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Understanding Perceptron Algorithm: Linear Threshold Unit and Learning Rule

Dive into the basics of the Perceptron Algorithm, utilizing Linear Threshold Units (LTU) to learn patterns. Explore its implementation, the sigmoid function, and the Perceptron Learning Rule for training.

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Understanding Perceptron Algorithm: Linear Threshold Unit and Learning Rule

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  1. Perceptron Algorithm

  2. x1 x2 xn Perceptron • Linear threshold unit (LTU) x0=1 w0 w1 w2  . . . i=0nwi xi g wn 1 if i=0nwi xi>0 o(xi) = -1 otherwise {

  3. Possibilities for function g Sign function Sigmoid (logistic) function Step function sign(x) = +1, if x > 0 -1, if x 0 step(x) = 1, if x> threshold 0, if x threshold (in picture above, threshold = 0) sigmoid(x) = 1/(1+e-x) Adding an extra input with activation x0 = 1 and weight wi, 0 = -T (called the bias weight) is equivalent to having a threshold at T. This way we can always assume a 0 threshold.

  4. Using a Bias Weight to Standardize the Threshold 1 -T w1 x1 w2 x2 w1x1+ w2x2 < T w1x1+ w2x2 - T< 0

  5. t = -1 t = 1 o=1 w = [0.25 –0.1 0.5] x2 = 0.25 x1 – 0.5 o=-1 (x, t)=([2,1], -1) o =sgn(0.45-0.6+0.3) =1 (x, t)=([-1,-1], 1) o = sgn(0.25+0.1-0.5) =-1 w = [0.2 –0.2 –0.2] w = [-0.2 –0.4 –0.2] (x, t)=([1,1], 1) o = sgn(0.25-0.7+0.1) = -1 w = [0.2 0.2 0.2] -0.5x1+0.3x2+0.45>0  o = 1 Perceptron Learning Rule x2 x2 x1 x1 x2 x2 x1 x1

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