Average Face:
EigenFaces:
Recognition Rate Chart & Table:
| EigenFaces | Recognition Rate |
| 1 | 0.21875 |
| 3 | 0.3125 |
| 5 | 0.5625 |
| 7 | 0.5625 |
| 9 | 0.625 |
| 11 | 0.625 |
| 13 | 0.625 |
| 15 | 0.625 |
| 17 | 0.59375 |
| 19 | 0.59375 |
| 21 | 0.59375 |
| 23 | 0.625 |
| 25 | 0.625 |
| 27 | 0.625 |
| 29 | 0.625 |
| 31 | 0.625 |
Describe the trends you see in your plots. Discuss the tradeoffs; how many eigenfaces should one use? Is there a clear answer?
Obviously, the accuracy increases dramatically as the number of faces reaches 9. After that point it's not clear what the optimal number of faces is. The more eigenfaces we use to generate the coefficient vectors, the more accurately we can represent the set of faces in the nonsmiling face-space. This decreases bias and increases variance, which can cause us to overfit the nonsmiling faces with our eigenface set. As a result, the recognition rates may drop slightly (as they do going from 15 to 17 eigenfaces).
You likely saw some recognition errors in step 3; show images of a couple. How reasonable were the mistakes? Did the correct answer at least appear highly in the sorted results?
Here are three examples of recognition failures with 10 eigenfaces.
| Test Face | The Face It Chose | The Real Answer | Comments |
 |  |  | This image was recognized with an MSE of 2428.6. The matching image showed up 6th in the list, with an MSE of 3174.98. In this example, the two mismatched faces looked extremely similar while the matching faces look very different. When I first glanced at the faces I thought they were the same. This mistake is very reasonable. |
 | |  | This image was recognized with an MSE of 1749.51. The matching image showed up 3rd in the list, with an MSE of 2829.29. These faces look uncannily similar - I am not surprised the program got it wrong. |
 |  |  | This image was recognized with an MSE of 805.783. The matching image showed up 2nd in the list, with an MSE of 812.249. Again, this was a fairly close match. |
Overall, the matches were pretty good.