artificial intelligence - What's the point of the threshold in a perceptron? -

i'm having trouble seeing threshold in single-layer perceptron. data separated no matter value of threshold is. seems lower threshold divides data more equally; used for?

actually, you'll set threshold when aren't using bias. otherwise, threshold 0.

remember that, single neuron divides input space hyperplane. ok?

now imagine neuron 2 inputs x=[x1, x2], 2 weights w=[w1, w2] , threshold th. equation shows how neuron works:

x1.w1 + x2.w2 = th 

this equals to:

x1.w1 + x2.w2 - 1.th = 0 

i.e., hyperplane equation divides input space.

notice that, neuron work if set manually threshold. solution change th weight, so:

x1.w1 + x2.w2 - 1.w0 = 0 

where term 1.w0 bias. still can draw plane in input space without set manually threshold (i.e, threshold 0). but, in case set threshold value, weights adapt adjust equation, i.e., weights (including bias) absorves threshold effects.