Activity 15 | Probabilistic Classification

Previously we have performed object classification by using the Minimum Euclidean Distance of the obtained features of the train and test objects. Another method for classifying objects is the Linear Discriminant Analysis or LDA. This method simply uses the probability that an object belongs to a certain group which depends on the features of that specific object and the mean feature vector for that certain group. This also depends on the number of samples present in a group. The highest probability that an object belongs to a group automatically classifies that object into that group. This is called Bayes Rule. LDA uses this rule but starts by assuming the distribution of each group which a multivariate Normal Distribution and that all groups share the same covariance matrix. The probability that an object belongs to a group is given by,

where, is the mean of features for group i, is the feature data of object/row k in x which is the matrix containing the features data, C is the pooled within group covariance matrix, and p is the prior probability vector for object i. Simply, object k is assigned to group with highest f. The results for the data collected from last activity is shown below.

The yellow highlighted areas are the maximum f values. The test objects were also jumbled to show that the method works no matter what the order of test objects is. It can be seen that there is a 100% accuracy in the classification of the objects. I give myself a grade of 10 for this activity for successfully implementing LDA and getting a 100% accurate object classification.

References: Kardi Teknomo's Page - Discriminant Analysis Tutorial http://people.revoledu.com/kardi/tutorial/LDA/index.html