Hierarchical classification: Consider the following two-stage classification system:

Classifier A: Classify input into Candidates and non-Candidates Classifier B: Classify Candidates

In this approach, the first classifier should be fast and simple.

a) Which ROC point would you pick for Classifier A? Sketch an example ROC curve and show the preferred values for Sensitivity and Specificity. Explain your answer.

b) Consider the following three-stage classification system: Classifier A: Classify input into CandidatesA and non-Candidates Classifier B: Classify CandidatesA into CandidatesB and non-Candidates Classifier C: Classify CandidatesB

Extend your answer in 1(a) for Classifiers A, B, and C. You will need to sketch possible ROC curves for A, B, C and select possible ROC points for each one.

c) A common mistake is to use cross-validation to train each classifier separately and then take the optimized classifiers, put them together into the combined system, and report accuracy on the cross-validated combined system. Explain why this approach is wrong and why it tends to over-estimate classification accuracy.

d) Suggest a correction to 1(c). How would you properly estimate the accuracy of the full system?

e) Artificial neural networks consist of several neural nodes. Each neural node uses an activation function as a detector. When the input to the activation function is positive, the neuron is said to fire. When the input to the activation function is negative, the neuron tries to ignore the input. Based on this property, it is suggested that neural networks have a large number of neural nodes that are connected to the input. Explain why this is a good idea.