Between-Class Covariance Matrix

See: Covariance Matrix, Class Mean, Between Covariance Matrix, Within-Class Covariance Matrix.

References

(Globerson & Roweis, 2006) ⇒ Amir Globerson, and Sam Roweis. (2006). “Metric Learning by Collapsing Classes.” In: Proceedings of Advances in Neural Information Processing Systems (NIPS 2005).
- QUOTE: The convex dual derived above reveals an interesting relation to covariance based learning methods. … This should be contrasted with the covariance matrices used in metric learning such as Fisher’s Discriminant Analysis. The latter uses the within and between class covariance matrices. The within covariance matrix is similar to the covariance matrix used here, but is calculated with respect to the class means, whereas here it is calculated separately for every point, and is centered on this point. This highlights the fact that MCML is not based on Gaussian assumptions where it is indeed sufficient to calculate a single class covariance.