University AI - SP (Simple Perceptron)

SP (Simple Perceptron)

• Convention: The input layer is not counted, it acts as a placeholder, therefore the SP is a $1$-Layer ANN
• Notation: ”$w_{ij}$ denotes the weight of the connection between the $j$-th input unit and the $i$-th output unit
• Computed Function $f:\mathbb{R}\to \mathbb{R}$ : let $f$ be the activation function, then:

$$y_i=f(a_i)=f\left(\sum _{j=1}^d{w}_{ij}{x}_j\right)$$

In particular if $f$ is linear then: $y_i={\sum }_j{w}_{ij}{x}_j={\underline{w_i}}^t\underline{x}$ Which is called Simple Linear Perceptron.

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