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I have data that I'm trying to classify into two different groups using Fisher linear discriminant analysis. This gives me a vector of weights $\vec w$, used in the equation $\vec w\cdot \vec x$ to give a value that's compared to a threshold in the classification stage.

What I'd like to know is, what kind of information can I extract from this vector $\vec w$ (from the magnitude of weights, their sign, etc.)? Can this, for example, tell me how much information a certain dimension gives about the class?

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    $\begingroup$ LDA extracts the discriminant function - a latent variable that best discriminates your two groups. This function is a linear combination of the input variables. The coefficients in this linear combination are the weights you are speaking about. A weight tells about the discriminative ability of a variable; it tells nothing about a class. $\endgroup$
    – ttnphns
    Aug 2, 2013 at 19:09

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you can treat w as a direction. you project x onto that direction (like you decompose a 3-dim vector into 3 components X, Y and Z), and w.x is then the component of x in w direction. because the vectors in different classes are supposed to have different components in that direction, so you can use it for classification purposes.

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