K-Means Algorithm Example

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  • 1. K-MEANS ALGORITHM EXAMPLEAuthor: Kasun Ranga WijeweeraEmail: krw19870829@gmail.com(TOTAL MARKS = 30)Consider following eight points.P1 (2, 2), P2 (1, 14), P3 (10, 7), P4 (1, 11), P5 (3, 4), P6 (11, 8), P7 (4, 3), P8 (12, 9)Take P1, P2, and P7 as initial centroids. Then apply k-means clustering algorithm to calculatetwo successive positions of those centroids.Note:The distance function between two points P1 (x1, y1) and P2 (x2, y2) is defined as:D (P1, P2) = | x1 – x2 | + | y1 – y2 |ANSWERTable 1 C1 = (2, 2) C2 = (1, 14) C3 = (4, 3)D (P, C1) D (P, C2) D (P, C3) ClusterP1 (2, 2) 0 13 3 C1P2 (1, 14) 13 0 14 C2P3 (10, 7) 13 16 10 C3P4 (1, 11) 10 3 11 C2P5 (3, 4) 3 12 2 C3P6 (11, 8) 15 16 12 C3P7 (4, 3) 3 14 0 C3P8 (12, 9) 17 16 14 C3C1 = (2/1, 2/ 1) = (2, 2); (1 marks)C2 = ((1 + 1)/2, (14 + 11)/2) = (1, 12.5); (1 marks)C3 = ((10 + 3 + 11 + 4 +12)/5, (7 + 4 + 8 + 3 + 9)/5) = (8, 6.2); (1 marks)
  • 2. Table 2 C1 = (2, 2) C2 = (1, 12.5) C3 = (8, 6.2)D (P, C1) D (P, C2) D (P, C3) ClusterP1 (2, 2) 0 11.5 10.2 C1P2 (1, 14) 13 1.5 14.2 C2P3 (10, 7) 13 14.5 2.8 C3P4 (1, 11) 10 1.5 11.8 C2P5 (3, 4) 3 10.5 7.2 C1P6 (11, 8) 15 14.5 4.8 C3P7 (4, 3) 3 12.5 7.2 C1P8 (12, 9) 17 14.5 6.8 C3C1 = ((2 +3 + 4)/3, (2 + 4 + 3)/3) = (3, 3); (1 marks)C2 = ((1 + 1)/2, (14 + 11)/2) = (1, 12.5); (1 marks)C3 = ((10 + 11 + 12)/3, (7 + 8 + 9)/3) = (11, 8); (1 marks)Each row of the tables (except first two rows) should be given marks as followsPn (x, y) a (1/3 marks) b (1/3 marks) c (1/3 marks) Ck (1/2 marks)