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I'm trying to understand this article in order which is a generalization of LDA to non-linear data using Kernels.

I have computed all the needed matrices and coefficients before the step 4, but then i got stuck on this:

On the step 4 of the algorithm (Page 6) it says to compute the eigenvectors $v$ using prior computed $\alpha$ through this equation

$$v = \sum_{p=1}^{N}\sum_{q=1}^{n_{p}}\alpha_{pq}\phi(x_{pq})$$

But though i have $\alpha$, since this article uses Kernel, $\phi$ is not defined, then i'm stuck in how i can find v.

I feel i'm missing something really small as this is the step before the last, i'm thinking about turning back to the initial equation $$\lambda Vv = Bv$$

as I have $\lambda$, but the article says i should use alpha, then i'm quite confused about how do I find v so I can project my test points and finally classify anything.

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