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#4
04-07-2012, 12:08 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Perceptron Learning Algorithm

Quote:
 Originally Posted by lacamotif Hi I have a question about how weighting is assigned and the meaning of the PLA . For point a1 which has assignment 1, does w(a1.y) + w(a1.x) = 1 ? ( '.' denotes subscript) And then, for point a2 which has assignment -1, would w(a1.y) + w(a1.x) + w(a1.x) + w(a2.x) = -1 , and so on? To adjust weighting of w for misclassified points, is w.x2 = w.x1 + x.2 * y.2 Thank you for the help!
Let me use the book notation to avoid confusion. You have two points and (which you called a1 and a2) and their target outputs (which you called assignment) are and .

Either point, call it just for simplicity, is a vector that has components . Notice that bold denotes a full data point, while italic denotes a component in that data point. We add a constant 1 component to each data point and call the component to simplify the expression for the perceptron. If the weight vector of the perceptron is (where takes care of the threshold value of that perceptron), then the perceptron implements

where returns if its argument is positive and returns if its argument is negative.

Example: Say the first data point (two dimensional, so ). Add the constant component and you have . Therefore, the percepton's output on this point is . If this formula returns which is different from the target output , the PLA adjusts the values of the weights trying to make the perceptron output agree with the target output for this point . It uses the specific PLA update rule to achieve that.
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