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I am trying to implement a kernalised perceptron, and one thing that I can't understand is what at the end is the predictor function and how do we use it?

I know that the update rule is $$\left (y_i \sum^n_{j=1}\alpha_jy_j<x_j,x_i> \right) < 0$$ And then we update the $\alpha_i$.

But what does the $h(x)$ is equal to? What I can't understand is that if I am given a new data point $z$, what do I do with it? What's the explicit formula for this? I look all over the internet, but it's really unclear for me.

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