Interpreting (negative) LDA classifier scores

Fiete

New Member
#1
Hi,
I performed an LDA in R using the lda() function. To my knowledge, this implements the LDA by Rao, 1948. From the results I derived the classification functions (not the discriminant functions) for each class of the model.
My data is pretty fuzzy and I'd rather perform a fuzzy than a crisp classification so I don't lose information in the process. I therefore intend to visualize the results of all classification scores to provide a quick and intuitive overview.

Now I would like to ask you for your help to interpret the following test data scenarios:

  • similarly high scores for two classes: (E.g. fourth graph from the left on example image.) Is it sensible to make a double classification?
  • score zero for a particular class: (E.g. 1st class in fifth graph from the left on example image.) Is it plausible to claim that the data does not fit into a certain class at all?
  • negative score of higher absolute value than highest positive score: (E.g. first graph from the left in example image, classes 2 and 4.) Does "negative concordance" mean anything at all?
  • single very low positive score compared to otherwise high absolute negative scores: (E.g. fifth graph from the left on example image but with class score as positive.) Can I argue that the "signal strength" is low or that "no known pattern was identified" and omit a classification altogether?
  • all negative scores: (E.g. fifth graph from the left on example image.) In the original interpretation of the method, the highest score determines the classification. Does the LDA design the classification function system in such a way that a certain class gets selected like this systematically? Or does it mean that really none of the classes is a good fit and one could say that "no known pattern could be identified"?

Maybe you can also recommend literature specifically on this subject?
Thanks a lot for your input!