Activity 15 - Probabilistic Classification

Objects can be classified into categories based on features that can be measured. In the previous activity, we determine class membership by determining which mean feature vector it is closer to. However, this may prove tricky when the distributions fall along parallel lines, for instance. A feature vector may fall along the line crossing one mean vector but be nearer the other mean vector.

Linear discriminant analysis may be used in such cases. This is a mathematically involved process. The formula to be used is given by

where C is the covariance matrix of a set of measurements x,
u is the mean of the set of measurements of the class i,
p is the prior probability (expected value prior to any measurement, usually given by
number of samples in a class/total number of samples)

An object with a particular measurement x belongs to the class i which has the largest discriminant function, f.

Using LDA, we obtain a 100% recognition rate. Below is a snapshot of a sample calculation. Note that we made use of the same data set as in the previous activity.

figure 1. Sample calculation

Rating: 10 for correct classification