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Two Questions About The Perceptron Algorithm
If anyone has any insight into any of the 2 questions below, I'd greatly appreciate it.
1) We know that the online perceptron algorithm can be used to learn a linear threshold function: w1*x1 + w2*x2 + w3*x3 >= 0". What if, there's a linear threshold function, and we already KNOW that:
a) the weights of this linear threshold function are always positive
b) the sum of the weights of our linear threshold function do not exceed a constant W.
How can we use the Perceptron algorithm to learn this particular linear threshold function? (As in, how would we modify the original Perceptron algorithm to learn this particular function)? And what is the most number of mistakes we can make with this Perceptron algorithm?
2) When learning using the perceptron algorithm, imagine there's one example where the wrong label is shown (eg: output should be 1, but it falsely told the algorithm that the output is 0). How does this change the maximum number of mistakes we make with the Perceptron?
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by: moorhouselondonPosted on 2009-11-01 at 12:50:46ID: 25715402
I was looking through the neglected questions and came across this. I am not into heavy theory on these things, so apologies for my rather naive approach to this. I started by looking at the Wikipedia article on this subject to see if I could make any sense of what you were talking about lol.
http://en.wikipedia.org/wi
There is talk of a "ratchet" which ignores the result given by the algorithm, but how is one supposed to know whether that result is more accurate than the one given by the algorithm, particularly when you are introducing inconsistencies into the process?
In the example given in the article (the NAND function) the algorithm homes in on the correct result. If one of the row results were incorrect e.g., X0=1, X1=1, X2=1, Z=1, then you could simulate the effect that would have on the homing process. Presumably as with a typical Sort algorithm you would have a variable which detects whether any changes have been made for a complete cycle of all the inputs, and when there are none, the process terminates. So to improve the accuracy of the process you would keep cycling through the combinations until changes cease to occur. I presume that if this stability were not reached that the other parameters would need to be wiggled, then further tests carried out? But this would be on a test-by-test basis, it doesn't look as if there is a universal rule of thumb.
I can imagine that it would be possible for the process to diverge rather than converge if the right (wrong) changes were made.
It mentions in the article that it is not possible to learn an Exclusive Or function. But that is treating XOR as a Black Box, with the feedback on "how well we are doing" not looking into that Black Box. The fact that the process converges for the NAND function, and XOR can be constructed purely using NAND functions means that if the process is split into those individual functions then surely the process will converge. But then you are introducing intelligence into the process which is presumably against the rules.