Clustering with asymmetrical distance measures

Question

How do you cluster a feature with an asymmetrical distance measure?

For example, let's say you are clustering a dataset with days of the week as a feature - the distance from Monday to Friday is not the same as the distance from Friday to Monday.

How do you incorporate this into the clustering algorithm's distance measure?

Answer 1

You can take some sort of a mean (like an arithmetic mean or, for probability distributions, the square root of the Jensen–Shannon divergence.)

Answer 2

You should have a look to circular statistics (if you want to work "within"a tunning week)