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Feature-Based Classification & Principle Component Analysis

Feature-Based Classification & Principle Component Analysis. Another Approach to Feature Based Classification. Offline: Collect examples of each class Determine features of each example Store the resulting features as points in “feature space” Online: Get a new instance

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Feature-Based Classification & Principle Component Analysis

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  1. Feature-Based Classification & Principle Component Analysis

  2. Another Approach to Feature Based Classification • Offline: • Collect examples of each class • Determine features of each example • Store the resulting features as points in “feature space” • Online: • Get a new instance • Determine its features • Choose the class that’s closest in “feature space”

  3. Advantages / Disadvantages + Simple to compute + Avoids partitioning feature space (classes can overlap) – Leaves the possibility of large “unmapped” areas in feature space – heavily dependent on good sample set – Highly dependent on good feature set

  4. Example: Letter Classification • Classifying Capital Letters with features: • Holes • A = 1, B = 2, C = 0 • Ends (does not count angles like the top of A) • A = 2, B = 0, C = 2, F = 3 • Straight • A = 3, B = 1, C = 0, D = 1 • Curve • A = 0, B = 2, C = 1, D = 1

  5. Feature Classification Example

  6. Classifying a New Letter • New letter is ø • Holes = • Ends = • Straight = • Curve = • Distance to “A” (1, 2, 3, 0) is: • Distance to “D” (1, 0, 1, 1) is:

  7. Continuing the Example

  8. Evaluating the Features • Does a slight modification of a letter still classify to the same letter? (Generalization) • Are all different letters distinguishable? (Representation) • Are all features independent and useful? • How can we modify this feature set to improve the representation?

  9. Multiple Examples per Class • Improves robustness (why?) • Increases space / time requirements (why?) • How can we gain benefits without too much cost? • K nearest neighbors • Clustering • Partitioning the space (as we saw before)

  10. Recognizing Sign Language Letters “A” “E” Also “I”, “O”, and “U”

  11. Input • 30 x 32 image of a hand signing the letter (grayscale) • 960 pixels, values 0-255 • We have a data set of 30 images per letter for the 5 vowels

  12. Features?

  13. Most Easily Available Features • Pixels from the image • 960 features per image! • These are very easy to compute, but we hope we don’t really need all of them • Maybe linear combinations (e.g. total of upper half) would be useful • How can we find out which linear combinations of pixels are the most useful features? • How can we decide how many (few) features we need?

  14. To Be Continued… • Smith, L.I., A Tutorial on Principal Component Analysis. February, 2002. http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf • Shiens, J., A Tutorial on Principal Component Analysis. December, 2005. http://www.snl.salk.edu/~shlens/pub/notes/pca.pdf • Kirby, M., and L. Sirovich. "Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces." IEEE Trans. Patt. Anal. Mach. Intell. 12.1 (1990): 103-108.

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