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

1. Title:
   Algorithms Requiring Rescaling Solution - Intro to Machine Learning
2. Description:

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   So Katie, what do you think?
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   Which ones are the right answers here?
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   >> The right answers, so the, the ones that do need rescaled features will
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   be the SVM and the k-means clustering.
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   >> So both and, support vector machines in, in, in k-means clustering, you're
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   really trading off one dimension to the other when you calculate the distance.
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   So take, for example, support vector machines.
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    And you look at the separation line that maximizes distance.
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    In there, you calculate a distance.
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    And that distance calculation, trade-offs one dimension against the other.
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    So we make one twice as big as the other, it counts for twice as much.
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    The same is true, coincidentally, for
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    k-means clustering, where you have a cluster center.
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    And you compute the distance of the cluster center, to all the data points.
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    And that distance itself has exactly the same characterization.
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    If you make one variable twice as big, it's going to count for twice as much.
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    So, as a result, support vector machines and
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    k-means both are affected by feature rescaling.
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    So, Katie, tell me about the decision trees and linear regression.
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    Why aren't they included?
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    Decision trees aren't going to give you a diagonal line like that, right?
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    They're going to give you a series of vertical and horizontal lines.
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    So there's no trade off.
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    You just, make a cut in one direction, and then a cut in another.
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    So, you don't have to worry about what's going on in one dimension,
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    when you're doing something with the other one.
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    >> So if you squeeze this area little area over here to half the size,
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    because you rescale the feature where the image line lies.
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    Well, it'll lie in a different place but
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    the separation is chronologically the same as before.
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    It scales with it,
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    so there's no trade-off between these two different variables.
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    And how about, linear regression?
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    >> Something similar happens in linear regression.
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    Remember that in linear regression,
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    each of our features is going to have a coefficient that's associated with it.
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    And that coefficient and that feature always go together.
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    What's going on with feature A doesn't effect anything with
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    the coefficient of feature B.
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    So they're separated in the same way.
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    >> In fact, if you were to double the variable scale of one specific variable,
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    that feature will just become half as big.
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    And the output would be exactly the same as before.
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    So it's really interesting to see, and for some algorithms,
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    rescaling is really a potential if we can use it, for others, don't even bother.