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learning classifiers from only positive and unlabeled data: theory ...

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30<br />

Support Vector Machines<br />

Support vector machines (SVM) are linear functions of<br />

the form f(x) = w T x + b, where w is the weight vector<br />

<strong>and</strong> x is the input vector.<br />

Let the set of training examples be {(x 1, y 1), (x 2, y 2),<br />

…, (x n, y n)}, where x i is an input vector <strong>and</strong> y i is its class<br />

label, y i {1, -1}.<br />

To find the linear function:<br />

Minimize:<br />

Subject to:<br />

1<br />

2<br />

w w<br />

T<br />

T<br />

yi ( w<br />

xi<br />

b)<br />

<br />

1,<br />

i<br />

1,<br />

2, ..., n

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