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## Homework Statement

I cant understand an equation to LDA. The context is:

Maybe the lecturer is trying to create a proof of the equation given below.The objective of LDA is to perform dimensionality reduction while

preserving as much of the class discriminatory information as

possible

I know the above that LDA projects the points along an axis so that we can have maximum separation between two classes.in addition to reducing dimesionality

## Homework Equations

I am not able to understand the following equation:

##Y =W^T## ##X##

It says that:

Assume we have a set of D-dimensional samples ##{x_1, x_2,...x_N},## ##N_1## of belong to class

##\Omega_1## and ##N_2## to class ##\Omega_2##. We seek to obtain a scalar ##Y## by projecting the samples ##X## onto a line:

In the above there is no W. So I want to know what is W?

## The Attempt at a Solution

W might represent the projection line? But T = transpose.

Somebody please guide me. For complete description, please see the attached file.

Zulfi.

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