  17. “Blocks” • Basis Images • Rank: 25 • Iterations: 408

  18. “Blocks” Original = x

  19. “Blocks” Originals (1-25) Output (1-25)

  20. “Blocks” Output (1-25)

  21. “Blocks” • Basis Images • Rank: 49 • Iterations: 345

  22. “Blocks” Originals (1-25) Output (1-25)

  23. “Blocks” Output (1-25)

  24. Cars • Training set: 200 examples • First 25 examples shown at right • Set consists of car images taken at various orientations

  25. Cars • Basis Images • Rank: 49 • Iterations: 310 • Number of samples: 200

  26. Cars Originals (1-25) Output (1-25)

  27. Cars

  28. Thanks! • CBCL for providing face and car images

  29. For code and data, go to: www.ai.mit.edu/~brussell/courses/6.899/nmf

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