Final answer:
While k-NN traditionally uses distance metrics like Manhattan, Minkowski, and Mahalanobis for numeric data, Jaccard distance is used for binary or non-numeric data. Therefore, all listed distance metrics can be used in k-NN, but suitability depends on the type of data.
Step-by-step explanation:
The question is asking which of the following distance metrics cannot be used in the k-Nearest Neighbors (k-NN) algorithm: (a) Manhattan, (b) Minkowski, (c) jaccard, and (d) Mahalanobis. All provided distance metrics can potentially be used in k-NN depending on the context and the data, but Jaccard distance measure is typically used for binary or non-numeric data. Contrastingly, Manhattan, Minkowski, and Mahalanobis distances are more traditionally applied to numeric datasets within the k-NN algorithm.
Manhattan distance, or L1 distance, computes the absolute differences between coordinates. Minkowski distance generalizes Manhattan and Euclidean distances and can be adjusted depending on the value of parameter 'p' used. Mahalanobis distance considers the correlation between features and is scale-invariant. Jaccard distance is a measure of similarity for sets, considering the size of the intersection over the union of the sample sets.