IGNOU MMTE 7 2026 - Consider a dataset of five observations given in the following t

Question

Consider a dataset of five observations given in the following table, each of which has two features f₁ and f₂:

	x₁	x₂	x₃	x₄	x₅
f₁	2	3	4	3	5
f₂	6	7	5	4	6

Assume the number of cluster $c = 3$ and the real number $m = 2$ . Also, assume the initial cluster centers as $V_1 = (1,1)$ and $V_2 = (2,2)$ . Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.

10 Jan 2026

Answer :

Word Count : 430

The five data points are x₁ = (2,6), x₂ = (3,7), x₃ = (4,5), x₄ = (3,4), x₅ = (5,6). The initial cluster centers are V₁ = (1,1) and V₂ = (2,2). The fuzzifier is m = 2, and Euclidean distance is used. First, compute distances of each point from the two cluster centers. For x₁ = (2,6): d₁₁ = √[(2−1)² + (6−1)²] = √26 d₁₂ = √[(2−2)² + (6−2)²] = √16 = 4 For x₂ = (3,7): d₂₁ = √[(3−1)² + (7−1)²] = √40 d₂₂ = √[(3−2)² + (7−2)²] = √26 For x₃ = (4,5): d₃₁ = √[(4−1)² + (5−1)²] = √25 = 5 d₃₂ = √[(4−2)² + (5−2)²] = √13 For x₄ = (3,4): d₄₁ = √[(3−1)² + (4−1)²] = √13 d₄₂ = √[(3−2)² + (4−2)²] = √5 For x₅ = (5,6): d₅₁ = √[(5−1)² + (6−1)²] = √41 d₅₂ = √[(5−2)² + (6−2)²] = √25 = 5 Membership values are computed using uᵢ₁ = 1 / [1 + (dᵢ₁ /

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