It is important to define$/$select similarity measures in data analysis. However, there is no commonly accepted subjective similarity measure. Results can vary depending on the similarity measures used. Nonetheless, seemingly different similarity measures may be equivalent after some transformation.

Suppose we have the following $2-$D data set:

Consider the data as a pair of data points. Given a new data point, x $=(1\mathrm{.}4,1\mathrm{.}6)$ as a query, rank the database points based on similarity with the query using Euclidean distance, Manhattan distance, supremum distance, and cosine similarity.It is important to define$/$select similarity measures in data analysis. However, there is no

commonly accepted subjective similarity measure. Results can vary depending on the

similarity measures used. Nonetheless, seemingly different similarity measures may be

equivalent after some transformation.

Suppose we have the following $2-$D data set:

Consider the data as a pair of data points. Given a new data point, $x=(1\mathrm{.}4,1\mathrm{.}6)$ as a

query, rank the database points based on similarity with the query using Euclidean

distance, Manhattan distance, supremum distance, and cosine similarity.