Prerequisites

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Description

An initial model for a function approximator is the perceptron. It has a set of learnable weights \( w_0, w_1, ... , w_K \) and outputs either \( 0 \) or \( 1 \) depending on its given \(K\)-dimensional input \( \htmlId{tooltip-input}{u} = (\htmlId{tooltip-input}{u}_1, \htmlId{tooltip-input}{u} _2, ..., \htmlId{tooltip-input}{u} _K) \). The perceptron can learn functions for solving a very simplistic classification problem.

Equation

\[\htmlId{tooltip-function}{f}(\htmlId{tooltip-input}{u}) = \begin{cases} 1, \text{ if } \;\displaystyle \sum_{\htmlId{tooltip-iter}{i}=1}^{K} w_{\htmlId{tooltip-iter}{i}} \htmlId{tooltip-input}{u}_{\htmlId{tooltip-iter}{i}} \geq 0 \\ 0, \text{ otherwise} \end{cases}\]

Symbols Used

\(i\)	This is the symbol for an iterator, a variable that changes value to refer to a sequence of elements.
\(f\)	This is the symbol for a function. It is commonly used in algebra, and (multivariate) calculus.
\(u\)	This symbol denotes the input of a model.

References

Jaeger, H. (n.d.). Neural Networks (AI) (WBAI028-05) Lecture Notes BSc program in Artificial Intelligence. Retrieved April 27, 2024, from https://www.ai.rug.nl/minds/uploads/LN_NN_RUG.pdf

Function Estimated by Perceptron

Prerequisites

Description

Equation

Symbols Used

References