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Linear Decision Boundary

Classify data points using a linear decision boundary.

Given weights $w$ and bias $b$ , classify each point $x$ using: $f(x) = \text{sign}(w \cdot x + b)$

where $\text{sign}(z) = +1$ if $z \geq 0$ , and $-1$ if $z < 0$ .

Return a list of predictions ( $+1$ or $-1$ ).

Input:

X = [[1, 2], [-1, -2], [2, 0]]
w = [1, 1]
b = 0

Output:

[1, -1, 1]

Reasoning:

We calculate the dot product of each point $x$ $x$ in $X$ $X$ with the weight $w$ $w$ :
- For $x = [1, 2]$ , $w \cdot x = (1)(1) + (1)(2) = 3$
- For $x = [-1, -2]$ , $w \cdot x = (1)(-1) + (1)(-2) = -3$
- For $x = [2, 0]$ , $w \cdot x = (1)(2) + (1)(0) = 2$
We add the bias $b$ $b$ to each result:
- For $x = [1, 2]$ , $w \cdot x + b = 3 + 0 = 3$
- For $x = [-1, -2]$ , $w \cdot x + b = -3 + 0 = -3$
- For $x = [2, 0]$ , $w \cdot x + b = 2 + 0 = 2$
We apply the sign function to each result to get the predictions:
- For $x = [1, 2]$ , $\text{sign}(3) = +1$
- For $x = [-1, -2]$ , $\text{sign}(-3) = -1$
- For $x = [2, 0]$ , $\text{sign}(2) = +1$
The final output is $[1, -1, 1]$

Editor

Python 3.13.1

0/0

Run code to see test results.

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