(1)In Isomap, instead of using Euclidean distance, we can also use Mahalanobis distance between neighboring points. What are the advantages and disadvantages of this approach, if any?
(2)In certain applications we can define hierarchies of classes, and this can make discrimination easier. For example, first we discriminate cats from dogs, and then we discriminate between different breeds of cat. Discuss how this can be done. Can we learn hierarchies from data?
(3) Let us say we have a two-class problem where both classes are normally distributed with the same mean but different variances. What will the discriminant function look like in this case?