# Showing that an algorithm is a gradient descent method

I am stuck on a question about gradient descent, it asks to "show that that the perceptron learning algorithm is a gradient descent method for the squared error target function $(y - \sum w_ix_i)^2$". I understand that by going through the perceptron algorithm the squared error target function will be decreased from one step of the algorithm to the next, but in general, how do I show that an algorithm is a gradient descent method for something?

• The gradient descent iteration for minimizing $f$ is $x^+ = x - t \nabla f(x)$. You could write this out explicitly for your particular $f$ and see if the iteration you get is the same as the perceptron algorithm. – littleO Nov 17 '13 at 20:06
• ok that makes sense, just to clarify I'm assuming $\nabla$ is the learning rate, but what would $t$ be? – azrosen92 Nov 17 '13 at 20:23
• Hi, @VividD; I see that you've been editing a lot of old posts in the last few minutes. This fills up the front page, and forces newer content off. Editing old posts to improve them is a good thing, but please limit it to a few ($2-3$ per day). In particular, please limit very minor edits, such as adding a single tag. – user61527 Jan 17 '14 at 22:43
• @T. Bongers I didn't know it has such an impact. Once I saw your rejections (and you asked me there also to limit edits), I limited my edits but to 1 in 3 min. :) – VividD Jan 17 '14 at 22:47
• @T. Bongers Can I just submit several more minor edits for today, and I am done? Please. – VividD Jan 17 '14 at 22:53

The gradient descent iteration for minimizing f is $$x \leftarrow x−t\nabla f(x)$$. You could write this out explicitly for your particular f and see if the iteration you get is the same as the perceptron algorithm
Note that, $t$ is the learning rate, and $\nabla f(x)$ is the derivative of the cost function. Now take the derivative of your cost function with respect to input and put in this iteration.