Machine learning

Perceptron

Repeat until convergence:

For t = 1 ... n

1. $y'$ = sign($\underline{x}_t\cdot\underline{\theta}$)
2. If $y'\ne y_t$ Then $\underline{\theta} = \underline{\theta} + y_t\underline{x}_t$, Else leave $\underline{\theta}$ unchanged.

Kernel form of the perceptron

• Definition: for any $\underline{x}$, define $g(x) = \sum_{j=1}^n\alpha_jy_jK(\underline{x}_j,\underline{x})$ where $K(\underline{x}_j,\underline{x}) = \phi(\underline{x}_j)\cdot\phi(\underline{x})$
• Repeat until convergence:
• For t = 1 ... n
1. y' = sign(g($\underline{x}_t$)
2. If $y'\ne y_t$ Then $\alpha_t = \alpha_t + 1$