Assume that we have two classes, A and B and a new document d to be classified.

The following training data is available:

di class cos(!! , !)

d1 A 1

d2 B 0.95

d3 B 0.93

d4 A 0.55

d5 A 0.45

d6 B 0.42

Suppose that we use the cosine as a distance measure, i.e., the higher the cosine, the closer are

two vectors.

Which class would be assigned to d with a k-nearest neighbor classifier using cosine if

1. k = 1 and simple majority vote;

2. k = 3 and simple majority vote;

3. k = 5 and simple majority vote.