This set of Machine Learning MCQs covers unsupervised learning. It includes k-means centroid and assignment calculations, k-means++ and the elbow method, single, complete and average linkage in hierarchical clustering, DBSCAN core and noise points, silhouette score, PCA explained variance, LDA and t-SNE, and the curse of dimensionality. It is aimed at GATE DA candidates, university semester exams, UGC NET and interviews for data science and ML engineering roles.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 18 questions.
Topics covered in this set
- k-means, k-means++ and the elbow method
- Hierarchical clustering and linkage criteria
- DBSCAN core, border and noise points
- Silhouette score for cluster quality
- PCA, eigenvalues and explained variance
- Curse of dimensionality, LDA and t-SNE
Machine Learning MCQs with answers and explanations
Q1. In one k-means iteration, a cluster is assigned the points (1, 2), (3, 4) and (5, 0). What is the updated centroid of this cluster?
a) (3, 3)
b) (3, 2)
c) (2, 3)
d) (4.5, 3)
Q2. In k-means with Euclidean distance, the current centroids are C1 = (1, 1) and C2 = (6, 5). To which centroid is the point (4, 3) assigned?
a) C2, at distance about 2.83
b) C1, at distance about 3.61
c) C1, at distance about 2.83
d) C2, at distance about 3.61
Q3. What objective does the standard k-means algorithm try to minimise?
a) The number of clusters
b) The distance between cluster centroids
c) The maximum distance between any two points
d) The within-cluster sum of squared distances to the centroids
Q4. When choosing k for k-means, an analyst plots inertia against k and looks for the point where the decrease sharply slows down. What is this technique called?
a) Gap pruning
b) Gradient checking
c) The elbow method
d) Bootstrapping
Q5. What problem of standard k-means does k-means++ mainly address?
a) Poor results caused by bad random initialisation of centroids
b) Inability to handle categorical features
c) The need to specify k in advance
d) Detection of outliers as noise
Q6. A dataset contains two interleaving crescent-shaped clusters plus scattered outliers. Which algorithm is best suited to separate them?
a) k-means with k = 2
b) DBSCAN
c) PCA
d) Single-pass k-medians with k = 2
Q7. In DBSCAN with parameters eps and minPts, when is a point classified as a core point?
a) When it lies at the centre of a cluster's bounding box
b) When it is the first point visited by the algorithm
c) When at least minPts points (counting itself) lie within distance eps of it
d) When it is within eps of exactly one other point
Q8. How does DBSCAN treat a point that is not a core point and is not within eps of any core point?
a) It is assigned to the nearest cluster
b) It forms its own single-point cluster
c) It becomes a new core point
d) It is labelled as noise
Q9. Cluster P = {A, B} and cluster Q = {C, D} have pairwise distances d(A,C) = 4, d(A,D) = 6, d(B,C) = 3 and d(B,D) = 5. What is the single-linkage distance between P and Q?
a) 6
b) 3
c) 4.5
d) 4
Q10. Using the same distances, d(A,C) = 4, d(A,D) = 6, d(B,C) = 3 and d(B,D) = 5, what is the average-linkage distance between clusters {A, B} and {C, D}?
a) 4.5
b) 3
c) 6
d) 5
Q11. Which statement about agglomerative hierarchical clustering is correct?
a) It requires the number of clusters before it starts
b) It starts with one cluster and repeatedly splits it
c) It starts with each point as its own cluster and repeatedly merges the closest pair
d) It can only use Manhattan distance
Q12. The eigenvalues of a dataset's covariance matrix are 5, 3, 1 and 1. What fraction of total variance is retained by keeping the first two principal components?
a) 50%
b) 62.5%
c) 90%
d) 80%
Q13. What are the principal components found by PCA?
a) Orthogonal eigenvectors of the data's covariance matrix, ordered by decreasing variance
b) The cluster centroids of the data
c) The original features with the largest means
d) Directions that best separate the class labels
Q14. A dataset has height in centimetres and annual income in rupees. Why should the features usually be standardised before applying PCA?
a) PCA cannot run on unscaled data
b) Otherwise the feature with the largest numerical variance dominates the principal components
c) Standardisation increases the number of components
d) It makes the covariance matrix non-symmetric
Q15. For a data point, the mean distance to other points in its own cluster is a = 2 and the mean distance to points in the nearest other cluster is b = 5. What is its silhouette coefficient?
s = (b - a) / max(a, b)
a) 0.4
b) -0.6
c) 1.5
d) 0.6
Q16. Which statement best describes the curse of dimensionality?
a) As dimensions grow, data becomes sparse and distances between points become less discriminative
b) Adding features always improves model accuracy
c) High-dimensional data always has low variance
d) It refers only to the cost of matrix inversion
Q17. Which technique is primarily used to visualise high-dimensional data in 2D while preserving local neighbourhood structure, rather than for general feature reduction?
a) Linear regression
b) Lasso
c) t-SNE
d) Min-max scaling
Q18. How does Linear Discriminant Analysis (LDA) differ from PCA as a dimensionality reduction method?
a) LDA is unsupervised while PCA uses labels
b) LDA uses class labels to find directions that maximise class separability
c) LDA always keeps more dimensions than PCA
d) LDA works only on images
Quick revision notes
- k-means: assign to nearest centroid, update centroid = mean; minimises within-cluster sum of squares.
- k-means++ improves initialisation; elbow method and silhouette help choose k.
- Linkage: single = min distance, complete = max distance, average = mean of all pairs.
- DBSCAN: core point has >= minPts within eps; finds arbitrary shapes and labels noise.
- Silhouette s = (b - a)/max(a, b), ranges from -1 to 1.
- PCA: eigenvectors of covariance matrix; explained variance ratio = eigenvalue / sum of eigenvalues.
- Standardise features before PCA; LDA is supervised, PCA is unsupervised.
Frequently asked questions
What is the difference between k-means and DBSCAN?
k-means needs the number of clusters in advance and works best with compact, roughly spherical clusters. DBSCAN needs a radius and a minimum point count instead, can discover clusters of arbitrary shape and marks sparse points as noise.
How many principal components should I keep in PCA?
A common rule is to keep enough components to explain about 90 to 95 percent of the total variance, read from a cumulative explained variance plot. You can also look for an elbow in the scree plot or tune the number by cross-validation of a downstream model.
Is PCA a feature selection method?
No, PCA is feature extraction. It creates new features that are linear combinations of all original features, whereas feature selection keeps a subset of the original features unchanged.
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