When applying K-means clustering to a dataset consisting of multiple numerical features, consider the following actions and their impact:

I The cluster centroids are computed as the mean of the observations assigned to each cluster.
II The K-means algorithm can be directly applied to datasets with mixed data types (e.g., numerical and categorical) without any preprocessing.
III Running K-means multiple times with different random initializations causes overfitting in any case.
IV K-means always finds the same final cluster configuration regardless of the initial centroids chosen.

Question

When applying K-means clustering to a dataset consisting of multiple numerical features, consider the following actions and their impact:

I	The cluster centroids are computed as the mean of the observations assigned to each cluster.
II	The K-means algorithm can be directly applied to datasets with mixed data types (e.g., numerical and categorical) without any preprocessing.
III	Running K-means multiple times with different random initializations causes overfitting in any case.
IV	K-means always finds the same final cluster configuration regardless of the initial centroids chosen.

BlackTom AI · Accepted Answer

Start by identifying what each statement is claiming about K-means behavior and data handling.
Option A: III and IV. This combination claims that running K-means multiple times with different random initializations always leads to overfitting, and that K-means always converges to the same final configuration regardless of starting centroids. In reality, multiple restarts are used to avoid poor local optima, not to cause overfitting; and different initializations can lead to different local optima, so the final clustering can vary. Therefore, this option is incorrect.

Option B: I and II. This pair asserts that centroids are computed as the mean of observations in each cluster (which is true for standard K-means), and that K-means can be directly applied to mixed data types without preprocessing (which is false: K-means assumes numerical distances; mixed data typically require encoding or alternative algorithms). Because II is false, this option is incorrect.

Option C: II, III and IV. This option includes II (the claim about direct applicability to mixed data without preprocessing), which is incorrect as explained above, and also includes III and IV which themselves are incorrect for the reasons discussed. Since it contains a false claim, this option is incorrect.

Option D: I. This option states only that centroids are computed as the mean of the observations assigned to each cluster, which is the standard and correct description of K-means, and does not make any false claims about preprocessing, initialization sensitivity, or determinism. As a result, this option accurately captures a true aspect of K-means while avoiding the incorrect statements.

In summary, the only statement that correctly describes a fundamental property of K-means is I, while the others contain misunderstandings about data types, initialization effects, or determinism of the algorithm.

FINTECH 540.01.Fa25 Quiz 5 - Unsupervised Clustering Methods

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