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Find clusters using k-means clustering algorithm if we have several objects (4 types of medicines) and each object have two attributes or features as shown in the table below.

The goal is to group these objects into k=2 group of medicine based on the two features (pH and weight index).

Object Attribute 1 (X) Weight Index Attribute 2 (Y) pH
Medicine A 1 1
Medicine B 2 1
Medicine C 4 3
Medicine D 5 4
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Object X Y
A 1 1
B 2 1
C 4 3
D 5 4

K = 2

- A B C D
A 0 - - -
B 1 0 - -
C $\sqrt{13}$ $\sqrt{8}$ 0 -
D 5 $\sqrt{9}$ $\sqrt{2}$ 0

2] Let $c_1$ = {A} & $c_2$ = {B}

$\therefore$ centroid of $c_1$ = {A} = { (1,1) }

" $c_2$ = {B} = { (2,1)}

3] $c_1$ = {A}

$c_2$ = { B, C, D}

$\therefore$ centroid of $c_1$ = {(1,1)}

" $c_2$ {( $\frac{2+4+5}{3}, \frac{1+3+4}{3} )$}

= {(3.67, 2.67)}

3] $c_1$ = {A , B}

$c_2$ = {C , D}

$\therefore$ centroid of $c_1$ = { (1.5, 1)}

" $c_2$ = {(4.5, 3.5)}

$\therefore$ $c_1$ = {A, B}

$c_2$ = { C, D}

$\because$ there is no change, these are the final clusters.