# What is Linear Discriminant Analysis (LDA)?

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?

• 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. Mar 6, 2015 at 6:11
• $a^Tx$ is the dot product of $a$ and $x$ and the magnitude of the dot product is the magnitude of the component of $a$ on $x$. Mar 6, 2015 at 6:21
• What do you mean by the magnitude of a scalar? $a^Tx$ is a scalar.
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.