This is kernel k-mean with k = 2. The K matrix below is the dot product of documents in a 1D space. dy d2 d3 d4 d2 d4 d1 1 3 d3 6 K di d2 d3 d4 X 3 9 10 30 18 0 0 1 2 3 4 5 6 7 8 9 10 6 10 18 30 36 60 60 100 Let the initial clusters be w, = {d1} and wz = {d2, d3, d4}. Run the iterations indicated below until there are no updates. Edsew Ed2w. K(d,dz) (wk/? Id'ews K(d, d') r(d) + arg min (Bx - 2 Bx | r(dl) | r(d2) 2 r(d3) 2 r(04) 2 wil 1 B 1 B2 40.1 1 3 initial iteration 1 1 iteration 2 iteration 3 iteration 4 Initial: B= K[d1, dl) = 1, B2 = (9+36 + 100 + 2(18+ 30 + 60))/9 = 361/9 = 40.1 Iteration 1: B-2(1)/1 = 1-2 =-1, B2-2(3 + 6 + 10)/3 = 40.1 -12.7 = 27.4 r(d1) 1 This is kernel k-mean with k = 2. The K matrix below is the dot product of documents in a 1D space. dy d2 d3 d4 d2 d4 d1 1 3 d3 6 K di d2 d3 d4 X 3 9 10 30 18 0 0 1 2 3 4 5 6 7 8 9 10 6 10 18 30 36 60 60 100 Let the initial clusters be w, = {d1} and wz = {d2, d3, d4}. Run the iterations indicated below until there are no updates. Edsew Ed2w. K(d,dz) (wk/? Id'ews K(d, d') r(d) + arg min (Bx - 2 Bx | r(dl) | r(d2) 2 r(d3) 2 r(04) 2 wil 1 B 1 B2 40.1 1 3 initial iteration 1 1 iteration 2 iteration 3 iteration 4 Initial: B= K[d1, dl) = 1, B2 = (9+36 + 100 + 2(18+ 30 + 60))/9 = 361/9 = 40.1 Iteration 1: B-2(1)/1 = 1-2 =-1, B2-2(3 + 6 + 10)/3 = 40.1 -12.7 = 27.4 r(d1) 1