All MCQs

K-means cluster labels have no inherent order or semantic meaning. Analysts must examine centroids and members to describe each group.

Each iteration reduces or preserves the objective, so the process eventually stabilizes at a local solution. A tolerance or maximum-iteration rule prevents endless computation.

A centroid cannot be updated by taking the mean of an empty set of assigned points. Implementations must reinitialize or otherwise handle such a center.

Centroids are means, which are sensitive to extreme observations. A distant point can substantially alter a cluster center and nearby assignments.

A centroid is an arithmetic mean, and Euclidean distance assumes meaningful numerical differences. Arbitrary codes for nominal categories can create false geometry.

Standard k-means relies on Euclidean distances, which depend on measurement units. Scaling helps prevent one high-range variable from controlling the partition.

Silhouette compares cohesion within the assigned cluster with separation from the nearest alternative cluster. Values near one indicate a well-matched and well-separated assignment.

The k-means objective always decreases as k increases, so the elbow looks for a useful trade-off. A noticeable bend suggests that additional clusters offer smaller gains in compactness.

Multiple starts reduce the chance of accepting a poor local optimum caused by unlucky initialization. A fixed random seed can also make experiments reproducible.

Different starting centers can lead the iterative process toward different local solutions. Initialization therefore affects the final partition and objective value.

After cluster assignments change, the center of each group is recalculated. These new means become the centroids for the next assignment step.

The assignment step compares each point with the current cluster centers. The point joins the cluster whose centroid is closest under the chosen distance.