Pattern Recognition, 4th Edition

Minimum Distance Classifiers

We will now view the task from a slightly different angle. Assuming equiprobable classes with the same covariance matrix, gⁱ(x) in (2.34) is simplified to(2.47)where constants have been neglected.

▪ Σ = σ²I: In this case maximum gⁱ(x) implies minimum(2.48)

Thus, feature vectors are assigned to classes according to their Euclidean distance from the respective mean points. Can you verify that this result ties in with the geometry of the hyperplanes discussed before?

Figure 2.13a shows curves of equal distance d^∈ = ...