best similarity measure for audio classification
I would like to know which is the best similarity measure that I can adopt to check test signal with training data.


Welcome to engineering. There is no universally "best" approach, as it always depends on your specific models. 

Mathematically, as soon as you can define what "similarity" should mean, you might be able to derive something.

Assuming that bird's auditory senses kind of work similar to human hearing, I'd try with the usual audio comparison models, probably a basic MFCC thing.

As a comment: A former advisor of me once said: 


  A week in the lab can easily save you up to two hours of reading literature.


Really, there's a whole lot of papers, textbook introductions and wikipedia articles on sound comparison. Start with anything, and read forward. That's going to be faster than asking for a single answer to your acute problem without getting the bigger picture of how things work.