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Perceptron

Perceptron

Structure

A perceptron is

  • a single-layer neural network
  • used for supervised learning of binary classifiers
Perceptron

Perceptron

g(x)=∑_i=0nw_ix_i⏟_linear separator+w_0⏟_offset/bias g(x) = \underbrace{\sum\_{i=0}^n w\_i x\_i}\_{\text{linear separator}} + \underbrace{w\_0}\_{\text{offset/bias}}

Decision for classification

y^={1if g(x)>0−1else \hat{y} = \begin{cases} 1 &\text{if } g(x) > 0 \\\\ -1 &\text{else}\end{cases}

Update Rule

w=w+yxw=w+y x if prediction is wrong

  • If label y=1y=1 but predict y^=−1\hat{y}=-1: w=w+xw = w + x

  • If label y=−1y=-1 but predict y^=1\hat{y}=1: w=w−xw = w - x