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Author Topic: hyperplane equation  (Read 945 times)
AMT
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« on: March 22, 2011, 04:44:35 PM »

I am trying to solve a simple toy classification problem ( a linear one) using the "linear regression", perceptron and svm (libsvm). Then read the parameters and try to find out the hyperplane equation
 and I got confused with the information that I got in the "text view" where the models are written. The bias term (b) of the model do not seem to be always written using same notation

I am trying to interpret as w1*attr1+w2*attr2+ ...+b.

In a 2D problem the hyperplane equation should then come from w1*attr1+w2*attr3+b=0
The problem I was solving was
((attr1,attr2),  label)    ----->    ( (-1,1),1); ((1,-1),1),((1,1),1),(-1,-1),-1).

with linear regression I got the following equation 0.25*attr1+0.25*attr2+0.25
with perceptron I got : intercept : -0.25  w(attr1)=0.25, w(attr2)=0.25
with svm I got : bias (offset): -1.0  w(attr1)=0.5 w(attr2)=0.5.

The question is the “bias” or “intercept”  are according with the output of linear regression. And in particular in these case  the solution found seems not solve the problem. What I am doing wrong?

AMT
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wessel
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« Reply #1 on: March 22, 2011, 04:51:27 PM »

((attr1,attr2),  label)    ----->    ( (-1,1),1); ((1,-1),1),((1,1),1),(-1,-1),-1).

So bottom left is -1, rest +1.

I think you need to use more data points.
There are many more functions that can fit these 4 data points perfectly,
other then the function f(x,y) = positive(x) or positive(y).

Also, it is important use use labels like a, b, instead of 1, -1, else its not a classification problem, but a regression problem.

You seem to want to find a function that is something like
y(x) = x - 1.
and then f(x,y) = y(x) > 0?

« Last Edit: March 22, 2011, 04:57:10 PM by wessel » Logged
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