Which of the following distance metrics is particularly effective for high-dimensional data but less interpretable compared to other metrics?

Question

BlackTom AI · Accepted Answer

Consider the question which asks about a distance metric that works well in high-dimensional spaces but tends to be less interpretable than some alternatives.
Option 1: Hamming Distance. This measure counts differing coordinates and is intuitive for categorical or binary data of fixed length. However, in high-dimensional continuous spaces, Hamming is often not the best choice because it ignores magnitude information and can become less informative when many dimensions exist. It is generally interpretable, but its suitability for high-dimensional real-valued data is limited.
Option 2: Cosine Distance. This metric assesses the angle between two vectors, effectively measuring orientation rather than magnitude. In high dimensions, cosine distance can remain stable and often separates vectors well when the magnitude varies a lot, which makes it effective for tasks like text similarity with bag-of-words representations. The trade-off is that it sacrifices direct interpretability in terms of distance magnitude, since it focuses on direction; this reduced interpretability is the very aspect highlighted in the question.
Option 3: Euclidean Distance. This is the straight-line, magnitude-based distance in feature space. It tends to be straightforward to interpret as a direct sense of “how far apart” two points are. However, in high dimensions, Euclidean distance can suffer from the curse of dimensionality, where distances become less informative, and interpretability about which features contribute is not built into the metric itself. Still, it is generally more interpretable than cosine in some contexts because it has a clear magnitude interpretation.
Option 4: Manhattan Distance. This sums absolute coordinate differences and is easy to interpret as a path length in grid-like spaces. Like Euclidean distance, it can degrade in very high dimensions due to the curse of dimensionality, but it remains comparatively interpretable because it directly reflects coordinate-wise differences. Its interpretability is typically higher than cosine in many practical scenarios.
Overall, among the options, cosine distance is the one most commonly cited as particularly effective in high-dimensional contexts due to its emphasis on direction over magnitude, while its interpretability as a distance value is reduced compared to Euclidean or Manhattan, aligning with the description in the question.

COMP90049_2025_SM1 Lecture 3 K-NN Practice Quiz

Which of the following distance metrics is particularly effective for high-dimensional data but less interpretable compared to other metrics?

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