Suppose I have a database of entities. The database has a column for the name of the entity, min A, max A, min B, max B. Where the min/max columns are the min/max for variables A and B. It is unknown how many samples were used to produce the min/max values.
We have a system that takes field samples, but the only output available is a series of min A, max A, min B, and max B. I now want to identify the field samples based on the entity values in the database.
Testing that sample min A >= db min A and sample max A <= db max A is not sufficient. We can have sample min A less than the correct entity min A value, for example.
I am considering the following approach:
Let $\alpha = (db_{\min} A - \text{sample}_{\min} A)^2 + (db_{\max} A - \text{sample}_{\max} A)^2$.
Let $\beta = (db_{\max} A - db_{\min} A)^2$.
Let $p = \exp(1 - \alpha/\beta) / e$.
I can repeat this for B, and then take the product of the $p$'s.
Then, the entity that produces the largest $p$ for a sample is the most likely match.
Is there a better approach to this problem?
