CompTIA DataX DY0-001 (V1) Practice Question

The correct answer is that k-means inherently assumes clusters are convex and isotropic. K-means clustering measures distance to a central point (the centroid) and aims to minimize the within-cluster sum of squares. This process naturally forms spherical or convex cluster shapes. When faced with data where the true underlying clusters are elongated or have irregular, non-convex shapes, k-means will often fail to identify them correctly, as described in the scenario.

Incorrectly choosing the value of 'k' would result in either splitting natural clusters or merging distinct ones, but it would not fundamentally solve the algorithm's inability to model non-spherical shapes. While suboptimal centroid initialization can lead to poor results by converging on a local minimum, this is a separate issue from the algorithm's intrinsic geometric bias, which is the direct cause for failing on elongated shapes regardless of the starting point. Similarly, the presence of unscaled features or categorical data are critical preprocessing concerns for k-means, but these issues would manifest differently, such as features with larger scales dominating the distance calculations, rather than specifically failing to model an elongated geometry.