Linear discriminant analysis
Linear Discriminant Analysis (LDA) is a supervised learning algorithm, often used for data dimensionality reduction.
LDA serves the classification problem, so it is necessary to find a projection direction picture first, so that the projected samples are separated as far as possible according to the original category.
For a simple binary classification problem, there are two categories of samples, pictures. The mean values of the two categories are 
pictures respectively .
We hope to separate the two data sets as much as possible after projection, that is, the larger the distance on the projection, the better. Distance representation: 
Picture
where the picture represents the projection vector of the center of the two types in the direction of the 
picture , the picture. Need to optimize the following issues
For pictures,
we need to find the largest possible distance projection between classes, but at the same time minimize the variance within classes.
image
So there are 
pictures
Where unit vector image, the two images represent the variance of the projected 
picture
image
is then defined between-class scatter matrix 
image, the image class scatter matrix 
simplification obtained
image
picture
image
generally binary, 
image and its number is two, make 
picture
picture
picture 
distance from the distance between maximizing and minimizing class category, it is also very simple to have better noise robustness of the model.