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I am having trouble to understand the following:

In the Fisher’s Linear Discrimination analysis, the idea was to base the discriminant rule on a projection $a^Tx$ such that a good separation was achieved. Now, I don't understand why $a^Tx$ is a projection? Isn't it just a linear combination?

Thanks in advance!

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  • $\begingroup$ I don't know. If you don't get any answers here, you might try asking on the statistics website, crossvalidated (there should be a link to it on this page). But be sure to leave a link at each site to the question at the other site. $\endgroup$ Mar 6, 2015 at 6:11
  • $\begingroup$ $a^Tx$ is the dot product of $a$ and $x$ and the magnitude of the dot product is the magnitude of the component of $a$ on $x$. $\endgroup$
    – Srinivas K
    Mar 6, 2015 at 6:21
  • $\begingroup$ What do you mean by the magnitude of a scalar? $a^Tx$ is a scalar. $\endgroup$
    – ADAM
    Mar 6, 2015 at 6:27
  • $\begingroup$ @GerryMyerson Is there different site for statistics where we can share our ideas? $\endgroup$
    – ADAM
    Mar 6, 2015 at 6:28
  • $\begingroup$ You mean, different from the one I told you about, ADAM? $\endgroup$ Mar 6, 2015 at 6:29

2 Answers 2

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Sure, $a^Tx$ is a linear combination or weighted sum. And, if $a$ is a unit vector, then $a^Tx$ is also the scalar projection of $x$ onto $a.$ And this is the interpretation that is used in two-class LDA, where $a$ provides the projection direction.

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See here: Fisher Linear Discriminant by Olga Veksler for good introduction.

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