Simple PLA

About PLA

This is only a simple/naive PLA that only on 2D for visualization, and didn't consider any noise or training/validation skills.

It follows the fundamental of PLA. Assume we have $points = [1, x, y]$ and $labels \in \{-1, +1\}$. A line $ax + by + c = 0, w = [c, a, b]$ separates points into two categories.

• Given $w$, we know it classifies a point $p$ by:

• Given its lable $l$, if its classification is wrong, then:

• Then we can update the $w$ / line by:

Implementation

The core part of PLA is simple as:

function pla_train(points, labels, iter = 500)
    w = rand(3)
    for i in 1:iter
        for idx in 1:size(points)[2]
            u = points[:, idx]'w
            if u*labels[idx] < 0 
                w += points[:, idx]*labels[idx]
            end 
        end 
    end 
    return w
end

function pla_predict(points, w)
    labels = sign.(points'w)
end

Other part of the code, including generation of train/test data set is here.

Test & Results

The points labeled by red/blue colours are ground truth labels.

After training, the training data set is classified as:

Use the testing data set, we got:

There were no miss classifications by counting:

sum(result_test .!= labels_test)

This was because the generated data is linear separatable, whithout noise. It's too simple 😹😹.

Ref

Machine Learning Fundations