Question

How to compute cluster center for a given set of cluster members?                                          
Just find the the average of each attribute.                                          
                                          
For the following given data points find two clusters using k-means clustering.
Each data points has two features: x, and y written as (x,y). Use Euclidean distance.                                          
                                          
(3,5)                                          
(4,4)                                          
(7,8)                                          
(6,6)                                          
(5,3)                                          
(10, 8)                                          
(2,1)  

Answer 1

If you have any doubts please comment !!!!!!!!!!!!

k- meant clustering : • exploratory data analysis technique : Implemento non hiemaychial method of grouping objecte -togethet. trmines the centrinid uning the cuclidean method for distante calculation. · Giocups the objecte based on minimum distance stait input no. el chistere / Calculate Centroid Calculate Distance Group based on minimum distance Sample NO a1 در رم برا ید 108 +

- Iteration - 1 A ini hal A. (3,5) Distance Mean 1 (introids 19- (4,4) Disfonte Hean 2 Point T clutch (3,657 1.414 1414 TO (4,4) (14,8) Au (6,6) NO - 3.162 18 - 2.628 : ® If 2.8 28 N3 =51.732) A6 (10,8) su 7.346 152 = 7.211 (2,19 15 - 2.236) Nis - - 3.600 i find uditane blw two pointy [point Centroid by using formulas ir euclidean editance = N(22-203+ (, -y, ja dist blw A1 (3,5) € (3,5) = N(3-2)+(555 0. dist blw A1 (315) Ar (114) (03. : W(4-2)+(4-5) ENT=1494 Si'mi lastly find all distancesa it. D. Mean 1 is less than Dilean & then cluster the point belongs to is 1 otherwise 2.

Loften "Iteration 1 ca propi A Clustey 1 G cluster , A3, Az A₂, Au, A5, A6 update Centroidi- Cluster a : all x values . 3 +4 + d. ? = 4 (a coordinate ] No.6 Values all y values No.of values . 578 3 = 3 (y coordinate). =) (4, 4.6) 4 44 6+ 5+10 • 6.25 cluster a : 4+ 6 + 3 + 8 5.25. 16.25,5.25). (wa

Itolation 2 (4,416) D. Mean 2 (6-25, 5.25) D. Man 2 I point cluster (315) 11.077 3.344 0.6 2.57390 (4,4) (7,6) (6,6) 4.534 2.850 10.790/ (5,3) 2.441 11.8861 T6.896 2.573 (10,8) 14,650 2- (2.1) 24.118] } 6.010 aesthay it Similarly (in iteration a) Calculate eclistance of point from the centroid using entideon distance to A1 (3,5) té ki (4, 4-) - (4-3)*+ (4:5-737 : +(014) dove = 1.044 A1 (3,) to K+ (6-25,5-25) = 0 625-35+ (5.25-6) = (13255€ +(01255 S 10.5625 + 0.625 in 11.1875 - 3,344

often ürelation 2 : clubter 9 chiuston 2 An As, A5, A4 A3, M4, A6. up dati lantioid :- 3+ 4+ 5+2 3.5 CAg tем 4 - ES5 + + 3+1 3.25 3.5, 3.25). cluster 2 1 + 6 + 10 7 .666 1.666, 1.333 ) 8 + 6 + 8 = 1333

Treiption 3 cluster point í (305,3125),(4.664 7.333), D. Meon's D. Hean 2 1.820 5.21 (3,5) 0.9011 4.954 (4,4) (18) (6,6) 5.900 0.942 3.716 11.520 2.133 5.087 7 (53) 8.050 2.427 (10,) (2,11 [2.704 8.497 iteration 3 : Cluster a Ali A2, A5, A7 cluster 2 → A3, A4, A6: update centroid :- cliester 1 (3.46, 3.25) Clusten a + ( +666, 7.333) as we can see the clustous in ut eration a and it eration 3 cdoesn't final clusters are (A1, A2, A5, A3 ) { (A3, Ay, Ac).

A3 (36,7-3) Centroid cluster a cluster 2. 11,3,5) (3.5,3-25 Centroid To Compute cluster Center :- Just average call a values of data points to get a coordinate of winter. į Similarly for y coordinater