Body: <p>I've been reading about <strong>Fisher's Linear Discriminant Analysis</strong> lately, and I noticed that the objective function (particularly for <em>two-class</em> classification) to be maximized contains <strong>scatter</strong> terms instead of <strong>variance</strong>, in the denominator. Why is that?</p>
  <p>To clarify, the scatter of a sample is just the variance multiplied by the number of data points in the sample.</p>
  <p>Thank you!</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-07-14T08:15:07.640Z
Comments.Text: I think this may be a better fit at stats.stackexchange.com - I'm not 100% sure, but I think the answer will be to do with how variance of dataset mean varies depending on variance of individual terms. There are far more experts in this kind of pure statistics over at Cross Validated, and LDA is only weakly related to AI and ML.
Comments.UserDisplayName: Neil Slater
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-07-19T18:05:42.550Z
Comments.Text: I think you may find the answer here:
  https://stats.stackexchange.com/questions/123490/what-is-the-correct-formula-for-between-class-scatter-matrix-in-lda
Comments.UserDisplayName: Daniel Wiczew
Tags: <machine-learning><classification><supervised-learning>
Title: Why is 'scatter' used instead of variance in LDA?
UserDisplayName: stoic-santiago
ThreadText: # Why is 'scatter' used instead of variance in LDA?
  
  (Asked by: username_0 on 2020-07-03)
  
  I've been reading about **Fisher's Linear Discriminant Analysis** lately, and I noticed that the objective function (particularly for *two-class* classification) to be maximized contains **scatter** terms instead of **variance**, in the denominator. Why is that?
  
  To clarify, the scatter of a sample is just the variance multiplied by the number of data points in the sample.
  
  Thank you!
  
  **Tags:** machine-learning, classification, supervised-learning
  > **Comments:**
  > **username_1**: I think this may be a better fit at stats.stackexchange.com - I'm not 100% sure, but I think the answer will be to do with how variance of dataset mean varies depending on variance of individual terms. There are far more experts in this kind of pure statistics over at Cross Validated, and LDA is only weakly related to AI and ML.  
  > **username_2**: I think you may find the answer here: https://stats.stackexchange.com/questions/123490/what-is-the-correct-formula-for-between-class-scatter-matrix-in-lda  
  
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