Compute the hierarchical F-measure for the eight objects {p1, p2, p3, p4, p5, p6, p7, p8} and hierarchical clustering shown in Figure 8.8. Class A contains points p1, p2, and p3, while p4, p5, p6, p7, and p8 belong to class B.

Question

Answer 1

Let R(i, j) = nij/ni indicate the recall of class i with respect to cluster j.

Let P(i, j) = nij/nj indicate the precision of class i with respect to cluster

j.

F(i, j)=2R(i, j) × P(i, j)/(R(i, j) + P(i, j)) is the F-measure for class i and

cluster j.

For cluster #1 = {p1, p2, p3, p4, p5, p6, p7, p8}:

Class = A:

R(A, 1) = 3/3=1, P(A, 1) = 3/8=0.375

F(A, 1) = 2 × 1 × 0.375/(1 + 0.375) = 0.55

Class = B:

R(B, 1) = 5/5=1, P(A, 1) = 5/8=0.625, F(A, 1) = 0.77

For cluster #2= {p1,p2,p4,p5}

Class = A:

R(A, 2) = 2/3, P(A, 2) = 2/4, F(A, 2) = 0.57

Class = B:

R(B, 2) = 2/5, P(B, 2) = 2/4, F(B, 2) = 0.44

For cluster #3= {p3, p6, p7, p8}

Class = A:

R(A, 3) = 1/3, P(A, 3) = 1/4, F(A, 3) = 0.29

Class =B:

R(B, 3) = 3/5, P(B, 3) = 3/4, F(B, 3) = 0.67

For cluster #4={p1, p2}

Class = A:

R(A, 4) = 2/3, P(A, 4) = 2/2, F(A, 4) = 0.8

Class =B:

R(B, 4) = 0/5, P(B, 4) = 0/2, F(B, 4) = 0

For cluster #5 = {p4, p5}

Class = A:

R(A, 5) = 0, P(A, 5) = 0, F(A, 5) = 0

Class =B:

R(B, 5) = 2/5, P(B, 5) = 2/