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Overview of NMF Computer Demonstration: Faces, Blocks, and Cars Implementation

This overview details a computer demonstration on Non-negative Matrix Factorization (NMF) applied to three distinct datasets: face images, block shapes, and car images. The demonstration utilizes training sets comprising 2,429 face examples, block images of squares, rectangles, and circles, and 200 car images from various orientations. Key aspects discussed include the rank of basis images, number of iterations for convergence, and random noise effects. An exploration of the objective and update equations in NMF is also provided, highlighting practical choices and issues encountered during the process.

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Overview of NMF Computer Demonstration: Faces, Blocks, and Cars Implementation

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  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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