Correctly match up the statements below in relation to choosing the most appropriate value of k when using the kNN algorithm:

Question

Correctly match up the statements below in relation to choosing the most appropriate value of k when using the kNN algorithm:

BlackTom AI · Accepted Answer

Question restatement: Correctly match up the statements below in relation to choosing the most appropriate value of k when using the kNN algorithm:

Answer options:
- less precise, neighbourhood may include points from other classes
- less precise, neighbourhood may include points from other classes
- less stable, sensitive to noise points
- If k is to small
- If k is to big

Analysis of each option:
- Option 1: "less precise, neighbourhood may include points from other classes" — This describes the effect of using a large k: as the neighborhood expands, the majority label may be influenced by distant or boundary points from other classes, reducing precision. It correctly captures a behavior associated with high k values, even though it is phrased generally. This option is a valid statement about how k affects the classifier when k is large.
- Option 2: "less precise, neighbourhood may include points from other classes" — This is a duplicate of Option 1 and conveys the same idea about large k producing less precise decisions due to neighbor mixing. It is also a correct description of large-k behavior, identical in meaning to Option 1 though repeated.
- Option 3: "less stable, sensitive to noise points" — This describes the effect of using a small k: with very few neighbors, a single mislabeled or noisy point can sway the predicted label, making the decision boundary more volatile. This is a correct characterization of small-k behavior, where stability deteriorates due to susceptibility to noise.
- Option 4: "If k is to small" — This is a truncated/grammatically incorrect statement. As an analysis point, it does not present a complete claim about k’s effect and therefore is not a proper descriptive statement about kNN behavior. Its incompleteness makes it unfit as a valid match.
- Option 5: "If k is to big" — Similarly, this is a truncated/grammatically incorrect claim. Even though it hints at a true concept (that k being too big affects performance), the wording is incomplete and thus not a proper standalone descriptive statement about the impact of large k. It fails as a clear match in this format.

In summary, the complete, well-formed, and meaningful statements correspond to:
- Large k: less precise, neighbourhood may include points from other classes (Options 1 and 2).
- Small k: less stable, sensitive to noise points (Option 3).
- The incomplete options 4 and 5 do not provide usable, complete claims about the influence of k and are not suitable matches in this context.

Correctly match up the statements below in relation to choosing the most appropriate value of k when using the kNN algorithm:

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