In chemometrics discrimination model using Mahalanobis distance, it would not work if the number of samples is less than the number of variables. From a book written by G. Brereton, he has mentioned that it is because the variance-covariance (matrix C) would not have an inverse.
Could anyone tell me why variance-covariance matrix would not have an inverse if the number of sample is less than the number of variable?
First of all there is a practical approach. Generally you should avoid applying this kind of analysis since when you have less samples than variables you are in some way overfitting your problem.
The second reason (if I understand well the citation) is that you cannot reduce your matrix to a square one. You can calculate eventually the pseudo inverse of a non square matrix. you may have a look also at this answer https://www.researchgate.net/post/How_one_can_find_the_inverse_of_a_non_square_matrix2
Dear Giorgio Luciano, can you suggest to me some real case study, or sample data which shows that the dimension of variance covariance matrix is not a square matrix when the number of variables exceed the number of samples when calculating Mahalanobis distance?
- Badges
- Science topic
- Similar topics
- Mathematics
- Algebra
- Matrix