There is a strand of virus MMXX that is infecting the population across the city of Montreal. There are several health care centers actively taking care of the population. Due to the unknown nature of the disease the health care workers have been instructed to collect and record the data of every patient with due diligence (30 features). You are a champion machine learning researcher hired by the city council to help them identify a pattern from the infected population. The data is presented to you in four files (D1, D2, D3, and D4). D1 corresponds to infants (age < 10 years), D2 for youth (10 years< age 25 years), D3 for adults (25 years 50 years). With your machine learning knowledge, you first choose PCA to convert the data to low dimensional representation (dimensionality of the projected representation, k = 2). For each file, you learn a low-dimensional representation using PCA and then train a linear classifier on the low-dimensional projected representation to predict whether a patient is Infected/Not Infected. The classifiers trained with D1, D2, D3 achieve 95% training F1 score while the classifier trained with D4 has only 40% training F1 score.

(a) What do you think best explains the poor performance in D4 ?

(b) Was the choice of k =2 appropriate for this classification task? What should your choice of k be based on ?

(c) Would LDA have provided a better low dimensional representation of data for this classification task? How ?

(d) If you have to improve the above mentioned PCA solution, suggest any two ways.