Somewhat frequent
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Unsupervised Learning
Clustering and dimensionality reduction, with the hand-computable details Round 1 asks for.
Clustering and dimensionality reduction, with the hand-computable details Round 1 asks for.
10 multiple choice at 2 marks and 2 fill-in-the-blank at 5, marked exactly as Round 1 marks them. Each answer is explained as soon as you check it. The clock is shown, not enforced.
Unsupervised learning is domain three of the syllabus. Both halves produce clean, hand-computable questions.
Minimise the within-cluster sum of squares:
The algorithm alternates two steps until assignments stop changing: assign each point to the nearest centroid, then recompute each centroid as the mean of its members.
Being asked to run one or two iterations on six two-dimensional points is entirely typical. Practise the layout so the arithmetic stays organised.
Examinable properties:
The silhouette for a point is , with the mean distance to its own cluster and the mean distance to the nearest other cluster. It ranges from to ; near zero means the point sits on a boundary.
Agglomerative clustering repeatedly merges the closest pair, producing a dendrogram you cut at a chosen height. The linkage criterion changes the result: single linkage chains, complete linkage produces compact clusters, Ward minimises within-cluster variance. No is needed in advance, which is its main advantage over k-means.
Density-based, parameterised by and min_samples. It finds arbitrarily shaped clusters, decides the number of clusters itself, and labels outliers as noise rather than forcing them somewhere. When a question describes non-convex clusters or explicit outliers, this is the expected answer.
PCA finds orthogonal directions of maximum variance - the eigenvectors of the covariance matrix. The explained variance ratio of component is .
Three points that recur in questions:
Practise k-means iterations by hand; check whether the question wants one or two. k-means needs scaling and assumes spherical clusters; DBSCAN handles shape and outliers.
Hierarchical clustering avoids choosing in advance. Centre before PCA, and remember high variance does not mean useful.
You run k-means and keep raising . What happens to inertia?
More centroids can only reduce (or hold) within-cluster sum of squares. At each point is its own cluster and inertia is 0.
Select an answer
Eigenvalues of the covariance are , , . How many components do you need to keep at least of the variance?
Total is . First component is . First two are . So 2.