﻿ Learn Perceptron math

# The Rosenblatt Perceptron

Definition of the Rosenblatt perceptron:

$$f(x) = \begin{cases} 1 & \text{if } \mathbf{w} \cdot \mathbf{x} > 0\\ 0 & \text{otherwise} \end{cases}$$

With a 2-dimensional feature space and the dot-product expanded we get:

$$f(x) = \begin{cases} 1 & \text{if } w_0x_0 + w_1x_1 + w_2x_2 > 0\\ 0 & \text{otherwise} \end{cases}$$

A sample:

$${}$$

The tree sliders allow to adapt the windividual weights of the preceptron. Notice how changing the sliders for weights $w_1$ and $w_2$ change the direction of the hyperplane while changing the slider for $w_0$ changes only the position of the hyperplane. Clicking inside the the grid applies the preceptron evaluation to the point clicked resulting in a colored dot:

• A red dot meaning the result of the dot-product is positive
• A green dot meaning the result of the dot-product is negative

Dragging the sliders and thus changing the weights of the preceptron will re-evaluate existing points.

Hovering with the cursor over the dots will reveal as a tooltip the calculation made for that point.

 $w_0$= $w_1$= $w_2$=