Which statement is TRUE?

Question

BlackTom AI · Accepted Answer

Let's evaluate each statement in turn, keeping in mind what PCA and K-Means do and how they are typically used in the workflow.

Option 1: 'K-Means clustering reduces features to principal components, whereas PCA projects data onto new axes that capture maximum variance.' This is a mix-up of concepts. K-Means is a clustering algorithm that partitions data into k groups based on distance to centroids; it does not directly reduce features or project data onto principal components. PCA, on the other hand, is a dimensionality reduction technique that projects data onto new axes (principal components) that capture the maximum variance. So this statement incorrectly assigns PCA’s projection role to K-Means and misstates K-Means’ purpose.

Option 2: 'Both PCA and K-Means clustering are unsupervised learning methods that can be used before using supervised learning methods.' This statement correctly characterizes both techniques as unsupervised. It also reflects a common practical workflow where dimensionality reduction (PCA) or clustering (K-Means) is performed as a preprocessing step prior to supervised learning, for example to reduce dimensionality, denoise data, or produce features.

Option 3: 'PCA is typically applied after K‑Means clustering to improve centroid stability.' In practice, PCA is usually applied before clustering (including K-Means) to reduce dimensionality and preserve variance, which can improve clustering performance and stability. Applying PCA after clustering would not affect the already computed centroids and is not the standard approach.

Option 4: 'PCA requires specifying the number of clusters, whereas K-Means clustering determines the number of components automatically.' This statement confuses the two methods. PCA does not involve clusters or a cluster count; it requires choosing how many principal components to retain. K-Means requires selecting the number of clusters k. The roles are opposite from what this option suggests.

Overall, the second option aligns with the actual nature of both methods and their common usage in a preprocessing stage before supervised learning, while the other options contain misconceptions about what each method does and how they are usually applied.

Which statement is TRUE?

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