Intuition for the perceptron weight update rule

Question

I am having trouble understanding the weight update rule for persetrons :

w (t + 1) = w (t) + y (t) x (t).

Suppose we have a linearly shared dataset.

• w is the set of weights [w0, w1, w2, ...], where w0 is the displacement.
• x is a set of input parameters [x0, x1, x2, ...], where x0 is fixed at point 1 to accommodate the offset.

At the iteration t, where t = 0, 1, 2, ...,

• w (t) is the set of weights at the iteration t.
• x (t) is a classified example of learning.
• y (t) is the target output x (t) (either -1 or 1).

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Why does this update rule move the border in the right direction?

Answer 1

. , .

w (t + 1) = w (t) + y (t) x (t),

x (t) & sdot; w (t + 1) = x (t) & sdot; w (t) + x (t) & sdot; (y (t) x (t)) = x (t) & sdot; w (t) + y (t) [x (t) & sdot; ())].

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, :

• , x (t) .
• x (t) & sdot; x (t) & ge; 0.

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x (t)?

• x (t) , , .
• x (t) , y (t) = 1. , x (t) & sdot; x (t) ( ). , x (t).
• , x (t) , y (t) = -1. , x (t) & sdot; x (t) ( ). , x (t).