K-means Clustering

Solved Problem

Use k-means clustering & partition into 2 clusters

$2, 4, 10, 12, 3, 20, 30, 11, 25$

(1) Randomly partition the data set & find cluster mean or select some mean

Let $m_1 = 4,\qquad m_2 = 12$

Form clusters:

$k_1 = \{2, 3, 4\}$

$k_2 = \{10, 11, 12, 20, 25, 30\}$

(a) Find mean:

$m_1 = \dfrac{2+3+4}{3} = 3$

$m_2 = 18$

Iteration 2: Assign the points again

$k_1 = \{2, 3, 4, 10\}$

$m_1 = \dfrac{2+3+4+10}{4} = 4.75 \approx 5$

$k_2 = \{11, 12, 20, 25, 30\}$

$m_2 = \dfrac{11+12+20+25+30}{5} = 19.6 \approx 20$

Iteration 3:

$k_1 = \{2, 3, 4, 10, 11, 12\}$

$m_1 = 7$

$k_2 = \{20, 25, 30\}$

$m_2 = 25$

Iteration: 4

$k_1 = \{2, 3, 4, 10, 11, 12\}$

$m_1 = 7$

$k_2 = \{20, 25, 30\}$

$m_2 = 25$

No Change in the mean

$\therefore$ The 2 clusters are

$k_1 = \{2, 3, 4, 10, 11, 12\}$

$k_2 = \{20, 25, 30\}$