## ← Maximal Variance - Intro to Machine Learning

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Showing Revision 4 created 05/25/2016 by Udacity Robot.

1. So that example that we just did was an example of combining the number of
2. rooms and the square footage into a size feature.
3. And I asked you to just take it on faith for
4. a moment that the principle component existed and it was where I said it was.
5. Now I'm going to use the neighborhood example to show you how to
6. determine the principle component.
7. First I want to start with a little bit of vocab.
8. And the word is variance, which is a little bit confusing because you
9. actually already know a definition of variance.
10. It's a very important definition.
11. It's the willingness or flexibility of an algorithm to learn.
12. But we're going to mean it in a different sense.
13. Variance is also a technical term in statistics,
14. which means roughly the spread of a data distribution.
15. It's something that's very similar to
16. the standard deviation if that's something that you're familiar with.
17. So a feature that has a large variance has instances that
18. fall over a very large numerical range of values that it can take.
19. Whereas something with a small variance means that the features tend to be
20. more clustered together tightly.
21. So here's an example using a as yet unlabeled data set.
22. So suppose this is my data.
23. Then what I can do is draw an oval around it that roughly contains most of
24. the data.
25. Maybe 95% of the data are within this oval.
26. Now this oval could be parametrized using two numbers.
27. One of them is the distance across the narrowest point.
28. The other one is the distance across the longest point.
29. Now here's the critical question.
30. Which of these two lines points along the direction of
31. the maximum variance of the data?
32. In other words, in which direction is the data more spread out?
33. Check the box that you think has the right answer.