Unsupervised Learning - Machine Learning - Data Science & Artificial Intelligence Previous Year Questions

Euclidean distance based k-means clustering algorithm was run on a dataset of 100 points with k = 3. If the points \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} -1 \\ 1 \end{bmatrix}\) are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3?

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 \(C_2\):
\[\mathbf{DIS-1}(C_1, C_2) = \max_{x \in C_1, y \in C_2} D(x, y)\]
\[\mathbf{DIS-2}(C_1, C_2) = \min_{x \in C_1, y \in C_2} D(x, y)\]
Which of the following statements is/are correct?

In the following table, the Task column lists a few tasks related to machine learning. The Algorithm column lists a few algorithms.
Each entry “t” from the Task column is to be matched with an appropriate entry “a” from the Algorithm column such that the task “t” can be solved using the algorithm “a”. Denote such a match as t : a

Task	Algorithm
T1 – Clustering	A1 – Markov Chain Monte Carlo
T2 – Classification	A2 – K-Medoid
T3 – Sampling	A3 – Linear Discriminant Analysis
T4 – Feature Extraction	A4 – Naive Bayes

Which of the following options is/are the correct matching(s)?

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?