Processing math: 100%

3/13/17

Multi classification - one v.s all

[Ex]
When the training data looks like this plot
[Plot 1]



We can use one v.s all classification help us.
First, we let red circle be the positive and the circle fill in purple as negative, then we may have the boundary h(1)θ(x) like this.
[Plot 2]

Second we let the green circle be the positive and the circle fill in purple as negative, then we can have the boundary h(2)θ(x) like this.
[Plot 3]

In the final, do the same thing, we can get the last boundary  h(3)θ(x) like this.
[Plot 4]

Concretely, we fit a classifier  h(i)θ(x) and estimate what is the probability that y = i class, or P(y=i|x;θ)

So, to wrap up, if we want to classify an k-class problem, we need to train k classifier to solve the problem.


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