K-Means Clustering 3D

Question 1

K-Means partitions data into…

Accepted Answer

k clusters, each with a centroid — It groups points into k clusters so each point belongs to the cluster whose centroid (mean) is nearest.

Question 2

Lloyd's algorithm for k-means alternates between which two steps?

Accepted Answer

Assign nearest centroid, update to mean — Repeating assignment and centroid-update steps monotonically reduces within-cluster variance until assignments stop changing.

Question 3

K-Means minimizes which objective?

Accepted Answer

The within-cluster sum of squared distances — It seeks centroids minimizing total squared distance from points to their assigned centroid — equivalently, within-cluster variance.

Question 4

K-Means is guaranteed to converge to…

Accepted Answer

A local optimum for inertia — Each step decreases inertia, but the result depends on the random starting centroids, so different runs can give different local optima.

Question 5

K-Means++ improves the algorithm by…

Accepted Answer

Spreading initial centroids to avoid poor optima — K-means++ picks initial centroids far apart (probabilistically), giving better, more reliable clusterings than purely random initialization.

Question 6

The 'elbow method' helps choose…

Accepted Answer

k, where adding clusters stops helping — Plotting inertia vs k shows a bend ('elbow') where extra clusters yield diminishing returns, suggesting a good k.

Question 7

The SILHOUETTE score evaluates clustering by measuring…

Accepted Answer

Closeness to own cluster vs nearest other — Silhouette ∈ [−1,1] is high when points are tight within clusters and far from other clusters — another way to pick k.

Question 8

K-Means implicitly assumes clusters are…

Accepted Answer

Roughly spherical and similarly sized — Using Euclidean distance to a mean biases toward round, equally-sized blobs; elongated or varying-density clusters are handled poorly.

Question 9

K-Means struggles with NON-CONVEX or varying-density clusters; a better choice then is…

Accepted Answer

Density-based clustering or a Gaussian Mixture Model — DBSCAN finds arbitrary shapes via density; GMMs allow elliptical, soft clusters — both handle cases where k-means' spherical assumption fails.

Question 10

Why is feature SCALING important for k-means?

Accepted Answer

Distance gets dominated by large ranges unscaled — Like KNN, k-means uses distances, so unscaled features distort which points are 'near' a centroid — standardize first.

K-Means Parameters

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One round of k-means

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K-Means partitions data into…

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