Hierarchical Clustering and Linkage Methods Previous Year Questions (PYQs) for GATE DA: 3+ Solved Questions with Step-by-Step Solutions

Consider the table below, where the $(i,j{)}^{th}$
element of the table is the distance
between points $x_i$
and $x_j$
. Single linkage clustering is performed on data points,
$x_1$
,$x_2$
, $x_3$
,$x_4$
, $x_5$
.

	$x_1$	$x_2$	$x_3$	$x_4$	$x_5$
$x_1$	0	1	4	3	6
$x_2$	1	0	3	5	3
$x_3$	4	3	0	2	5
$x_4$	3	5	2	0	1
$x_5$	6	3	5	1	0

Which ONE of the following is the correct representation of the clusters produced?

Let four points in three-dimensional space be:

P1: [2, 3, −1], P2: [3, 1, 1], P3: [5, −2, 3] and P4: [3, 3, 3].

Hierarchical Agglomerative Clustering is used to cluster the above points. If Manhattan Distance is used as the distance metric during clustering, which of the following options indicates the two points that will be merged first?

Let $C_1$ and $C_2$ be two sets of objects. Let $D(x,y)$ be a measure of dissimilarity between two objects $x$ and $y$. Consider the following definitions of dissimilarity between $C_1$ and $C_2$.

$$\mathrm{DIS}\text{-}1(C_1,C_2)=\underset{x\in C_1,y\in C_2}{\max }D(x,y)$$ $$\mathrm{DIS}\text{-}2(C_1,C_2)=\underset{x\in C_1,y\in C_2}{\min }D(x,y)$$
Which of the following statements is/are correct?