perceptron.jl

using Plots
x = reshape(collect(Iterators.flatten(Iterators.product(0:1,0:1))),(2,4))'
y_and = float(mapslices(x -> x[1] & x[2],x,2))*2-1
y_xor = float(mapslices(x -> x[1] ⊻ x[2],x,2))*2-1
x = hcat(ones(4),float(x))*2-1

ΔW(x, y, σ, lr) = σ==y ? 0 : 2*σ*x*lr

type Perceptron
    W::Array{<:Real,2}
end

(model::Perceptron)(X::Array{<:Real,1}) = ((model.W*X).>0)*2-1

function train(model::Perceptron, X::Array{<:Real,2}, Y::Array{<:Real,2}, nepochs=1, lr=1)
    for e = 1:nepochs
        # iterate examples
        for n in 1:size(X,1)
            x = X[n,:]
            y = Y[n,:]
            pred = model(x)
            # iterate outputs
            for (i,p) in enumerate(pred)
                # update weight vector
                model.W[i,:] .+= ΔW.(x, p, y[i],lr)
            end
        end
    end
end


##
model = Perceptron(rand((1,3)))
train(model,x, y_and,10,1)
print("AND succedded: $(0==sum(y_and-mapslices(model,x,2)))")

##
model = Perceptron(rand((1,3)))
train(model,x, y_xor,100,1)
print("XOR succedded: $(0==sum(y_xor-mapslices(model,x,2)))")

reps = 25
maxpatterns = 100
successes = zeros(maxpatterns)
for r=1:reps
    for i=1:maxpatterns
        X = rand(0:1,i,10)*2-1
        Y = rand(0:1,i,1)*2-1
        model = Perceptron(rand((1,10)))
        train(model, X, Y, 100, 1)
        if 0==sum(Y-mapslices(model,X,2))
            successes[i]+=1
        end
    end
end
plot(successes/reps, legend=false)
ylabel!("Recall Probability (%)")
xlabel!("Number of patterns")
title!("Success rate for single binary perceptron with 25 repetitions")
savefig("recall_prob.png")