In linear discriminant analysis, how is the linear discriminant function determined? Assuming equal variance-covariance matrices, is the linear discriminant function determined from the training data?

  • $\begingroup$ The formula given by @Mimshot is only for 2-class situation. See complete set of formulas to get the discriminants for k-class situation here $\endgroup$ – ttnphns Oct 28 '13 at 17:23

For Linear discriminant analysis the linear discriminant function is just the inner product of a given data point $\vec{x}$ with the vector $\vec{w}$, with the criterion $\vec{x} \cdot \vec{w} > c$. The vector $\vec{w}$ is calculated as:

$$\vec{w} = \Sigma^{-1}(\vec{\mu_0} - \vec{\mu_1})$$

Where $\vec{\mu_n}$ is the vector mean of sample class $n$, that is, the mean of the training data for class $n$.

  • $\begingroup$ So you could not compute a linear discriminant function given just one point? $\endgroup$ – DonutPhil Oct 28 '13 at 15:12
  • $\begingroup$ @DonutPhil If you have just one point, what is there to discriminate? $\endgroup$ – Nick Cox Oct 28 '13 at 18:02

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