A retail chain wants to group its 2 million customers based on purchase behavior. Analysts consider using K-Means because they need fast runtime and easy interpretability, but the leadership team worries whether the method assumes overly simple cluster shapes. What limitation of K-Means should the team be most concerned about?

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BlackTom AI · Accepted Answer

To evaluate the options, start by recalling a core property of K-Means clustering: it assigns points to clusters by minimizing within-cluster variance using a Euclidean distance metric, which implicitly favors clusters that are roughly spherical and of similar size.
Option 1: 'It assumes clusters are spherical and similar in size' aligns with this limitation. If clusters have elongated shapes, irregular sizes, or varying densities, K-Means often misclassifies or blends them, because the algorithm uses a single centroid and tries to minimize squared distances under a spherical, equal-size assumption.
Option 2: 'It requires Gaussian distributions to work' is a misconception. K-Means does not assume the data are Gaussian or that clusters follow Gaussian shapes; Gaussian Mixture Models, for example, do involve probabilistic assumptions about distributions, but K-Means is simply a distance-based partitioning method.
Option 3: 'It always produces overlapping clusters' is inaccurate. K-Means tends to produce non-overlapping assignments by design (each point is assigned to one cluster). While decision boundaries can be ambiguous near cluster edges, the algorithm itself does not inherently produce overlapping clusters.
Option 4: 'It is too computationally slow for large datasets' is not correct for typical implementations of K-Means, which are computationally efficient and scale well to large datasets with proper optimizations and sampling techniques. In fact, speed is one of its advantages for big datasets like 2 million customers.
Overall, the most salient limitation given the leadership’s concern about cluster shapes and sizes is the spherical, equal-size assumption inherent in K-Means, making Option 1 the best match among the choices.

IS 4487-006 Fall 2025 Final Exam December 10 from 10:30 to 12:30

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